mm-4499 === Subject: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, or just write a bit about the topic, it would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics (Well, you would probably still need logic...). === Subject: Re: Foundations of Mathematics, help? > mathematics, what I mean by that is the things that > define mathematics, and which it is based on. Much in > the same was that mathematics defines much of physics > (I think...) I disagree very sharply with that, by the way. Physics is 'defined' by what we observe in experiments, not by mathematics! > Anyway, I am posting here because I don't have much > of an idea of where to start. If anyone could advise > there, or just write a bit about the topic, it would > be greatly appreciated. > Oh, and if there is anyone out there who wouldn't > mind me asking them some questions that will > undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and > formal logic, and I will. But it also occurred to me > that these cannot be the only ways to define the > basis of mathematics (Well, you would probably still > need logic...). === Subject: Re: Foundations of Mathematics, help? mathematics, what I mean by that is the things > that define mathematics, and which it is based on. Much > in the same was that mathematics defines much of > physics (I think...) > I disagree very sharply with that, by the way. > way. Physics is 'defined' by what we observe in > experiments, not by mathematics! > I figured someone would say something like that... And I agree mostly, but it helped express the idea I was trying to, so I used it :) Anyway, I am posting here because I don't have > much of an idea of where to start. If anyone could > advise there, or just write a bit about the topic, it > would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me > know. P.S. I have been told before to study set theory > and formal logic, and I will. But it also occurred to > me that these cannot be the only ways to define the basis of mathematics (Well, you would probably > still need logic...). > ics and got a lot of intersting hits. Have you tried > that? Yup... === Subject: Re: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, You could read Fraenkel, Bar-Hillel and Levy, _Foundations of Set Theory_ which covers more than its title suggests; and Feferman _The Number Systems_ the subtitle of which is _Foundations of Algebra and Analysis_. > or just write a bit about the topic, it would be greatly appreciated. > Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. sci.logic might be good for that. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics You could try Mac Lane _Categories for Working Mathematicians_ > (Well, you would probably still need logic...). -- How unlike the home life of our own dear Queen. === Subject: Re: Foundations of Mathematics, help? === Subject: hey guys posting-account=vz_6QQoAAABOxomOXgeWKt9p9p4FZ-ez SV1),gzip(gfe),gzip(gfe) people join this new group and make it an interactive place !! === Subject: solutions manuals posting-account=m06QOgkAAACFEdunwVichFUaRyeknXjQ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Can I get the manuals for: 1) Linear Algebra with Applications, Otto Bretscher,( Pearson Custom Publishing) 2) Fundamentals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Edward B. Saff, Arthur David Snider, (Pearson Custom Publishing) Are they the complete set? You can e-mail me at === Subject: implementation of simplex method in C language hi, I am looking for an implementation of simplex method in C language. === Subject: Re: implementation of simplex method in C language : > I am looking for an implementation of simplex method in C language. Just by any wild chance, could this be a homework assignment? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: implementation of simplex method in C language >hi, >I am looking for an implementation of simplex method in >C language. http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html === Subject: Re: implementation of simplex method in C language posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > hi, > I am looking for an implementation of simplex method in C language. Why C? What difference does the language make? Or have you been asked to implement it yourself in C as part of an assignment???? I can suggest a number of commercially available LP packages. What are you willing to pay? === Subject: Water Treatment: Principles and Design, 2nd Edition posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) Can you send me Water Treatment: Principles and Design, 2nd Edition thank you very much liew168@sina.com === Subject: Re: Water Treatment: Principles and Design, 2nd Edition Can you send me Water Treatment: Principles and Design, 2nd Edition > thank you very much The answer is of course no. (If someone reading your post has the book and wishes to give it away, they would not know how to get it to you.) May I ask you a question? Why don't you go to a book shop and buy it like any normal person? (If you do so, do remember to mention the author and publisher.) -- How unlike the home life of our own dear Queen. === Subject: Re: List of solutions manual (thousands) posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) BERGH .8eæ.93.b9.81F > My List of Solutions Manual > contact me to : newbergh123@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. > This list (not links) is available from : > http://rapidshare.com/files/59002351/List of solutions manual.txt > > - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files > converted to pdf, real instructor sol. manual > Principles of Statics (10th Ed., Hibbeler) > Engineering Mechanics : Dynamics (11th Ed., Hibbeler)-Not mathcad > files converted to pdf, real instructor sol. manual > Principles of Dynamics (10th Ed., Hibbeler) > Mechanics of Materials (4th Ed, Hibbeler) > Mechanics of Materials (6th Ed, Hibbeler) > Mechanics of Materials (7th Ed, Hibbeler) > Statics and Mechanics of Materials (2nd Ed., Hibbeler) > Energy Principles and Variational Methods in Applied Mechanics (2nd > Ed., Reddy) > Theory of Vibrations with Applications (5th Ed., Thomson & Dahleh) > Engineering Vibrations (2nd Ed., Inman) > Engineering Vibrations (3rd Ed., Inman) > Theory of Vibration: An Introduction (2nd Ed., A.A. Shabana) > Vibration of Discrete and Continuous Systems (2nd Ed., Ahmed Shabana) > Introduction to Finite Element Vibration Analysis (Maurice Petyt) > Vibrations and Stability: Advanced Theory, Analysis, and Tools (2nd > Ed., Jon J. Thomsen) > Mechanical Vibrations (4th Ed., Rao) > Mechanical Vibration (William J. Palm, III) > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Finite Element Analysis Theory and Application with ANSYS (2nd Ed., > Moaveni) > Finite Element Analysis Theory and Application with ANSYS (3rd Ed., > Moaveni) > The Finite Element Method and Applications in Engineering Using ANSYS > (Madenci & Guven) + original Ebook > Modeling and Analysis of Dynamic Systems (3rd Ed, Close, Frederick & > Newell) > System Dynamics (1st Ed., William J Palm III) > System Dynamics: Modeling and Simulation of Mechatronic Systems (4th > Ed., Karnopp, Margolis & Rosenberg) > Concepts and Applications of Finite Element Analysis (4th Ed., Cook, > Malkus, Plesha & Witt) > Finite Element Modeling for Stress Analysis (Robert Cook) > Advanced Strength and Applied Elasticity (4th Ed., Ugural) > Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) + > original Ebook > Fracture Mechanics (2nd Ed., Anderson) > Mechanical Behavior of Materials (2nd Ed. Dowling) > Mechanical Behavior of Materials (3rd Ed. Dowling) > Mechanical Behavior of Materials (W.F. Hosford) + original Ebook > Mechanical Behavior of Materials (Keith Bowman) > Theory and Design for Mechanical Measurements (4th Ed, Figliola & > Beasley) > Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Principles of Metal Manufacturing Processes (Beddoes & Bibby) > Materials Selection in Mechanical Design (3rd Ed., Michael Ashby) > Introduction to Manufacturing Processes (3rd Ed., Schey) > Manufacturing Processes for Engineering Materials (5th Ed. Kalpakjian > & Smith) > Manufacturing, Engineering & Technology (4th Ed. Kalpakjian & Smith) > Manufacturing, Engineering & Technology (5th Ed. Kalpakjian & Smith) > Automation, Production Systems, and Computer-Integrated Manufacturing > (2nd Ed., Groover) > Introduction to Robotics: Mechanics and Control (3rd Ed, Craig) > Applied Manufacturing Process Planning: With Emphasis on Metal Forming > and Machining (Nelson, Schneider) > Linear State-Space Control Systems (Robert L. Williams, II & Douglas > A. Lawrence) > Rocket Propulsion Elements (7th Ed., George P. Sutton & Oscar Biblarz) > Mechanics of Flight (Warren F. Phillips) > Fundamentals of Airplane Flight Mechanics (David G. Hull) > Flight Performance of Fixed and Rotary Wing Aircraft (Antonio > Filippone) > Aircraft Structures for Engineering Students (3rd Ed., T.H.G. Megson) > + original ebook > Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson) > + original ebook > Mechanics of Aircraft Structures (2nd Ed, C. T. Sun) > Principles of Helicopter Aerodynamics (2nd Ed., Leishman) > Interactive Aerospace Engineering and Design (Dava Newman) > Fundamentals of Aerodynamics (3th Ed., Anderson) > Fundamentals of Aerodynamics (4th Ed., Anderson) > Introduction to Flight (5th Ed., Anderson) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Mechatronics (Sabri Cetinkunt) > Introduction to Mechatronics and Measurement Systems (3rd Ed., David > G. Alciatore & Michael B. Histand) > Introduction to Engineering Experimentation (2nd Ed., Wheeler & Ganji) > Gas Dynamics (3rd Ed., John & Keith) > Fundamentals of Gas Dynamics (2nd Ed, Robert D. Zucker) + original > Ebook > Internal Combustion Engines: Applied Thermosciences (2nd Ed., Ferguson > & Kirkpatrick) > Automotive Engines (8th Ed., Crouse) > Automotive Brake Systems Package (4th Ed., Rehkopf) > Automotive Engine Performance (2nd Ed., Halderman) > Automotive Mathematics (Jason C. Rouvel) > Blueprint Reading for the Machine Trades (6th Ed., Schultz & Smith) > Modern Welding Technology (6th Ed., Cary & Helzer) > Theory of Ground Vehicles (3rd Ed., J. Y. Wong) > Hydraulic Control Systems (Noah Manring) > Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. > Dixon) + original Ebook > Principles of Turbomachinery in Air-Breathing Engines (Baskharone) > Fundamentals of Jet Propulsion with Applications (Ronald D. Flack) > Fundamentals of Robotic Mechanical Systems: Theory, Methods, and > Algorithms (3rd Ed., Jorge Angeles) > Tissue Mechanics (Cowin, Doty) > BTEC First Engineering Curriculum Support Pack (Mike Tooley) > BTEC First Engineering (Mike Tooley) > Exploring Engineering: An Introduction for Freshmen to Engineering and > to the Design Process (Philip Kosky, George Wise, Robert Balmer & > William Keat) > Engineering Science (5th Ed., W. Bolton) > Fundamentals of Renewable Energy Processes (Aldo da Rosa) + original > Ebook > Renewable Energy (3rd Ed., SÀrensen or Sorensen) + original Ebook > Power Generation Technologies (Paul Breeze) + original Ebook > Concepts in Engineering (Holtzapple & Reece) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Autodesk Inventor (James M. Leake) > Foundations of Engineering (2nd Ed, Holtzapple & Dan Reece) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) - Electrical, Electronics & Computer Engineering > > Electrical Engineering: Principles and Applications (4th Ed., Allan R. > Hambley) > Electric Circuits (8th Ed., James W Nilsson & Susan Riedel) > Electric Circuits (7th Ed., James W Nilsson & Susan Riedel) > Introductory Circuits for Electrical and Computer Engineering (James > W. Nilsson, Susan A. Riedel) > Applied Electromagnetics: Early Transmission Lines Approach (Stuart M. > Wentworth) > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Introduction to Electric Circuits (6th Ed., Richard Dorf & James > Svoboda) > Introduction to Electric Circuits (7th Ed., Richard Dorf & James > Svoboda) > Modern Control Systems (11th Ed., Dorf) > System Dynamics (1st Ed., William J Palm III) > Electric Machines Analysis and Design Applying MatLab (Cathey) > Principles and Applications of Electrical Engineering (4th Ed, > Rizzoni) > Principles and Applications of Electrical Engineering (5th Ed, > Rizzoni) > Fundamentals of Electric Circuits (2nd Ed., Charles Alexander & > Matthew Sadiku) > Fundamentals of Electric Circuits (3rd Ed., Charles Alexander & > Matthew Sadiku) > Microelectronic Circuit Design (2nd Ed., Richard Jaeger & Travis > Blalock) > Microelectronic Circuit Design (3rd Ed., Richard Jaeger & Travis > Blalock) > Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with VHDL Design (2nd Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (1st Ed., Stephen > Brown & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (2nd Ed., Stephen > Brown & Zvonko Vranesic) > Continuous and Discrete Control Systems (Dorsey) > Design with Operational Amplifiers and Analog Integrated Circuits (3rd > Ed., Sergio Franco) > Engineering Circuit Analysis (6th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Circuit Analysis (7th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Electromagnetics (7th Ed., William H. Hayt & John A. Buck) > Principles of Electronic Materials and Devices (2nd Ed, Safa O. Kasap) > Principles of Electronic Materials and Devices (3rd Ed, Safa O. Kasap) > A First Lab in Circuits and Electronics (Yannis Tsividis) > Power Electronic Circuits (Issa Batarseh) > Power Electronics: Converters, Applications, and Design (3rd Ed., Ned > Mohan, Tore Undeland & William Robbins) > An Introduction to Digital and Analog Communications (2nd Ed., Simon > Haykin & Michael Moher) > Communication Systems (4th Ed., Simon Haykin) > Signals and Systems (2nd Ed., Simon Haykin & Barry Van Veen) > Programming in Haskell (Graham Hutton) > Logic in Computer Science: Modelling and Reasoning about Systems > (Michael Huth & Mark Ryan) > Introduction to Distributed Algorithms (2nd., Gerard Tel) > Information Theory, Inference and Learning Algorithms (David J. C. > MacKay) > Digital Systems Engineering (William J. Dally & John W. Poulton) > Concepts in Programming Languages (by John C. Mitchell) > Simulation Modeling and Analysis with Expertfit Software (4th Ed., > Averill Law) > Measurement Systems (5th Ed, Ernest Doebelin) > Wireless Communications (Andrea Goldsmith) > Testing of Digital Systems (N. K. Jha & S. Gupta) > Space-Time Coding (Hamid Jafarkhani) > Space-Time Block Coding for Wireless Communications (Erik G. Larsson & > Petre Stoica) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Radio-Frequency Electronics: Circuits and Applications (Jon B. Hagen) > Photonic Devices (Jia-ming Liu) > Networking Wireless Sensors (Bhaskar Krishnamachari) > Mobile Wireless Communications (Mischa Schwartz) > Introduction to Color Imaging Science (Hsien-Che Lee) > Fundamentals of Wireless Communication (David Tse & Pramod Viswanath) > Fundamentals of Modern VLSI Devices (Yuan Taur & Tak H. Ning) > Electronic and Optoelectronic Properties of Semiconductor Structures > (Jasprit Singh) > Digital Signal Processing System Analysis and Design (Paulo S. R. > Diniz) > An Introduction to Statistical Signal Processing (Robert M. Gray) > An Introduction to Radio Frequency Engineering (Christopher Coleman) > Algebraic Codes for Data Transmission (Richard E. Blahut) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Fundamentals of Semiconductor Fabrication (Gary S. May, Simon M. Sze) > Semiconductor Devices: Physics and Technology (2nd Ed, Simon M. Sze) > Electric Machinery (6th Ed., Fitzgerald) + Ebook > Electric Machinery Fundamentals (4th Ed., Chapman) > Electric Machinery and Power System Fundamentals (Chapman) > Local Area Networks (2nd Ed., Keiser) > Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka) > Introduction to Signals and Systems (Lindner) > Digital Signal Processing (3rd Ed., Mitra) > Semiconductor Physics and Devices (3rd Ed., Donald A. Neamen) > Design for Electrical and Computer Engineers (1st Ed., Ralph Ford & > Chris Coulston) > Fundamentals of Modeling and Analyzing Engineering Systems (Cha, > Rosenberg, Dym) > Principles of Linear Systems (Philip E. Sarachik) > Power Systems Harmonics: Fundamentals, Analysis and Filter Design > (George J. Wakileh) > Principles of Adaptive Filters and Self-learning Systems (Anthony > Zaknich) > Control of Robot Manipulators in Joint Space (R. Kelly, V. Santib.87.96ez, > A. Lor.92a) > Modelling and Control of Robot Manipulators (2nd Ed., Lorenzo > Sciavicco, Bruno Siciliano) > Algebraic Methods for Nonlinear Control Systems (2nd Ed., Giuseppe > Conte, Claude H. Moog, Anna Maria Perdon) > Modern Control Engineering - Problems B (3rd Ed. K.OGATA) + Ebook > Modern Control Engineering (4th Ed. K.OGATA) > LabVIEW 8 Student Edition (Bishop) > Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami- > Naeini) > Modeling and Simulation of Dynamic Systems (Woods, Lawrence) > Computer Numerical Control: Operation and Programming (3rd Ed., > Stenerson & Curran) > Engineering Problem Solving with C (3rd Ed., Etter) > Process Control Instrumentation Technology (8th Ed., Johnson) > Electrical Power and Controls (2nd Ed., Skvarenina & DeWitt) > Electronics and Computer Math (8th Ed., Deem & Zannini) > Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based > Introduction (John Semmlow) > Aircraft Digital Electronic and Computer Systems: Principles, > Operation and Maintenance (Mike Tooley) > VLSI Test Principles and Architectures: Design for Testability (Chen, > Cheng, Eklow et al.) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Machine Vision: Theory, Algorithms, Practicalities (3rd Ed., E. R. > Davies) > Instrumentation and Control Systems (W. Bolton) > Essential Java for Scientists and Engineers (Brian D Hahn & Katherine > M Malan) > Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Ed., > Bernard V. Liengme) > Electric Motors and Drives : Fundamentals, Types and Applications (3rd > Ed., Austin Hughes) > 10-Key Touch Key: Developing Speed and Accuracy (Burton) > Introduction to C++ Programming, Brief (Y. Daniel Liang) > C++ for Business Programmers (2nd Ed., John C. Molluzzo) > Introduction to Java Programming-Comprehensive Version (6th Ed., Y. > Daniel Liang) > Introduction to Java Programming: Fundamentals First (6th Ed., Y. > Daniel Liang) > Objects First With Java: A Practical Introduction Using BlueJ (3rd > Ed., David J. Barnes & Michael Kolling) > Java: An Introduction to Problem Solving and Programming (4th Ed., > Walter Savitch) > Simply Java Programming: An Application-Driven» Tutorial Approach > (Deitel) > Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & > Jeffrey Nyhoff) > Advanced Java» 2 Platform How to Program (Deitel & Santry) > SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) > Introduction to Programming Using Visual Basic 2005 (6th Ed., David I. > Schneider) > Simply Visual Basic 2005 (2nd Ed., Harvey & Paul Deitel & Associates) > Visual Basic 2005 How to Program (3rd Ed., Deitel & Associates) > Introduction to Programming with Visual Basic 6.0 (4th Ed., David I. > Schneider) > Visual Basic.Net Programming (2nd Ed., Jeffrey Tsay) > Simply Visual Basic .NET (Deitel & Nieto) > Mechatronics (Sabri Cetinkunt) > Introduction to Linear Programming (Leonid N. Vaserstein) > Science of Electronics, The: DC/AC (David M. Buchla, Thomas L. Floyd) > Introductory Circuit Analysis (11th Ed., Robert L. Boylestad) > Principles of Electric Circuits: Conventional Current Version (8th > Ed., Thomas Floyd) > Contemporary Electric Circuits: Insights and Analysis (2nd ed., > Strangeway, Petersen, Gassert & Lokken) > Electronics Technology Fundamentals - Conventional Flow (2nd Ed., > Robert T. Paynter & Toby Boydell) > Electronics Fundamentals: Circuits, Devices and Applications (7th Ed., > Thomas L. Floyd) > Principles of Electric Circuits: Electron Flow Version (8th Ed., > Thomas L. Floyd) > Electronics Technology Fundamentals - Electron Flow (2nd Ed., Robert > T. Paynter, Toby Boydell) > Introductory DC/AC Circuits (6th Ed., Nigel P. Cook) > Introductory DC/AC Electronics (6th Ed., Nigel P. Cook) > Electronic Devices - Conventional Current Version (7th Ed., Thomas L. > Floyd) > Electronic Devices - Conventional Current Version (8th Ed., Thomas L. > Floyd) > Electronic Devices - Electron Flow Version (8th, Thomas L. Floyd) > Electronic Devices and Circuit Theory (9th Ed., Robert L. Boylestad, > Louis Nashelsky) > Introductory Electronic Devices and Circuits: Electron Flow Version > (7th Ed., Robert T. Paynter) > Introductory Electronic Devices and Circuits: Conventional Flow > Version (7th Ed., Robert T. Paynter) > Electronic Devices - Electron Flow Version (5th, Thomas L. Floyd) > Science of Electronics, The: Digital (Thomas L. Floyd & David M. > Buchla) > Science of Electronics, The: Analog Devices (Thomas L. Floyd, David M. > Buchla) > Digital Electronics: A Practical Approach (7th Ed., William Kleitz) > Digital Electronics: A Practical Approach (8th Ed., William Kleitz) > Digital Systems: Principles and Applications (10th Ed., Ronald Tocci, > Neal Widmer, Greg Moss) > Digital Electronics with VHDL - Quartus II Version (William Kleitz) > Digital Fundamentals (9th Ed., Thomas L. Floyd) > Digital Fundamentals with PLD Programming (Thomas L. Floyd) > The 8051 Microcontroller (4th Ed., I. Scott MacKenzie, Raphael Chung- > Wei Phan) > The 8051 Microcontroller and Embedded Systems (2nd Ed., Muhammad Ali > Mazidi, Janice Mazidi & Rolin McKinlay) > INTEL Microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486, > Pentium, Prentium ProProcessor, Pentium II, III, 4, (7th Ed., Barry B. > Brey) > Microcontroller Technology: The 68HC11, 5/E (Peter Spasov) > PIC Microcontroller (Muhammad Ali Mazidi, Rolin McKinlay & Danny > Causey) > Industrial Electronics (James A. Rehg, Glenn J. Sartori) > Programmable Controllers Using the Allen-Bradley SlC-500 Family (2nd > Ed., Dave Geller) > Programmable Logic Controllers (James A. Rehg, Glenn J. Sartori) > Fundamentals of Programmable Logic Controllers, Sensors, and > Communications (3rd Ed., Jon Stenerson) > An Introduction to Programming with Visual Basic 6.0, Update Edition > (4th Ed., Schneider) > C++ Programming Today (Barbara Johnston) > Introduction to Data Communications and Networking (Wayne Tomasi) > Introduction to Telecommunications (2nd Ed., Martha Rosengrant) > Network Security Essentials: Applications and Standards (3rd Ed., > William Stallings) > Information Security: Principles and Practices (Mark Merkow, James > Breithaupt) > Principles and Practice of Information Security (Linda Volonino, > Stephen R. Robinson) > Modern Electronic Communication (8th Ed., Jeff Beasley, Gary M. > Miller) > Modern Electronic Communication (9th Ed., Jeff Beasley, Gary M. > Miller) > Electronic Communications for Technicians (2nd ed., Tom Wheeler) > Concepts In Systems and Signals (2nd Ed., John D. Sherrick) > Understanding Fiber Optics (5th Ed., Jeff Hecht) > Understanding UNIX/LINUX Programming: A Guide to Theory and Practice > (Bruce Molay) > Applying PIC18 Microcontrollers: Architecture, Programming, and > Interfacing using C and Assembly (Barry B. Brey) > Electrical Power and Controls (2nd Ed., Timothy L. Skvarenina, William > E. DeWitt) > Process Control Instrumentation Technology (8th Ed., Curtis Johnson) > Electrical Machines, Drives and Power Systems (6th Ed., Theodore > Wildi) > Introduction to Vacuum Technology (David M. Hata) > Electronic Project Design and Fabrication (6th Ed., Ronald A. Reis) > Technology and Society (3rd Ed., Linda Hjorth, Barbara A. Eichler, > Ahmed S. Khan, John Morello) > Solid State Electronic Devices (6th Ed., Ben Streetman, Sanjay > Banerjee) > Approaching Quantum Computing (Dan C. Marinescu & Gabriela M. > Marinescu) > Foundations of MEMS (Chang Liu) > Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby) > Elements of Engineering Electromagnetics (6th Ed., Nannapaneni > Narayana Rao) > Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti) > Digital Design: Principles and Practices Package (4th Ed., John F. > Wakerly) > VHDL: A Starter's Guide (2nd Ed., Sudhakar Yalamanchili) > Computer Organization and Architecture: Designing for Performance (7th > Ed., William Stallings) > Parallel Programming: Techniques and Applications Using Networked > Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & > Michael Allen) > Fundamentals of Parallel Processing (Harry F. Jordan & Gita Alaghband) > Feedback Control of Dynamic Systems (5th Ed., Gene Franklin, J.D. > Powell, Abbas Emami-Naeini) > Digital & Analog Communication Systems (7th Ed., Leon W. Couch) > Fundamentals of Communication Systems (John G. Proakis, Masoud Salehi) > Modern Wireless Communications (Simon Haykin, Michael Moher) > Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud > Salehi) > Data and Computer Communications (8th Ed., William Stallings) > Cryptography and Network Security (4th Ed., William Stallings) > Computer Networking with Internet Protocols (William Stallings) > Probabilistic Systems and Random Signals (Abraham H Haddad) > Error Control Coding (2nd Ed., Shu Lin & Daniel J. Costello) > Wireless Communications & Networks (2nd ed., William Stallings) > Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) > Detection and Estimation:Theory; and Its Applications (Thomas > Schonhoff & Arthur Giordano) > Signals, Systems, and Transforms (3rd Ed., Charles L. Phillips, John > M. Parr & Eve A. Riskin) > Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., > Edward W. Kamen & Bonnie S Heck) > Digital Signal Processing (4th Ed., John G. Proakis, Dimitris K > Manolakis) > Adaptive Filter Theory (4th Ed., Simon Haykin) > Spectral Analysis of Signals (Petre Stoica & Randolph L. Moses) > Fluency with Information Technology: Skills, Concepts, and > Capabilities (2nd Ed., Lawrence Snyder) > Fluency with Information Technology, Brief Edition (Lawrence Snyder) > Jolly) > Comprehensive Excel 2002 for Office XP (4th Ed., Karen J. Jolly) > Ethics for the Information Age (2nd Ed., Michael J. Quinn) > Computer Science: An Overview (8th Ed., J. Glenn Brookshear) > Computer Science: An Overview (9th Ed., J. Glenn Brookshear) > Concise Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Concise Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Extended Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Extended Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Logic and Design of Computer Programs (Jim Messinger) > Absolute C++ (2nd Ed., Walter Savitch) > Absolute C++ (3rd Ed., Walter Savitch) > Starting Out with C++: Early Objects (6th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > Problem Solving with C++: The Object of Programming (5th Ed., Walter > Savitch) > Problem Solving with C++ (6th Ed., Walter Savitch) > Problem Solving, Abstraction, and Design using C++ (4th Ed., Frank L. > Friedman & Elliot B. Koffman) > Problem Solving, Abstraction & Design Using C++ (5th Ed., Frank L. > Friedman & Elliot B. Koffman) > Ed., Tony Gaddis) > Starting out with C++ Brief Version Updated (4th Ed., Tony Gaddis & > Barret Krupnow) > Starting out with C++ Brief Version (5th Ed., Tony Gaddis & Barret > Krupnow) > Starting Out with C++: Brief Version Update, Visual C++ .NET (4th Ed., > Tony Gaddis & Barret Krupnow) > Starting Out with C++: Early Objects (5th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > C++ By Dissection (Ira Pohl) > Essential C++ for Engineers and Scientists (2nd Ed., Jeri R. Hanly) > C++ Coach: Essentials for Introductory Programming (Jeff Salvage) > C++ Primer (4th Ed., Stanley B. Lippman, Jos.8ee Lajoie & Barbara E. > Moo) > Engineering Computation with MATLAB (David Smith) > Absolute Java with Student Resource Disk (2nd Ed., Walter Savitch) > Absolute Java (3rd Ed., Walter Savitch) > The Art and Science of Java (Eric Roberts) > Building Java Programs: A Back to Basics Approach (Stuart Reges & > Martin Stepp) > Introduction to Programming in Java: An Interdisciplinary Approach > (Robert Sedgewick & Kevin Wayne) > Java Foundations: Introduction to Program Design and Data Structures > (John Lewis, Peter DePasquale & Joe Chase) > Starting Out with Java: Early Objects (3rd Ed., Tony Gaddis) > Ed., Tony Gaddis) > Java Software Solutions (Java 5.0 version): Foundations of Program > Design (4th Ed., John Lewis & William Loftus) > Java Software Solutions: Foundations of Program Design (5th Ed., John > Lewis & William Loftus) > Structures (Tony Gaddis & Godfrey Muganda) > Object of Java, The: Introduction to Programming Using Software > Engineering Principles (2nd Ed, David D. Riley) > Object-Oriented Programming in Java: A Graphical Approach, Preliminary > Edition (Kathryn E. Sanders & Andy van Dam) > Starting Out with Java 5: Control Structures to Objects (Tony Gaddis) > Starting Out with Java 5: Early Objects (Tony Gaddis) > Introduction to Programming Using Java: An Object-Oriented Approach > (2nd Ed., David Arnow, Scott Dexter & Gerald Weiss) > Computing with Java (2nd Ed., Art Gittleman) > Problem Solving with Java, Update (2nd Ed., Elliot B. Koffman & Ursula > Wolz) > Starting Out with Alice: A Visual Introduction to Programming (Tony > Gaddis) > Problem Solving and Program Design in C (4th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Problem Solving and Program Design in C (5th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Starting Out with Visual Basic 2005 (3rd Ed., Tony Gaddis & Kip > Irvine) > Starting Out with Visual Basic 6 (Tony Gaddis, Kip Irvine & Bruce > Denton) > Starting Out with Visual Basic.Net (2nd Ed., Tony Gaddis, Kip Irvine & > Bruce Denton) > Computer Programming Fundamentals with Applications in Visual Basic¬ > 6.0 (Mitchell C. Kerman & Ronald L. Brown) > Advanced VB.NET Alternate with VB.Net CD's (3rd Ed., Kip Irvine & Tony > Gaddis) > Advanced Visual Basic 2005 (4th Ed., Kip Irvine & Tony Gaddis) > C# Software Solutions: Foundations of Program Design (John Lewis) > Problem Solving, Abstraction and Design Using C++, Visual C++.NET > Edition (Frank L. Friedman & Elliot B. Koffman) > Ada 95: Problem Solving and Program Design (3rd Ed., Michael B. > Feldman & Elliot B. Koffman) > Programming and Problem Solving with Delphi (Mitchell C. Kerman) > C Program Design for Engineers (2nd Ed., Jeri R. Hanly & Elliot B. > Koffman) > Data Abstraction & Problem Solving with C++ (5th ed., Frank M. > Carrano) > Data Structures and Algorithm Analysis in C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in C++ (3rd Ed., Mark Allen > Weiss) > Data Abstraction and Problem Solving with C++: Walls and Mirrors (4th > Ed., Frank M. Carrano) > Data Structures and Other Objects Using C++ (3rd Ed., Michael Main & > Walter Savitch) > Data Structures and Problem Solving Using C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in Java (2nd Ed., Mark Allen > Weiss) > Collections Framework (Simon Gray) > Data Abstraction and Problem Solving with Java (2nd Ed., Frank M. > Carrano & Janet J. Prichard) > Data Structures and Other Objects Using Java (3rd Ed., Michael Main) > Data Structures and Problem Solving Using Java (3rd Ed., Mark Allen > Weiss) > Java Software Structures: Designing and Using Data Structures (2nd > Ed., John Lewis, Joseph Chase) > The Object of Data Abstraction and Structures (using Java) (David > Riley) > Classic Data Structures in Java (Timothy Budd) > Data Structures in Java (Thomas A. Standish) > Introduction to the Design and Analysis of Algorithms (1st Ed., Anany > V. Levitin) > Introduction to the Design and Analysis of Algorithms (2nd Ed., Anany > V. Levitin) > Algorithm Design (Jon Kleinberg & .83va Tardos) > Data Structures and Algorithm Analysis in C (2nd Ed., Mark Allen > Weiss) > Computer Algorithms: Introduction to Design and Analysis (3rd Ed., > Sara Baase & Allen Van Gelder) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (4th Ed., George F. Luger) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (5th Ed., George F. Luger) > The Complete A+ Guide to PC Repair (3rd Ed., Cheryl A. Schmidt) > The Complete A+ Guide to PC Repair (4th Ed., Cheryl A. Schmidt) > Complete Computer Repair Textbook (4th Ed., Cheryl A. Schmidt) > Computer Systems Organization and Architecture (John D. Carpinelli) > CMOS VLSI Design: A Circuits and Systems Perspective (3rd Ed., Neil > H.E. Weste & David Harris) > Interactive Computer Graphics: A Top-Down Approach Using OpenGL (4th > Ed., Edward Angel) > File Structures: An Object-Oriented Approach with C++ (3rd Ed., > Michael J. Folk, Bill Zoellick & Greg Riccardi) > Oracle 10g Programming: A Primer (Rajshekhar Sunderraman) > Darwen) > Fundamentals of Database Systems (5th Ed., Ramez Elmasri & Shamkant B. > Navathe) > Database Systems: An Application Oriented Approach, Compete Version > (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > DataBase Systems: A Practical Approach to Design, Implementation and > Management (4th Ed., Thomas M. Connolly & Carolyn E. Begg) > Database Systems: An Application-Oriented Approach, Introductory > Version (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > Fundamentals of Database Systems/Oracle 9i Programming (4th Ed., Ramez > Elmasri, Shamkant B. Navathe & Rajshekhar Sunderraman) > Oracle 9i Programming: A Primer (Rajshekhar Sunderraman) > Principles of Database Systems with Internet and Java Applications > (Greg Riccardi) > Introduction to Data Mining (Pang-Ning Tan, Michael Steinbach & Vipin > Kumar) > Data Mining: A Tutorial Based Primer (Richard Roiger & Michael Geatz) > Learning SQL: A Step-by-Step Guide Using Access (Sikha Bagui & Richard > Earp) > Access 2007 Guidebook (6th Ed., Maggie Trigg & Phyllis Dobson) > Dobson) > Implementing Databases in Oracle 9i (John Day & Craig Van Slyke) > Web 101: Making the Net Work for You (2nd Ed., Wendy G. Lehnert) > Web 101 (3rd Ed., Wendy G. Lehnert & Richard L. Kopec) > Web Developer Foundations: Using XHTML (2nd Ed., Terry Felke-Morris) > Web Development & Design Foundations With XHTML (3rd Ed., Terry Felke- > Morris) > Internet Effectively: A Beginner's Guide to the World Wide Web (Tyrone > Adams & Sharon Scollard) > Light on the Web: Essentials to Making the 'Net Work for You (Wendy G. > Lehnert) > Programming the World Wide Web (3rd Ed., Robert W. Sebesta) > Programming the World Wide Web (4th Ed., Robert W. Sebesta) > XML: Language Mechanics and Applications (Dwight Peltzer) > Practical Perl with CGI Applications (Elizabeth Chang) > Developing Web Applications with Active Server Pages (Thom Luce) > Structure and Interpretation of Signals and Systems (Edward A. Lee & > Pravin Varaiya) > Languages and Machines: An Introduction to the Theory of Computer > Science (3r Ed., Thomas A. Sudkamp) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) > Galin) > Object Oriented Software Development Using Java (2nd Ed., Xiaoping > Jia) > Introduction to the Team Software Process (Watts S. Humphrey) > Software Project Management: A Real-World Guide to Success (Joel > Henry) > Software Engineering (8th Ed., Ian Sommerville) > Object-Oriented Programming featuring Graphical Applications in Java > (Michael J. Laszlo) > Project-Based Software Engineering: An Object-Oriented Approach > (Evelyn Stiller & Cathie LeBlanc) > Engineering of Software, The: A Technical Guide for the Individual > (Dick Hamlet & Joe Maybee) > Concepts of Programming Languages (7th Ed., Robert W. Sebesta) > Concepts of Programming Languages (8th Ed., Robert W. Sebesta) > Advanced Java: Internet Applications (2nd Ed., Art Gittleman) > Objects to Components with Java 2 Platform (Art Gittleman) > C for Java Programmers (Tomasz Muldner) > Pointers on C (Kenneth Reek) > C++ Programming with Design Patterns Revealed (Tomasz Muldner) > The C++ Programming Language (3rd Ed., Bjarne Stroustrup) > Operating Systems: A Systematic View (6th Ed., William S. Davis & T.M. > Rajkumar) > Unix: The Textbook (2nd Ed., Syed Mansoor Sarwar, Robert Koretsky & > Syed Aqeel Sarwar) > Operating Systems (3rd Ed., Gary Nutt) > LINUX & UNIX Programming Tools: A Primer for Software Developers (Syed > Mansoor Sarwar & Khaled H. Al-Saqabi) > Addison-Wesley's Interactive Linux Tutorial and Reference (Edutrends, > Inc.) > Linux: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel > Sarwar) > Kernel Projects for Linux (Gary Nutt) > OSP: An Environment for Operating System Projects (Michael Kifer & > Scott A. Smolka) > Distributed Computing: Principles and Applications (M.L. Liu) > Distributed Operating Systems and Algorithm Analysis (Randy Chow & > Theodore Johnson) > Mastering Networks: An Internet Lab Manual (Jorg Liebeherr & Magda El > Zarki) > Computer Networking: A Top-Down Approach Featuring the Internet (3rd > Ed., James F. Kurose & Keith W. Ross) > Computer Networking: A Top-Down Approach (4th Ed., James F. Kurose & > Keith W. Ross) > Computer Networking Complete Package (3rd Ed., James F. Kurose & Keith > W. Ross) > Network Management: Principles and Practice (Mani Subramanian) > Computer Security: Art and Science (Matt Bishop) > Introduction to Computer Security (Matt Bishop) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) - Math, Statistics & Probability > > Advanced Engineering Mathematics (8th Ed., Erwin Kreyszig) > Advanced Engineering Mathematics (9th Ed., Erwin Kreyszig) > Elementary Differential Equations (7th Ed., Boyce) > Elementary Differential Equations (8th Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (7th > Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (8th > Ed., Boyce & Diprima) > Differential Equations: An Introduction to Modern Methods and > Applications (James Brannan & William Boyce) > Introduction to the Finite Element Method: Theory, Programming and > Applications (Erik G. Thompson) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Elementary Linear Algebra (9th Ed., Anton) > Elementary Linear Algebra with Applications (9th Ed., Howard Anton & > Chris Rorres) > Applied Statistics and Probability for Engineers (3rd Ed., Douglas > Montgomery & George Runger) > Applied Statistics and Probability for Engineers (4th Ed., Douglas > Montgomery & George Runger) > Engineering Statistics (3rd Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Engineering Statistics (4th Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Probability and Statistics in Engineering (4th Ed., William W. Hines, > Douglas Montgomery, David Goldsman & Connie Borror) > Design and Analysis of Experiments (6th Ed., Douglas Montgomery) > Spreadsheet Tools for Engineers using Excel (2nd Ed. Byron S > Gottfried) > Spreadsheet Tools for Engineers using Excel (3rd Ed. Byron S > Gottfried) > Numerical Methods for Engineers (4th Ed. Steven C. Chapra) > Numerical Methods for Engineers (5th Ed. Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (1st Ed., Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (2nd Ed., Steven C. Chapra) > Statistics for Engineers and Scientists (1st Ed, William C. Navidi) > Statistics for Engineers and Scientists (2nd Ed, William C. Navidi) > Probability (Jim Pitman) > Numerical Methods with Matlab (Amos Gilat & Vish Subramaniam) > MATLAB: An Introduction with Applications (2nd Ed., Amos Gilat) > Discrete and Combinatorial Mathematics (5th ed., Ralph P. Grimaldi) > Discrete Mathematics (Sherwood Washburn, Thomas Marlowe & Charles T. > Ryan) > Discrete Mathematics (5th ed., John Dossey, Albert Otto, Lawrence > Spence & Charles Vanden Eynden) > Mathematics for New Technologies (Don Hutchison & Mark Yannotta) > An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy) > Fundamentals of Finite Element Analysis (1st Ed., David V. Hutton) > The Finite Element Method: Its Basis and Fundamentals (6th Ed., > Zienkiewicz, R. L. Taylor & J.Z. Zhu) > Differential Equations (A. King, J. Billingham, S. Otto) > Regression Methods in Biostatistics: Linear, Logistic, Survival, and > Repeated Measures Models (Eric Vittinghoff, David Glidden, Stephen > Shiboski, Charles McCulloch) > A Modern Introduction to Probability and Statistics: Understanding Why > and How (F.M. Dekking, C. Kraaikamp, H.P. Lopuha.8a, L.E. Meester) > Statistical Methods for the Analysis of Repeated Measurements (Charles > S. Davis) > Bayesian Core: A Practical Approach to Computational Bayesian > Statistics (Jean-Michel Marin, Christian Robert) > Essentials of Stochastic Processes (Rick Durrett) > Regression Analysis: Theory, Methods, and Applications (Ashish Sen & > Muni Srivastava) > Applied Probability and Statistics (Mario Lefebvre) > Foundations of Hyperbolic Manifolds (2nd Ed., John Ratcliffe) > Fourier and Laplace Transforms (R. J. Beerends , H. G. ter Morsche) > Infinite-Dimensional Dynamical Systems (James C. Robinson) > Mathematical Methods for Physics and Engineering, (3rd Ed., Riley, > Hobson & Bence) + original Ebook > Numerical Methods in Engineering with MATLAB (Jaan Kiusalaas) + > original Ebook > Numerical Methods in Engineering with Python (Jaan Kiusalaas) + > original Ebook > An Introduction to Numerical Analysis (Endre Suli and David Mayers) + > original Ebook > Fundamentals of Engineering Numerical Analysis (Parviz Moin) > Monte Carlo Statistical Methods (2nd Ed., Christian P. Robert, George > Casella) > Introduction to Mathematical Structures and Proofs (Larry J. Gerstein) > Analyzing Categorical Data (Jeffrey S. Simonoff) > Fundamentals of Complex Analysis with Applications to Engineering, > Science, and Mathematics (3rd Ed., E. Saff & Arthur Snider) > Probability & Statistics for Engineers & Scientists (8th Ed., Walpole, > Myers, Ye) > Statistics for Engineering and the Sciences (5th Ed., Mendenhall & > Sincich) > Miller & Freund's Probability and Statistics for Engineers (7th Ed., > Johnson, Miller, Freund) > Applied Numerical Analysis Using MATLAB (2nd Ed., Fausett) > Numerical Methods Using Matlab (4th Ed., Mathews & Fink) > Applied Numerical Methods for Engineers and Scientists (Rao) > Applied Numerical Analysis Using MATLAB (2nd Ed., Laurene v. Fausett) > Friendly Introduction to Numerical Analysis (Bradie) > Elementary Linear Algebra (2nd Ed., Spence, Insel & Friedberg) > Elementary Linear Algebra with Applications (9th Ed., Kolman & Hill) > Introductory Linear Algebra: An Applied First Course (8th Ed., Kolman > & Hill) > Linear Algebra with Applications (7th Ed., S. Leon) > Linear Algebra for Engineers and Scientists Using Matlab (Hardy) > Linear Algebra with Applications (3rd Ed., Bretscher) > Modern Matrix Algebra (Hill & Kolman) > Partial Differential Equations and Boundary Value Problems with > Fourier Series (2nd ed., Asmar) > Applied Partial Differential Equations (4th Ed., Haberman) > Technical Calculus (5th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics (2th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics with Calculus (2th Ed., Dale Ewen, Joan S. Gary > & James E. Trefzger) > Introductory Mathematics (4th Ed., Cook) > Mathematics for the Technical Trades (Cook) > College Mathematics (7th Ed., Cleaves & Hobbs) > Fundamentals of Statistics (2nd Ed., Michael III Sullivan) > Statistics: Informed Decisions Using Data (2nd Ed., Michael III > Sullivan) > Modern Elementary Statistics (12th Ed., John E. Freund, Benjamin M. > Perles) > Franklin) > Elementary Statistics: Picturing the World (3rd Ed., Larson & Farber) > First Course in Statistics (9th Ed., James T. McClave & Terry Sincich) > Statistics (10th Ed., McClave & Terry Sincich) > Interactive Statistics (3rd Ed., Martha Aliaga & Brenda Gunderson) > Statistics for the Life Sciences (3rd Ed., Samuels & Witmer) > Applied Statistics and the SAS Programming Language (5th Ed., Cody & > Smith) > Biostatistics for the Health Sciences (R. Clifford Blair & Richard > Taylor) > Biostatistics: How It Works (Steve Selvin) > Business Statistics: First Course and Student CD (4th Ed., David M. > Levine, Timothy C. Krehbiel & Mark L. Berenson) > Course in Business Statistics with CD-ROM (4th Ed., Groebner, Shannon, > Fry & Smith) > Business Statistics: Decision Making and Student CD Package (7th Ed., > Groebner) > Business Statistics: A Decision-Making Approach and Student CD Update > Package (6th Ed., Groebner, Shannon, Fry & Smith) > Statistics for Business & Economics (10th Ed., McClave, Benson & > Sincich) > Statistics for Managers Using Excel and Student CD Package (5th Ed., > Levine) > Statistics for Managers Using Microsoft Excel and Student CD Package > (4th Ed., Levine, Stephan, Krehbiel & Berenson) > Statistics for Business and Economics and Student CD (6th Ed., > Newbold, Carlson & Thorne) > Statistics for Business and Economics and Student CD-ROM (5th Ed., > Newbold, Carlson & Thorne) > Basic Business Statistics: Concepts and Applications and CD package > (10th Ed., Berenson, Krehbiel & Levine) > John E. Freund's Mathematical Statistics with Applications (7th Ed., > Miller) > Probability and Statistical Inference (7th Ed., Hogg & Tanis) > Introduction to Mathematical Statistics (6th Ed., Hogg, Craig & > McKean) > Introduction to Mathematical Statistics and Its Applications (4th Ed., > Larsen & Marx) > Brief Course in Mathematical Statistics (Hogg & Tanis) > Fundamentals of Probability, with Stochastic Processes (3rd Ed., Saeed > Ghahramani) > First Course in Probability (7th Ed., Sheldon Ross) > Applied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern) > Multivariate Data Analysis (6th Ed., Hair, Black, Babin, Anderson & > Tatham) > Essential MATLAB for Engineers and Scientists (3rd Ed., Brian D Hahn & > Dan Valentine) > Introduction to Applied Statistical Signal Analysis: Guide to > Biomedical and Electrical Engineering Applications (3rd Ed. Richard > Shiavi) > Construction Mathematics (Surinder Virdi & Roy Baker) > Numerical Methods in Biomedical Engineering (Stanley Dunn, Alkis > Constantinides & Prabhas Moghe) > Probability and Statistics with Integrated Software Routines (Ronald > Deep) > Boundary Value Problems and Partial Differential Equations (5th Ed., > David Powers) > Finite Element Analysis with Error Estimators : An Introduction to the > FEM and Adaptive Error Analysis for Engineering Students (J. Akin) > Basic Engineering Mathematics (4th Ed., John Bird) > Engineering Mathematics (4th Ed., John Bird) > Higher Engineering Mathematics (5th Ed., John Bird) > Mathematics for Electrical Engineering and Computing (Mary > Attenborough) > Introductory Statistics for Engineering Experimentation (Peter Nelson, > Karen Copeland & Marie Coffin) > Understanding Engineering Mathematics (Bill Cox) > Statistics And Probability For Engineering : Applications With > Microsoft Excel (Decoursey) > Business Math Using Calculators: With 10-Key Computer Assisted > Instruction (Burton) > Mathematics for Economics and Business (5th Ed., Ian Jacques) > Business Math, Brief w/CD & Study Guide & Tutor Center Access Card Pkg > (7th Ed., Cleaves & Hobbs) > Math for Merchandising: A Step-by-Step Approach (3rd Ed., Moore) > Mathematics for Business (7th Ed., Salzman , Miller & Clendenen) > Mathematics for Business (8th Ed., Salzman , Miller & Clendenen) > Advanced Engineering Mathematics (2nd Ed, Michael Greenberg) > Basic College Mathematics with Early Integers (K. Elayn Martin-Gay) > Developmental Mathematics (K. Elayn Martin-Gay) > Essentials of Basic College Mathematics (John Jr Tobey, Jr., Jeffrey > Slater) > Basic College Mathematics (5th Ed., John Tobey & Jeffrey Slater) > Prealgebra (5th Ed., K. Elayn Martin-Gay) > Prealgebra & Introductory Algebra (2nd Ed., K. Elayn Martin-Gay) > Prealgebra (3rd Ed., Jamie Blair, John Tobey & Jeffrey Slater) > Elementary Algebra Early Graphing for College Students (3rd Ed., Allen > R. Angel) > Elementary Algebra (Michael Sullivan III, Katherine R. Struve & Janet > Mazzarella) > Elementary Algebra for College Students (7th Ed., Allen R. Angel) > Experiencing Introductory and Intermediate Algebra Through Functions > and Graphs (3rd Ed., JoAnne Thomasson & Robert Pesut) > Introductory Algebra (3rd Ed., K. Elayn Martin-Gay) > Beginning Algebra (6th Ed., John Jr Tobey & Jeffrey Slater) > Beginning Algebra: Early Graphing (Jamie Blair, John Tobey & Jeffrey > Slater) > Beginning and Intermediate Algebra (2nd Ed., Jamie Blair, John Tobey & > Jeffrey Slater) > Introductory Algebra (4th Ed., Robert F Blitzer) > Introductory and Intermediate Algebra (2nd Ed., Robert F Blitzer) > Intermediate Algebra for College Students (7th Ed., Allen R. Angel) > Intermediate Algebra (Michael Sullivan III & Katherine R. Struve) > Intermediate Algebra (3rd Ed., K. Elayn Martin-Gay) > Essentials of Intermediate Algebra for College Students (Robert F. > Blitzer) > Intermediate Algebra (4th Ed., Robert F Blitzer) > Algebra A Combined Approach (3rd Ed., K. Elayn Martin-Gay) > Elementary & Intermediate Algebra (Michael Sullivan III, Katherine R. > Struve & Janet Mazzarella) > Essentials of Introductory and Intermediate Algebra for College > Students (Robert F. Blitzer) > Algebra for College Students (3rd Ed., Allen R. Angel) > Algebra for College Students (5th Ed., Robert F Blitzer) > College Geometry: A Problem Solving Approach with Applications (2nd > Ed., Gary L. Musser, Lynn Trimpe & Vikki R. Maurer) > College Algebra (8th Ed., Michael Sullivan) > College Algebra Essentials (8th Ed., Michael Sullivan) > College Algebra (4th Ed., Robert F. Blitzer) > College Algebra Essentials (2nd Ed., Robert F. Blitzer) > College Algebra: An Early Functions Approach (Robert F. Blitzer) > College Algebra: Concepts Through Functions (Michael Sullivan III & > Michael Sullivan) > College Algebra Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Essentials of College Algebra: Enhanced with Graphing Utilities (4th > Ed., Michael Sullivan III & Michael Sullivan) > Algebra and Trigonometry (8th Ed., Michael Sullivan) > Algebra and Trigonometry (3rd Ed., Robert F. Blitzer) > Algebra and Trigonometry: An Early Functions Approach (Robert F. > Blitzer) > Precalculus: Concepts Through Functions, A Right Triangle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Algebra & Trigonometry (7th Ed., Michael Sullivan) > Algebra and Trigonometry Enhanced With Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Trigonometry (7th Ed., Michael Sullivan) > Trigonometry (8th Ed., Michael Sullivan) > Trigonometry Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus (8th Ed., Michael Sullivan) > Precalculus (3rd Ed., Robert F. Blitzer) > Precalculus Essentials (2nd Ed., Robert F. Blitzer) > Precalculus: Concepts Through Functions, A Unit Circle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Precalculus Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus Essentials: Enhanced with Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Thinking Mathematically (4th Ed., Robert F. Blitzer) > Excursions in Modern Mathematics (5th Ed., Peter Tannenbaum) > Excursions In Modern Mathematics with Mini-Excursions (6th Ed., Peter > Tannenbaum) > Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) > Fundamentals of Mathematics (10th Ed., William M Setek & Michael A > Gallo) > Learning Math in Elementary and Middle School & IMAP Package (4th Ed., > George Cathcart, Yvonne M. Pothier, James H. Vance & Nadine S. Bezuk) > Understanding the Math You Teach: Content and Methods for > Prekindergarten Through Grade 4 (Anita C. Burris) > Algebra Connections (Ira J. Papick & UMO University of Missouri) > Calculus Connections (Asma Harcharras, Dorina Mitrea) > Data Analysis and Probability Connections: Mathematics for Middle > School Teachers (Debra A. Perkowski & Michael Perkowski) > Geometry Connections (John K. Beem) > Elementary Math Modeling Updated (2nd Ed., Mary Ellen Davis & C. Henry > Edwards) > Additional Calculus Topics (11th Ed., Raymond Barnett, Michael Ziegler > & Karl Byleen) > Finite Math and Its Application (9th Ed., Larry J Goldstein, David I > Schneider & Martha J. Siegel) > Introductory Mathematical Analysis for Business, Economics and the > Life and social Sciences (11th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Introductory Mathematical Analysis for Business, Economics and the > Life and Social Sciences (12th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Additional Calculus Topics (9th Ed., Raymond A. Barnett, Michael R. > Ziegler & Karl E. Byleen) > College Mathematics for Business, Economics, Life Sciences and Social > Sciences (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. > Byleen) > Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, > David I Schneider, David I. Lay & Nakhle Asmar) > Calculus and its Applications (11th Ed., Larry J Goldstein, David I > Schneider, David I. Lay & Nakhle Asmar) > Calculus for Business, Economics, Life Sciences and Social Sciences > (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) > Calculus, Early Transcendentals (6th Ed., C. Henry Edwards & David E. > Penney) > Calculus, Early Transcendentals (7th Ed., C. Henry Edwards & David E. > Penney) > Calculus (9th Ed., Dale Varberg, Edwin Purcell & Steve Rigdon) > Calculus Early Transcendentals (Dale Varberg, Edwin Purcell & Steve > Rigdon) > Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley & Karl J. > Smith) > Calculus (6th Ed., Henry Edwards & David E. Penney) > Single Variable Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley > & Karl J. Smith) > Vector Calculus (3rd Ed., Susan J. Colley) > Applied Linear Algebra (Peter J. Olver & Cheri Shakiban) > Introductory Linear Algebra: An Applied First Course (8th Ed., Bernard > Kolman & David R. Hill) > Differential Equations and Linear Algebra (2nd Ed., Jerry Farlow, > James E. Hall, Jean Marie McDill & Beverly H. West) > Differential Equations and Linear Algebra (2nd Ed., C. Henry Edwards & > David E. Penney) > Differential Equations (2nd Ed., John Polking, Al Boggess & David > Arnold) > Differential Equations with Boundary Value Problems (2nd ed., John > Polking, Al Boggess & David Arnold) > Discrete Mathematics with Graph Theory (3rd Ed., Edgar G. Goodaire & > Michael M. Parmenter) > Discrete Mathematics (6th Ed., Richard Johnsonbaugh) > Essential Discrete Mathematics (Todd Feil & Joan Krone) > Business Mathematics, 10th Ed. (Charles D. Miller, Stanley A. Salzman > & Gary Clendenen) > Elementary Statistics (6th Ed., Neil A. Weiss) > Elementary Statistics (7th Ed., Neil A. Weiss) > Elementary Statistics Using the Graphing Calculator: For the TI-83/84 > Plus (Mario F. Triola) > Elementary Statistics Using the TI-83/84 Plus Calculator (2nd Ed., > Mario F. Triola) > Elementary Statistics Update (9th Ed., Mario F. Triola) > Elementary Statistics (10th Ed., Mario F. Triola) > Elementary Statistics With Multimedia Study Guide (10th Ed., Mario F. > Triola) > Essentials of Statistics (2nd Ed., Mario F. Triola) > Essentials of Statistics (3rd Ed., Mario F. Triola) > Introductory Statistics (7th Ed., Neil A. Weiss) > Introductory Statistics (8th Ed., Neil A. Weiss) > Intro Stats (2nd Ed., Richard D. De Veaux, Paul F. Velleman & David E. > Bock) > Stats: Data and Models, (Richard D. De Veaux, Paul F. Velleman & David > E. Bock) > Stats: Data and Models, (2nd ed., Richard D. De Veaux, Paul F. > Velleman & David E. Bock) > Elementary Statistics Using Excel (2nd Ed., Mario F. Triola) > Elementary Statistics Using Excel (3rd Ed., Mario F. Triola) > Stats: Modeling the World (2nd Ed., David E. Bock, Paul F. Velleman & > Richard D. De Veaux) > Statistical Reasoning for Everyday Life (2nd Ed., Jeffrey O. Bennett, > William L. Briggsr & Mario F. Triola) > Business Statistics (Mario F. Triola & LeRoy A. Franklin) > Biostatistics for the Biological and Health Sciences with Statdisk > (Marc M. Triola & Mario F. Triola) > A Course in Probability (Neil A. Weiss) > Probability and Statistics (3rd Ed., Morris H. DeGroot & Mark J. > Schervish) > Statistics for Science and Engineering (John Kinney) > Developmental Mathematics (7th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Mathematical Proofs: A Transition to Advanced Mathematics (Gary > Chartrand, Albert D. Polimeni & Ping Zhang) > Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Ed., > Carol Schumacher) > Elementary Number Theory (5th Ed., Kenneth H. Rosen) > History of Mathematics: Brief Version (Victor J. Katz) > College Geometry: A Discovery Approach (2nd Ed., David Kay) > Geometry: An Investigative Approach (2nd Ed., Phares G. O'Daffer & > Stanley R. Clemens) > A First Course in Abstract Algebra (7th Ed., John B. Fraleigh) > Complex Variables with Applications (3rd Ed., David A. Wunsch) > Numerical Analysis with CD-ROM (Timothy Sauer) > Numerical Analysis and Scientific Computation (Jeffery J. Leader) > Linear Algebra and Differential Equations (Gary L. Peterson & James S. > Sochacki) > Elementary Differential Equations Bound with IDE CD Package (2nd Ed., > Werner E. Kohler & Lee W. Johnson) > Elementary Differential Equations with Boundary Value Problems with > IDE CD Package (2nd Ed., Werner E. Kohler & Lee W. Johnson) > Fundamentals of Differential Equations (6th Ed., Kent B. Nagle, Late, > Edward B. Saff & Arthur David Snider) > Fundamentals of Differential Equations and Boundary Value Problems > (4th Ed., Kent B. Nagle, Late, Edward B. Saff & Arthur David Snider) > Linear Algebra and Its Applications with CD-ROM, Update (3rd Ed., > David C. Lay) > Introduction to Linear Algebra (5th ed., Lee W. Johnson, R. Dean Riess > & Jimmy T. Arnold) > Calculus for the Life Sciences (Marvin L. Bittinger, Neal Brand & John > Quintanilla) > Calculus with Applications for the Life Sciences (Raymond N. > Greenwell, Nathan P. Ritchey & Margaret L. Lial) > Calculus: An Integrated Approach to Functions and Their Rates of > Change, Preliminary Edition (Robin J. Gottlieb) > Calculus (9th Ed., George B. Thomas, Jr. & Ross L. Finney) > Thomas' Calculus, Alternate Edition (9th Ed., George B. Thomas, Jr. & > Ross L. Finney) > Calculus: A Complete Course (2nd Ed., Ross L. Finney, Franklin D. > Demana, Bert K. Waits & Daniel Kennedy) > Calculus (Elgin H. Johnston & Jerry Mathews) > Thomas' Calculus, Updated (10th Ed., George B. Thomas, Jr., Ross L. > Finney, Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus (11th Ed., George B. Thomas, Jr., Maurice D. Weir, > Joel D. Hass & Frank R. Giordano) > Thomas' Calculus Early Transcendentals (11th Ed., George B. Thomas, > Jr., Maurice D. Weir, Joel D. Hass & Frank R. Giordano) > University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, > Jr.) > University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir > & George B. Thomas, Jr.) > Thomas' Calculus, Media Upgrade (11th Ed., George B. Thomas, Jr., > Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Ed., > George B. Thomas, Jr., Maurice D. Weir, Joel D. Hass & Frank R. > Giordano) > Calculus with Applications (8th Ed., Margaret L. Lial, Raymond N. > Greenwell & Nathan P. Ritchey) > Calculus with Applications, Brief Version (8th Ed., Margaret L. Lial, > Raymond N. Greenwell & Nathan P. Ritchey) > Finite Math with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics (8th Ed., Margaret L. Lial, Raymond N. Greenwell & > Nathan P. Ritchey) > Mathematics with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics and Calculus with Applications (7th Ed., Margaret > L. Lial, Raymond N. Greenwell & Nathan P. Ritchey) > Mathematical Ideas (10th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas (11th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas Expanded Edition (10th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Mathematical Ideas Expanded Edition (11th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (3rd Ed., Jeffrey O. Bennett & William L. Briggs) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (4th Ed., Jeffrey O. Bennett & William L. Briggs) > A Problem Solving Approach to Mathematics (9th Ed., Rick Billstein, > Shlomo Libeskind & Johnny W. Lott) > A Survey of Mathematics with Applications (7th Ed., Allen R. Angel, > Christine D. Abbott & Dennis C. Runde) > A Survey of Mathematics with Applications: Expanded Edition (7th Ed., > Allen R. Angel, Christine D. Abbott & Dennis C. Runde) > Mathematics All Around (3rd Ed., Tom Pirnot) > Mathematics for Elementary School Teachers (3rd Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary School Teachers (4th Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary Teachers with Activities (Sybilla > Beckmann) > Mathematics for Elementary Teachers plus Activities Manual (2nd Ed., > Sybilla Beckmann) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (8th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (9th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > Mathematical Reasoning for Elementary Teachers (4th Ed., Calvin T. > Long & Duane W. DeTemple) > Essentials of Using and Understanding Mathematics: A Quantitative > Reasoning Approach (Jeffrey O. Bennett & William L. Briggs) > Technical Calculus with Analytic Geometry (4th Ed., Allyn J. > Washington) > Basic Technical Mathematics (8th Ed., Allyn J. Washington) > Basic Technical Mathematics with Calculus (8th Ed., Allyn J. > Washington) > Basic Technical Mathematics with Calculus Metric Version (8th Ed., > Allyn J. Washington) > Introduction to Technical Mathematics (5th Ed., Allyn J. Washington, > Mario F. Triola & Ellena E. Reda) > A Graphical Approach to Precalculus (4th Ed., John Hornsby, Margaret > L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits (3rd Ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits: A Unit Circle > Approach (4th Ed., John Hornsby, Margaret L. Lial & Gary K. Rockswold) > Precalculus: Functions and Graphs (5th Ed., Franklin Demana, Bert K. > Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphical, Numerical, Algebraic (7th Ed., Franklin > Demana, Bert K. Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphs and Models Graphing Calculator Manual Package (3rd > Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & > Judith A. Penna) > Functioning in the Real World: A Precalculus Experience (2nd Ed., > Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker & Martha J. > Siegel) > Precalculus with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Precalculus (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Mark Dugopolski) > Precalculus (4th Ed., Mark Dugopolski) > Precalculus (3rd Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Precalculus: Functions and Graphs (2nd Ed., Mark Dugopolski) > Fundamentals of Precalculus (Mark Dugopolski) > Trigonometry (Mark Dugopolski) > Trigonometry (2nd Ed., Mark Dugopolski) > Trigonometry (8th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Trigonometry: A Circular Function Approach (Marie Aratari) > A Graphical Approach to Algebra and Trigonometry (4th ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > Algebra and Trigonometry: Graphs and Models Graphing Calculator Manual > Package (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. > Ellenbogen & Judith A. Penna) > Algebra and Trigonometry (2nd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > Algebra and Trigonometry (3rd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > College Algebra and Trigonometry (J. S. Ratti & Marcus S. McWaters) > College Algebra and Trigonometry (3rd Ed., Mark Dugopolski) > College Algebra and Trigonometry (4th Ed., Mark Dugopolski) > Algebra and Trigonometry with Modeling and Visualization (3rd Ed., > Gary K. Rockswold) > College Algebra and Trigonometry (3rd Ed., Margaret L. Lial, John > Hornsby & David I. Schneider) > A Graphical Approach to College Algebra (4th Ed., John Hornsby, > Margaret L. Lial & Gary K. Rockswold) > College Algebra: Graphs and Models Graphing Calculator Manual Package > (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen > & Judith A. Penna) > College Algebra (J. S. Ratti & Marcus S. McWaters) > College Algebra with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Essentials of College Algebra with Modeling and Visualization (3rd > Ed., Gary K. Rockswold) > Essentials of College Algebra (Margaret L. Lial, John Hornsby & David > I. Schneider) > Essentials of College Algebra, Alternate Edition (Margaret L. Lial, > John Hornsby & David I. Schneider) > College Algebra (3rd Ed., Mark Dugopolski) > College Algebra (4th Ed., Mark Dugopolski) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (2nd Ed., Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin > L. Bittinger) > College Algebra (9th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Essentials of Geometry for College Students (2nd Ed., Margaret L. > Lial, Barbara A. Brown, Arnold R. Steffenson & L. Murphy Johnson) > Algebra for College Students (5th Ed., Margaret L. Lial, John Hornsby > & Terry McGinnis) > Introductory and Intermediate Algebra (3rd Ed., argaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (3rd Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (4th Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Elementary and Intermediate Algebra (1st Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Elementary and Intermediate Algebra (2nd Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Introductory and Intermediate Algebra: A Combined Approach (2nd Ed., > Marvin L. Bittinger & Judith A. Beecher) > Introductory and Intermediate Algebra (3rd Ed., Marvin L. Bittinger & > Judith A. Beecher) > Elementary and Intermediate Algebra (George Woodbury) > Elementary and Intermediate Algebra: Concepts and Applications (4th > Ed., Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Beginning and Intermediate Algebra with Applications and Visualization > (Gary K. Rockswold & Terry A. Krieger) > Elementary and Intermediate Algebra: Graphs & Models (2nd Ed., Marvin > L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Foundations of Mathematics (Marvin L. Bittinger & Judith A. Penna) > Intermediate Algebra (9th Ed., Marvin L. Bittinger) > Intermediate Algebra (10th Ed., Marvin L. Bittinger) > Intermediate Algebra: Graphs & Models (2nd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra: Graphs & Models (3rd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra with Applications and Visualization (2nd Ed., > Gary K. Rockswold & Terry A. Krieger) > Intermediate Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Intermediate Algebra (Tom Carson, Ellyn Gillespie & Bill E. Jordan) > Intermediate Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Intermediate Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Beginning Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Developmental Mathematics: Basic Mathematics and Algebra (Margaret L. > Lial, John Hornsby, Terry McGinnis, Stanley A. Salzman & Diana L. > Hestwood) > Prealgebra and Introductory Algebra (Marvin L. Bittinger & David J. > Ellenbogen) > Prealgebra and Introductory Algebra (2nd Ed., Marvin L. Bittinger & > David J. Ellenbogen) > Elementary Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Introductory Algebra (9th Ed., Marvin L. Bittinger) > Introductory Algebra (10th Ed., Marvin L. Bittinger) > Prealgebra and Introductory Algebra (2nd Ed., Margaret L. Lial, John > Hornsby, Terry McGinnis & Diana L. Hestwood) > Elementary Algebra with Early Systems of Equations (Tom Carson & Ellyn > Gillespie) > Elementary Algebra: Concepts and Applications (6th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Elementary Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Introductory Algebra (Richelle M. Blair) > Introductory Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Beginning Algebra with Applications and Visualization (Gary K. > Rockswold & Terry A. Krieger) > Integrated Arithmetic and Basic Algebra (3rd Ed., Bill E. Jordan & > William P. Palow) > Introductory Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Developmental Mathematics (6th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Prealgebra (3rd Ed., Margaret L. Lial & Diana L. Hestwood) > Prealgebra (4th Ed., Marvin L. Bittinger & David J. Ellenbogen) > Prealgebra (5th Ed., Marvin L. Bittinger, David J. Ellenbogen & > Barbara L. Johnson) > Prealgebra (2nd Ed., Tom Carson) > Basic Mathematics (9 th Ed., Marvin L. Bittinger) > Basic Mathematics (10 th Ed., Marvin L. Bittinger) > Basic Mathematics Preliminary Edition (Robert Prior) > Basic Mathematics with Early Integers (Marvin L. Bittinger & Judith A. > Penna) > Basic College Mathematics (7th Ed., Margaret L. Lial, Stanley A. > Salzman & Diana L. Hestwood) > Basic Mathematics through Applications (3rd Ed., Geoffrey Akst & Sadie > Bragg) > Fundamental Mathematics through Applications (3rd Ed., Geoffrey Akst & > Sadie Bragg) > Wave Motion (J. Billingham & A. C. King) > Solving ODEs with MATLAB (L. F. Shampine, I. Gladwell & S. Thompson) > Numerical Solution of Partial Differential Equations: An Introduction > (2nd Ed., K. W. Morton & D. F. Mayers) > Measure Theory and Filtering: Introduction and Applications (Lakhdar > Aggoun & Robert J. Elliott) > Mathematical Models in Biology: An Introduction (Elizabeth S. Allman & > John A. Rhodes) > Insurance Risk and Ruin (David C. M. Dickson) > Data Analysis and Graphics Using R: An Example-based Approach (2nd > Ed., John Maindonald & John Braun) > Convex Optimization (Stephen Boyd & Lieven Vandenberghe) > Lauritzen) > Calculus: Concepts and Methods (Ken Binmore & Joan Davies) > An Introduction to Partial Differential Equations (Yehuda Pinchover & > Jacob Rubinstein) > An Introduction to Ordinary Differential Equations (James C. Robinson) > An Introduction to Mathematical Physiology and Biology (2nd Ed., J. > Mazumdar) > An Introduction to Financial Option Valuation: Mathematics, > Stochastics and Computation (Desmond Higham) > An Interactive Introduction to Mathematical Analysis (Jonathan Lewin) > An Elementary Introduction to Mathematical Finance: Options and other > Topics (2nd Ed., Sheldon M. Ross) > A Course in Financial Calculus (Alison Etheridge) - Physics & Astronomy : > > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Fundamentals of Physics (8th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (6th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (7th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > An Introduction to Thermodynamics and Statistical Mechanics (2nd Ed, > Keith Stowe) > Equilibrium and Non-Equilibrium Statistical Thermodynamics (Michel Le > Bellac, Fabrice Mortessagne & G. George Batrouni) > Elements of Statistical Mechanics: With an Introduction to Quantum > Field Theory and Numerical Simulation (Ivo Sachs & Siddhartha Sen) > Quantum Transport (2nd Ed., Supriyo Datta) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Applied Quantum Mechanics (1st Ed., A. F. J. Levi) + original Ebook > Applied Quantum Mechanics (2nd Ed., A. F. J. Levi) > Astronomy A Physical Perspective (2nd Ed., Marc L. Kutner) + original > Ebook > Classical Mechanics (Douglas Gregory) + original Ebook > Electromagnetic Field Theory Fundamentals (2nd Ed., Singh Guru & > Hiziroglu) > Fundamentals of Quantum Mechanics (C.L. Tang) + original Ebook > Special Relativity (P.M. Schwarz & J.H. Schwarz) > Statistical Thermodynamics (Normand Laurendeau) > Statistical Thermodynamics and Microscale Thermophysics (Van P. Carey) > Thermal Physics (Ralph Baierlein) > Topics in Atomic Physics (Charles E. Burkhardt, Jacob J. Leventhal) > Applied Physics (8th Ed., Dale Ewen, Ronald Nelson, Neill Schurter & > Erik Gundersen) > Orbital Mechanics for Engineering Students (Howard Curtis) > Diagnostic Ultrasound Imaging: Inside Out (Thomas Szabo) > Astronomy: A Beginner's Guide to the Universe (5th Ed., Eric Chaisson > & Steve McMillan) > The Cosmic Perspective Media Update with MasteringAstronomy» and > Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with MasteringAstronomy» > and Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. > Bennett, Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with Astronomy Place > website, Skygazer Planetarium Software (3rd Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective (3rd Ed., Jeffrey O. Bennett, Megan > Donahue, Nicholas Schneider & Mark Voit) > Astronomy Today (5th Ed., Eric Chaisson & Steve McMillan) > An Introduction to Modern Astrophysics (2nd Ed., Bradley W. Carroll & > Dale A. Ostlie) > Conceptual Physical Science (3rd Ed., Paul G. Hewitt, John A. Suchocki > & Leslie Hewitt) > Conceptual Integrated Science (Paul G. Hewitt, Suzanne Lyons, John A. > Suchocki & Jennifer Yeh) > Physics: Concepts & Connections (4th Ed., Art Hobson) > Conceptual Physics (10th Ed., Paul G. Hewitt) > College Physics (6th Ed., Jerry D Wilson, Anthony J Buffa & Bo Lou) > Physics with Mastering Physics (3rd Ed., James S. Walker) > Active Learning Guide (Alan Van Heuvelen & Eugenia Etkina) > E&M TIPERs: Electricity & Magnetism Tasks (C. J. Hieggelke, D. P. > Maloney, T. L. O'Kuma & Steve Kanim) > Physics: Principles with Applications (6th Ed., Douglas C. Giancoli) > Physlet¬ Physics: Interactive Illustrations, Explorations and Problems > for Introductory Physics (Wolfgang Christian & Mario Belloni) > University Physics with Modern Physics with Mastering Physics (11th > Ed., Hugh D. Young & Roger A. Freedman) > Physics for Scientists and Engineers (3rd Ed., Douglas C. Giancoli) > Physics for Scientists and Engineers with Modern Physics (3rd Ed., > Douglas C. Giancoli) > Physlet¬ Quantum Physics: An Interactive Introduction (Mario Belloni, > Wolfgang Christian & Anne Cox) > Introduction to Electrodynamics (3rd Ed., David J. Griffiths) > Introduction to Optics (3rd Ed., Frank L Pedrotti, Leno M Pedrotti & > Leno S Pedrotti) > Introduction to Quantum Mechanics (2nd Ed., David J. Griffiths) > Quantum Mechanics: An Accessible Introduction (Robert Scherrer) > The Physics of Sound (3rd Ed., Richard E Berg & David G Stork) > Classical Electromagnetism (Jerrold Franklin) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Introduction to Color Imaging Science (Hsien-Che Lee) > An Introduction to Astrobiology (Iain Gilmour & Mark A. Sephton) > An Introduction to Galaxies and Cosmology (Mark H. Jones & Robert J. > Lambourne) > An Introduction to the Solar System (Neil McBride & Iain Gilmour) > Quantum Physics (Michel Le Bellac) > Laser Fundamentals (2nd Ed., William T. Silfvast) > Introductory Quantum Optics (Christopher Gerry & Peter Knight) > Introduction to Plasma Physics: With Space and Laboratory Applications > (D. A. Gurnett & A. Bhattacharjee) > A Short Introduction to Quantum Information and Quantum Computation > (Michel Le Bellac) > A Quantum Approach to Condensed Matter Physics (Philip L. Taylor & > Olle Heinonen) > A First Course in String Theory (Barton Zwiebach) > A First Course in Computational Physics and Object-Oriented > Programming with C++ (David Yevick) > A Course in Modern Mathematical Physics: Groups, Hilbert Space and > Differential Geometry (Peter Szekeres) > Time Series Analysis and Its Applications: With R Examples (2nd Ed., > Robert Shumway & David Stoffer) > Introduction to Time Series and Forecasting (Peter Brockwell & Richard > Davis) > Ultrasonic Nondestructive Evaluation Systems: Models and Measurements > (Lester W. Schmerr & Sung-Jin Song) - Civil Engineering : > > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Fundamentals of Structural Analysis, (1st Ed., Leet & Uang) > Fundamentals of Structural Analysis, (2nd Ed., Leet & Uang) > Fundamentals of Structural Analysis, (3rd Ed., Leet & Uang) > Structural and Stress Analysis (2nd Ed., Megson) + Ebook > Statics and Strength of Materials for Architecture and Building > Construction (3rd Ed., Onouye & Kane) > Open Channel Hydraulics (A. Osman Akan) > Fundamentals of Structural Stability (George Simitses & Dewey Hodges) > Introduction to Naval Architecture : Formerly Muckle's Naval > Architecture for Marine Engineers (4th Ed., E C Tupper) > The Management of Construction: A Project Lifecycle Approach (F. > Lawrence Bennett) > Advanced Topics in Finite Element Analysis of Structures: With > Mathematica and MATLAB Computations (Asghar Bhatti) > Elementary Structures for Architects and Builders (5th Ed., Ronald E. > Shaeffer) > Surveying with Construction Applications (6th Ed., Barry F. Kavanagh) > Structural Analysis (6th Ed., Hibbeler) > Dynamics of Structures (3rd Ed., Chopra) > Structures (6th Ed., Daniel Lewis Schodek & Martin Bechthold) > Concrete Structures (Mehdi Setareh & Robert M. Darvas) > Reinforced Concrete Design (6th Ed., Chu-Kia Wang, Charles G. Salmon) > Reinforced Concrete Design (7th Ed., Chu-Kia Wang, Charles G. Salmon & > Jos.8e A. Pincheira) > Reinforced Concrete Design (6th Ed., George F. Limbrunner & Abi > Aghayere) > Reinforced Concrete: Mechanics and Design (4th Ed., James G. MacGregor > & James K. Wight) > Structural Steel Design (4th Ed., Jack C. McCormac) > Design of Reinforced Concrete (6th Ed., Jack C. McCormac & James K. > Nelson) > Design of Reinforced Concrete (7th Edition, ACI 318-05 Code Edition, > by Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (3rd Ed., > James K. Nelson, Jr., Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (4th Ed., Jack > C. McCormac) > Surveying (5th Ed., Jack C. McCormac) > Introduction to Structural Analysis & Design (S. D. Rajan) > Soil Mechanics and Foundations (2nd Ed., Muniram Budhu) > Soils and Foundations (7th Ed., Liu & Evett) > Essentials of Soil Mechanics and Foundations: Basic Geotechnics (7th > Ed., David F. McCarthy) > Building Construction: Principles, Materials, and Systems (Madan > Mehta, Diane Armpriest & Walter Scarborough) > Construction Methods and Management (7th Ed., Stephens W. Nunnally) > Construction Project Administration (8th Ed., Ed Fisk Wayne Reynolds) > Construction Accounting and Financial Management (Steven J. Peterson) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Construction Estimating Using Excel (Stephen J. Peterson) > Heating and Cooling of Buildings: Design for Efficiency (2nd Ed., Jan > F. Kreider, Peter S. Curtiss & Ari Rabl) > Steel Structures: Behavior and LRFD (1st Ed., Ramulu S Vinnakota) > The Engineering of Foundations (1st Ed., Rodrigo Salgado) > Introduction to Transportation Engineering (2nd Ed., Banks) > Construction Contracts (2nd Ed., Hinze) > Urban Transportation Planning (2nd Ed., Meyer & Miller) > Construction Planning, Equipment, and Methods (6th Ed., Peurifoy & > Schexnayder) > Construction Planning, Equipment, and Methods (7th Ed., Peurifoy, > Schexnayder & Aviad Shapira) > Open Channel Hydraulics (Terry Sturm) > Construction Management Fundamentals (Schexnayder & Mayo) > Fundamentals of Structural Dynamics (2nd Ed., Roy R. Craig & Andrew J. > Kurdila) > Structural Concrete: Theory and Design (3rd Ed., M. Nadim Hassoun & > Akthem Al-Manaseer) > Principles of Highway Engineering and Traffic Analysis (3rd Ed., Fred > Mannering, Walter Kilareski & Scott Washburn) - Environmental Engineering, Earth and Environmental Sciences : > > Principles of Environmental Engineering and Science (Mackenzie L Davis > & Susan J Masten) > Introduction to Environmental Engineering (4th Ed., MacKenzie L. Davis > & David A. Cornwell) > Introduction to Environmental Engineering and Science (2nd Ed., > Gilbert M. Masters) > Introduction to Environmental Engineering and Science (3rd Ed., > Gilbert M. Masters & Wendell P. Ela) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) > Introduction to Engineering and the Environment (1st Ed., Edward S. > Rubin) > Basic Environmental Technology: Water Supply, Waste Management & > Pollution Control (5th Ed., Jerry A. Nathanson) > Small and Decentralized Wastewater Management Systems (1st Ed, Crites > & Tchobanoglous) > Water Resources Engineering (R. Wurbs, W. James) > Water and Wastewater Technology (6th Ed., Mark J. Hammer, Sr. & Mark > J. Hammer, Jr.) > Principles of Sequence Stratigraphy (Octavian Catuneanu) > Atmospheric Science: An Introductory Survey (2nd Ed., John Wallace, > Peter Hobbs) > Plant Pathology (5th Ed., George Agrios) > Environmental Engineering (4th Ed., Ruth F Weiner & Robin Matthews) > Groundwater Hydrology (3rd Ed., David Keith Todd & Larry W. Mays) > Groundwater Science (Charles Fitts) > Agriculture's Ethical Horizon (Robert Zimdahl) > Environmental Contaminants: Assessment and Control (Daniel Vallero) > Water Resources Engineering 2005 Edition (Larry W. Mays) > Water-Resources Engineering (2nd Ed., Chin) > Water Chemistry (Benjamin) > Hazardous Waste Management (2nd Ed., Michael D. LaGrega, Phillip L > Buckingham & Jeffrey C Evans) > Environmental Biotechnology: Principles and Applications (1st Ed., > Bruce E. Rittmann & Perry L. McCarty) > Chemistry for Environmental Engineering and Science (5th Ed., Clair N > Sawyer, Perry L. McCarty & Gene F. Parkin) > Geology for Engineers and Environmental Scientists (3rd Ed., Alan E. > Kehew) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Water Treatment: Principles and Design (2nd Ed., by MWH) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & > Baxter Vieux) - Chemistry and Chemical Engineering : > > Mass Transfer Operations (3rd Ed., Treybal) > Mass Transfer in Multicomponent Mixtures (J.A. Wesseling & R. Krishna) > + original Ebook > Principles and Modern Applications of Mass Transfer Operations (Jaime > Benitez) > Diffusion - Mass Transfer in Fluid Systems (2nd Ed., Cussler) > Separation Process Principles (1st Ed, Seader & Henley) > Separation Process Principles (2nd Ed, Seader & Henley) > Equilibrium Staged Separations (Wankat) > Principles of Chemical Separations with Environmental Applications > (Richard D. Noble) > Product and Process Design Principles: Synthesis, Analysis, and > Evaluation (2nd Ed., Seider & Seader) + Ebook > Principles and Practices of Automatic Process Control (3rd Ed., Smith > & Corripio) + Ebook > Process Dynamics and Control (2nd Ed., Seborg & Edgard) > Process Control - A First Course with MATLAB (P.C. Chau) + Ebook > Process Dynamics: Modeling, Analysis and Simulation (Wayne Bequette) > Plant Design and Economics for Chemical Engineers, (5th Ed., Peters & > Timmerhaus) + Ebook > Basic Principles and Calculations in Chemical Engineering (6th Ed., > Himmelblau) > Basic Principles and Calculations in Chemical Engineering (7th Ed., > Himmelblau) > Unit Operations of Chemical Engineering (6th Ed., McCabe & Smith) > Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) > Advanced Transport Phenomena (John C. Slattery) > Introduction to Transport Phenomena (W. Thomson) > Transport Phenomena: A Unified Aprroach (Robert S. Brodkey & Harry C. > Hershey) + Ebook > Transport Phenomena in Multiphase Systems (Faghri & Zhang) > Modeling in Transport Phenomena: A Conceptual Approach (2nd Ed., > Ismail Tosun) + original Ebook > Transport Phenomena (2nd Ed., Bird & Stewart) + Ebook > Solutions to Class 1&2 - Transport Phenomena (Bird) > Chemical Engineering Design (Coulson & Richardson's Chemical > Engineering - Volume 6) - (4th Ed., Sinnott) + original Ebook > Chemical Engineering Design and Analysis - An Introduction (Duncan & > Reimer) > Chemical Reaction Engineering (3rd Ed., Levenspiel) + Ebook > Chemical Reactor Analysis and Design Fundamentals (Rawlings & Ekerdt) > + Ebook > Fundamentals of Chemical Reaction Engineering (1st Ed., Davis) > Conceptual Design of Distillation Systems (1st Ed., Doherty & Malone) > Distillation Theory and its Application to Optimal Design of > Separation Units (F.B. Petlyuk) + original Ebook > Batch Distillation: Simulation, Optional Design and Control (Diwekar) > + Ebook > Fluid Mechanics for Chemical Engineers, (3rd Ed., Noel de Nevers) > Introduction to Chemical Processes: Principles, Analysis, Synthesis > (1st Ed., Regina M. Murphy) > Optimization of Chemical Processes (2nd Ed., Edgar & Himmelblau) + > Ebook > Chemical and Engineering Thermodynamics (3rd Ed., Stanley I. Sandler) > Chemical, Biochemical, and Engineering Thermodynamics (4th Ed., > Stanley I. Sandler) > Introduction to Chemical Engineering Thermodynamics (6th Ed., Smith & > Van Ness) > Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & > Van Ness) > Introductory Chemical Engineering Thermodynamics (J. Elliott, C. Lira) > Engineering and Chemical Thermodynamics (Koretsky) > Phase Equilibria, Phase Diagrams and Phase Transformations - Their > Thermodynamic Basis (2nd Ed., Mats Hillert) > Introduction to Chemical Kinetics and Chemical Reaction Engineering > (Missen, Mims) + original Ebook > Principles of Chemical Kinetics (James House) > Transport Processes and Unit Operations (3rd Ed., Christie J. > Geankoplis) > Transport Processes and Separation Process Principles (4th Ed., > Christie J. Geankoplis) > Elementary Principles of Chemical Processes (3rd Ed., Felder & > Rousseau) + Ebook > Chemical Process Safety: Fundamentals with Applications (2nd Ed., > Crowl & Louvar) + Ebook > Elements of Chemical Reaction Engineering (3rd Ed., Fogler) > Elements of Chemical Reaction Engineering (4th Ed., Fogler) > Group Theory with Applications in Chemical Physics (Patrick Jacobs) > Food Analysis (3rd Ed., Suzanne Nielsen) > Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, > v2.5, 3rd Ed. (Brian F. Woodfield & Matthew C. Asplund) > Introductory Chemistry and CW+ GradeTracker Access Card Package, 2nd > Ed. (Nivaldo J. Tro) > Introductory Chemistry: Concepts and Connections, 4th Ed. (Charles H > Corwin) > Prentice Hall Lab Manual Introductory Chemistry, 4th Ed. (Charles H > Corwin) > General, Organic and Biological Chemistry: Structures of Life with > Student Access Kit for MasteringGOBChemistry», 2nd ed. (Karen C. > Timberlake) > Chemistry: An Introduction to General, Organic, and Biological > Chemistry with The Chemistry Place CD-ROM, 9th Ed (Karen C. > Timberlake) > Conceptual Chemistry, 3rd Ed (John A. Suchocki) > Explorations in Conceptual Chemistry: A Student Activity Manual > (Jeffrey Paradis) > Criminalistics: An Introduction to Forensic Science (9th Ed., Richard > Saferstein) > Physical Chemistry with Spartan Student Physical Chemistry Software > (Thomas Engel & Philip Reid) > Quantum Chemistry and Spectroscopy with Spartan Student Physical > Chemistry Software (Thomas Engel & Philip Reid) > Themodynamics, Statistical Thermodynamics, and Kinetics (Thomas Engel > & Philip Reid) > Physical Chemistry (7th. Ed., Peter Atkins & Julio de Paula) > Chemistry An Introduction to Organic, Inorganic and Physical Chemistry > (3rd Ed., Catherine E. Housecroft & Edwin Constable) > General Chemistry: The Essential Concepts (4th Ed., Raymond Chang) > Chemistry: The Molecular Nature of Matter and Change (3rd Ed., Martin > Silberberg) > Chemistry: The Molecular Nature of Matter and Change (4th Ed., Martin > Silberberg) > General, Organic and Biochemistry (3rd ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (4th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (5th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > Fundamentals of Chemistry (3rd Ed., David E Goldberg) > Fundamentals of Chemistry (4th Ed., David E Goldberg) > Fundamentals of Chemistry (5th Ed., David E Goldberg) > Modern Analytical Chemistry (Harvey) > General Chemistry Lab Manual (Petra A. M. van Koppen) > Practical Interfacing in the Laboratory: Using a PC for > Instrumentation, Data Analysis and Control (Stephen E. Derenzo) > Bioprocess Engineering Principles (Pauline M. Doran) - Industrial Engineering, Business, Economics and Finance : > > Engineering Economy (5th Ed., Leland T Blank & Anthony Tarquin) > Engineering Economy (6th Ed., Leland T Blank & Anthony Tarquin) + > original Ebook > Contemporary Engineering Economics (4th Ed., Chan Park) > Engineering Economy (13th Ed, Sullivan) > Introduction to Statistical Quality Control (5th Ed., Douglas C. > Montgomery) > Managing Engineering and Technology (4th, Morse & Babcock) > (4th Ed, Gryna) > Juran's Quality Planning and Analysis for Enterprise Quality (5th Ed., > Gryna, Chua & DeFeo) > Quality (4th Ed., Summers) > Quality Management (5th Ed., Goetsch & Davis) > Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) > Value Driven Product Planning and Systems Engineering (H. E. Cook & L. > A. Wissmann) > Work Systems: The Methods, Measurement & Management of Work (Mikell P. > Groover) > Occupational Safety and Health for Technologists, Engineers, and > Managers (5th Ed., Goetsch) > Occupational Safety and Health for Technologists, Engineers, and > Managers (6th Ed., Goetsch) > Introduction to Engineering Technology (6th Ed., Robert J. Pond) > Manufacturing Facilities Design and Material Handling (3rd Ed., Meyers > & Stephens) > Fundamentals of Forensic Science (Max Houck & Jay Siegel) > Introduction to Optimum Design (2nd Ed., Jasbir Arora) > Project Management for Business and Engineering : Principles and > Practice (2nd Ed., John Nicholas) > ISO 9001:2000 Quality Registration Step-by-Step (3rd Ed., Fred Dobb) > Systems for Planning and Control in Manufacturing (D. K. Harrison & D. > J. Petty) > Planning and Control of Manufacturing Operations (John Kenworthy) > Professionalism: Real Skills for Workplace Success (Anderson & Bolt) > Customer Service: Career Success Through Customer Loyalty (4th Ed., > Timm) > Customer Service: A Practical Approach (3rd Ed., Harris) > Customer Service: A Practical Approach (4th Ed., Harris) > Serving Internal and External Customers (Anne Swartzlander) > Customer Relationship Management: The Bottom Line to Optimizing Your > ROI (Anton & Petouhoff) > Engineering Economy and the Decision-Making Process (Joseph C. > Hartman) > Engineering Management: Challenges in the New Millennium (C M Chang) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Supply Chain Management (3rd Ed., Sunil Chopra & Peter Meindl) > Industrial Safety and Health Management (5th Ed., C. Ray Asfahl) > Computer Numerical Control: Operation and Programming (3rd Ed., Jon S. > Stenerson & Kelly Curran) > Introduction to Management Science and Student CD Package (8th Ed., > Bernard W. Taylor) > Introduction to Management Science with Student CD (9th Ed., Bernard > W. Taylor) > Operations Research: An Introduction (8th Ed., Taha) > Decision Support Systems and Intelligent Systems (7th Ed., Turban, > Aronson, Ting-Peng Liang) > Decision Support and Business Intelligence Systems (8th Ed., Turban, > Aronson, Ting-Peng Liang & Sharda) > Operations Management and Student CD Package (7th Ed., Krajewski, > Ritzman) > Operations Management: Process and Value Chains (8th Ed., Krajewski, > Ritzman & Malhotra) > Operations Management (8th Ed., Jay Heizer & Render) > Introduction to Operations and Supply Chain Management with Advanced > Decision Support Tools (Cecil Bozarth) > Managing Business Process Flows: Principles of Operations Management > (2nd Ed., Anupind, Chopra, Deshmukh, et al) > Operations Management & Student CD Package (8th Ed., Heizer & Render) > Principles Of Operations Management and Student CD (6th Ed., Heizer & > Render) > Foundations of Operations Management (Ritzman & Krajewski) > Decision Modeling with Microsoft¬ Excel (6th Ed., Moore & Weatherford) > Managing Quality: Integrating The Supply Chain (3rd Ed., S. Thomas > Foster) > Six Sigma: Basic Tools and Techniques (Donna C.S. Summers) > First Course in Quality Engineering (KS Krishnamoorthi) > Statistical Quality Design and Control (2nd Ed., DeVor, Chang & > Sutherland) > Economics: A Tool for Critically Understanding Society (7th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Economics: A Tool for Critically Understanding Society (8th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Introduction to Economic Reasoning (6th Ed., William D. Rohlf, Jr.) > Introduction to Economic Reasoning (7th Ed., William D. Rohlf, Jr.) > Essential Foundations of Economics (3rd Ed., Robin Bade & Michael > Parkin) > Understanding Modern Economics (Roger LeRoy Miller) > The Economics of Macro Issues (3rd Ed., Roger LeRoy Miller & Daniel K. > Benjamin) > Foundations of Economics (3rd Ed., Robin Bade & Michael Parkin) > Economics Today (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (14th Ed., Roger LeRoy Miller) > Economics (Michael A. Leeds, Peter von Allmen & Richard C. Schiming) > Economics: Private Markets and Public Choice (7th Ed., Robert B. > Ekelund, Jr., Rand W. Ressler & Robert D. Tollison) > Principles of Economics, 7th Ed. (Roy J. Ruffin & Paul R. Gregory) > The Economics of Public Issues (14th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > The Economics of Public Issues (15th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > Macroeconomics (7th Ed., Michael Parkin) > Macroeconomics (8th Ed., Michael Parkin) > Foundations of Microeconomics (3rd Ed., Robin Bade & Michael Parkin) > Foundations of Macroeconomics (3rd Ed., Robin Bade & Michael Parkin) > Microeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Macroeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Economics Today: The Micro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Micro View (14th Ed., Roger LeRoy Miller) > Microeconomics (7th Ed., Michael Parkin) > Microeconomics (8th Ed., Michael Parkin) > Macroeconomics (2nd Ed., Stephen D. Williamson) > Macroeconomics (3rd Ed., Stephen D. Williamson) > Macroeconomics Update Edition (5th Ed., Andrew B. Abel, Ben S. > Bernanke) > Macroeconomics (6th Ed., Andrew B. Abel, Ben S. Bernanke & Dean > Croushore) > Macroeconomics (10th Ed., Robert J. Gordon) > Economic Growth (David N. Weil) > Money, the Financial System, and the Economy (5th Ed., R. Glenn > Hubbard) > Money, the Financial System, and the Economy (6th Ed., R. Glenn > Hubbard) > The Economics of Money, Banking and Financial Markets (8th Ed., > Frederic S. Mishkin) > Principles of Money, Banking, and Financial Markets (11th Ed., > Lawrence S. Ritter, William L. Silber & Gregory F. Udell) > International Economics (3rd Ed., James Gerber) > International Economics (4th Ed., James Gerber) > International Economics (7th Ed., Steven Husted & Michael Melvin) > World Trade and Payments: An Introduction (9th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > World Trade and Payments: An Introduction (10th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > International Economics: Theory and Policy (7th Ed., Paul R. Krugman & > Maurice Obstfeld) > International Money and Finance (7th Ed., Michael Melvin) > Economic Development (9th Ed., Michael P. Todaro & Stephen C. Smith) > Microeconomics (4th Ed., Jeffrey M. Perloff) > Microeconomics (Don E. Waldman) > Microeconomics: Theory and Applications with Calculus (Jeffrey M. > Perloff) > Environmental Economics and Policy (5th Ed., Tom Tietenberg) > Environmental and Natural Resource Economics (7th Ed., Tom Tietenberg) > Health Economics (3rd Ed., Charles E. Phelps) > & Elizabeth J. Jensen) > Modern Industrial Organization (4th Ed., Dennis W. Carlton & Jeffrey > M. Perloff) > Modern Labor Economics: Theory and Public Policy (9th Ed., Ronald G. > Ehrenberg & Robert S. Smith) > Law and Economics (4th Ed., Robert Cooter & Thomas Ulen) > Law and Economics (5th Ed., Robert Cooter & Thomas Ulen) > Market Regulation (Roger Sherman) > Public Finance and the American Economy (2nd Ed., Neil Bruce) > The Economics of Sports (2nd Ed., Michael A. Leeds & Peter von Allmen) > The Economics of Sports (3rd Ed., Michael A. Leeds & Peter von Allmen) > Introduction to Econometrics, Brief Edition (James H. Stock & Mark W. > Watson) > Introduction to Econometrics (2nd ed., James H. Stock & Mark W. > Watson) > Econometrics: A Modern Introduction (Michael P. Murray) > Using Econometrics: A Practical Guide (5th Ed., A.H. Studenmund) > Mathematical Methods for Economics (2nd Ed., Michael Klein) > Personal Finance with Financial Planning Software (3rd Ed., Jeff > Madura) > Finance: Investments, Institutions, and Management - Update (2nd Ed., > Stanley G. Eakins) > Introduction to Finance (Lawrence J. Gitman & Jeff Madura) > Principles of Managerial Finance Brief plus MyFinanceLab Student > Access Kit (4th Ed., Lawrence J. Gitman) > Principles of Managerial Finance plus MyFinanceLab Student Access Kit > (11th Ed., Lawrence J. Gitman) > Corporate Finance plus MyFinanceLab Student Access Kit (Jonathan Berk > & Peter DeMarzo) > Risk Takers: Uses and Abuses of Financial Derivatives (John > Marthinsen) > Theory of Asset Pricing (George Pennacchi) > Multinational Business Finance (11th Ed., David K. Eiteman, Arthur I. > Stonehill & Michael H. Moffett) > Fundamentals of Multinational Finance (2nd Ed., Michael H. Moffett, > Arthur I. Stonehill & David K. Eiteman) > Cases in International Finance (2nd Ed., Gunter Dufey & Ian H. Giddy) > Fundamentals of Investing plus MyFinanceLab Student Access Kit and > OTIS Student Access Kit (10th Ed., Lawrence J. Gitman & Michael D. > Joehnk) > Fundamentals of Investing & Wharton's OTIS Student Access Kit Package > (9th Ed., Lawrence J. Gitman & Michael D. Joehnk) > OTIS: Online Trading and Investment Simulator Student Access Kit > (Wharton Learning Lab) > Derivatives Markets (2nd Ed., Robert L. McDonald) > Principles of Risk Management and Insurance (9th Ed., George E. Rejda) > Principles of Risk Management and Insurance (10th Ed., George E. > Rejda) > Financial Markets and Institutions (5th Ed., Frederic S. Mishkin & > Stanley G. Eakins) > Statistical Analysis of Financial Data in S-PLUS (Rene A. Carmona) > Statistics and Finance: An Introduction (David Ruppert) > Mathematical Statistics for Economics and Business (Ron C. > Mittelhammer) - Materials Engineering : > > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials Science and Engineering: An Introduction (6th Ed., William > D. Callister, Jr.) > Materials Science and Engineering: An Introduction (7th Ed., William > D. Callister, Jr.) > Fundamentals of Materials Science and Engineering : Integrated > Approach (2nd Ed., William D. Callister, Jr.) > Science and Design of Engineering Materials (2nd Ed., Schaffer, > Saxena, et al) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Foundations of Materials Science and Engineering (3rd Ed, Smith) > Foundations of Materials Science and Engineering (4th Ed, Smith) > Plastics: Materials and Processing (3rd Ed., Strong) > Engineering Materials: Properties and Selection (8th Ed., Budinski) > Introduction to Materials Science for Engineers (6th Ed., Shackelford) > Materials: Engineering, Science, Processing and Design (Michael Ashby, > Dr Hugh Shercliff & David Cebon) > Principles of Corrosion Engineering and Corrosion Control (Zaki Ahmad) > Analysis and Performance of Fiber Composites (3rd Ed., Bhagwan > Agarwal, Lawrence Broutman & K. Chandrashekhara) > Basic Engineering Plasticity: An Introduction with Engineering and > Manufacturing Applications (David Rees) > Steels: Microstructure and Properties (3rd Ed. Bhadeshia & Honeycombe) > Theory of Plasticity (3rd Ed. Jagabanduhu Chakrabarty) > Engineering Materials Vol. 1 : An Introduction to Properties, > Applications and Design (3rd Ed., Michael Ashby & David R H Jones) > Engineering Materials Vol. 2 : An Introduction to Microstructures, > Processing and Design (3rd Ed., Michael Ashby & David R H Jones) > Plastics: Microstructure and Engineering Applications (3rd Ed., Nigel > Mills) > Laser Processing of Engineering Materials : Principles, Procedure and > Industrial Application (John Ion) > Sintering : Densification, Grain Growth and Microstructure (Suk-Joong > Kang) > Biomaterials Science : An Introduction to Materials in Medicine (2nd > Ed., Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Laminar Composites (by George Staab) + original Ebook > contact me to : newbergh123@yahoo.com > Water Treatment: Principles and Design, 2nd Edition for me. thank you very much! liew168@sina.com > === Subject: Re: List of solutions manual (thousands) posting-account=U0LgTAoAAACT3plNs1Bj32A1VT9Tz6dl 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; InfoPath.2),gzip(gfe),gzip(gfe) > My List of Solutions Manual > contact me to : newbergh...@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. This list (not links) is available from : http://rapidshare.com/files/59002351/List of solutions manual.txt - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files ... read more > I Am in possesion of the following Solution Manuals and will give them for free!!!!!!!!!!!!!!!!!!!!!! just email me at mickeydizzle@gmail.com -Engineering Mechanics Statics 10th & 11th by Hibbeler -Engineering Mechanics Dynamics 11th by Hibbeler -Engineering Mechanics Dynamics 4th Bedford === Subject: mike lalonde posting-account=3isBZgoAAADJM-2G3Oc0CRLy9Sk4yeg_ 5.0),gzip(gfe),gzip(gfe) 42434 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle bacini sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde 4 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde michael lalonde mike lalonde temagami henry merchant tammy dubriel gerry dubriel victor dubriel yvan tonge yvan steve tonge 3 === Subject: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=nsrQxAoAAACDkV1_uYvq7QQjzxtFXYoo Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Do you have this one available? How can I get it? Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton please email me if you have it. I only need solution for ch 9 to 13 I have the rest if you're interested let me know student482@gmail.com alt.history.british, alt.guitar.amps === Subject: See the accepted papers, keynote lecture, plenary lectures, the contents of the Book of the Proceedings (i.e. accepted papers). WSEAS Post-Conference Report for the Conferences MACMESE '07 and DNCOCO '07 (124 images) posting-account=KWYMKQoAAAArfstGv6VUH6u1SaWpz4Xi 5.1),gzip(gfe),gzip(gfe) Click on the link below and see the accepted papers, the keynote and Plenary Speeches, the contents of the Book of the Proceedings as well as nice photos from an MACMESE '07 and DNCOCO '07 excellent conferences in Trinidad and Tobago Islands , co-organized by the University of West Indies and WSEAS ------------------------------------- http://www.wseas.com/wseas/reports/trinidadandtobago/index.html Post-Conference Report for the WSEAS Conferences: MACMESE '07 and DNCOCO '07 Trinidad and Tobago Islands (Caribbean Sea), November 5-7, 2007 http://www.wseas.com/wseas/reports/trinidadandtobago/index.html * This report contains 124 images copyrighted by the WSEAS. All rights reserved. * If you need some image with high resolution please click on the images below * If you need some image with extremely high resolution, contact us by email The University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences, Department of Mathematics and Computer Science, St. Augustine, Trinidad (W. I.) http://www.wseas.com/wseas/reports/trinidadandtobago/index.html and the WSEAS Society (http://www.wseas.org) , coorganized the following two parallel conferences: * 9th WSEAS Int. Conf. on MATHEMATICAL and COMPUTATIONAL METHODS in SCIENCE and ENGINEERING (MACMESE'07) (This conference was part of the MMACTEE international conference until 2006) * 6th WSEAS Int. Conf. on DATA NETWORKS, COMMUNICATIONS, COMPUTERS (DNCOCO '07), (The name of this conference was ISCOCO until 2005) OPENING, KEYNOTE, PLENARY SPEECHES: The two parallel Conferences were opened by Professor Bal Bhatt, who is director of the Department of Mathematics and Computer Science of the University of West Indies and he was the chairman of the conference and Professor Winston Mellowes, who is the Chairman, Professor Dyer Narinesingth, who is the Dean of the University of West Indies, the Campus Principal Professor Bridget Brereton, Mr. John Roopchan of the Ministry of Education and Dr. Bhoendradatt Tewarie, Director of the Institute of Critical Thinking, where the conference was held. After the opening ceremony the first keynote speaker was Professor Biswa N. Datta (Distinguished Research Professor at the Northern Illinois University, USA), who has presented the recent advances on computational methods for active vibration control and model updating in vibrating structures. Professor Eyad H. Abed (Institute for Systems Research, Electrical and Computer Engineering, University of Maryland, USA) who was PLENARY SPEAKER also presented new results on selective modal analysis of dynamic systems On Tuesday, 6th November 2007 (2nd day of the conference), Professor Imre J. Rudas (Institute of Intelligent Engineering Systems John von Neumann Faculty of Informatics Budapest Tech, Budapest, Hungary) who was PLENARY SPEAKER also described interesting aggregation procedures in intelligent systems. http://www.wseas.com/wseas/reports/trinidadandtobago/index.html On Tuesday evening was the cocktail party for all participants of the WSEAS Conference, who were invited at the office of the Campus Principal Professor Bridget Brereton (See pictures below) Both of the WSEAS Conferences in Trinidad were characterized by their friendly atmosphere (see photos below) as well as the high quality of the presentations and discussions. A variety of topics constituted the focus of paper submissions. In regular sessions papers addressed several interesting topics. Prominent lectures provided key-note and plenary speeches for the conference. Moreover, special sessions were organized, and invited lectures were given by well-known researchers. With pride, the WSEAS received the following Important Contributions and upgraded them as Keynote and Plenary Lectures.: KEYNOTE LECTURE: Recent Advances on Computational Methods for Active Vibration Control and Model Updating in Vibrating Structures : Linking Control to Industry by Prof. Biswa N. Datta, Northern Illinois University, USA. PLENARY LECTURE 1: New Results on Selective Modal Analysis of Dynamic Systems by Prof. Eyad H. Abed, University of Maryland, Maryland, USA. PLENARY LECTURE 2: Polynomial Optimization via Sums of Squares Relaxations by Prof. Mihai Putinar, University of California at Santa Barbara, CA, USA. PLENARY LECTURE 3: Aggregation procedures in intelligent systems by Prof. Imre J. Rudas, Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Hungary. PLENARY LECTURE 4: Selection Problems and Multi-criteria Decision Making by Dr. Alexey L Sadovski, Texas A&M University-Corpus Christi, USA. BENEFITS FOR THE PARTCIPANTS: WSEAS, http://www.wseas.org gave a very strong and important tool to all the participants: A new username and password without expiry date for on-line access in the WSEAS Conference proceedings FOR EVER. Conference Statistics Submitted papers: 335 Accepted papers: 147 acceptance ratio = (Number of accepted papers / Number of Submitted)*100 = 43.88% Remark: Two withdrawn accepted papers are considered as accepted papers in our Statistics. .: REVIEW PROCESS: Each paper was reviewed at least by 3 independent reviewers. The WSEAS Secretariat sent each paper to 5 reviewers. Some papers received reviews from 5 different referees. The WSEAS Secretariat forwarded these comments by personalized emails to the responsible for the correspondence author. The full list of the reviewers will be available in the web page: http://www.worldses.org/reviewers.htm The additional features of these 2 conferences 1) Publication of the Proceedings in 3 media: hard-copy, CD, E-Library (A) One Book in the Electrical and Computer Engineering Series and Energy and Environmental Engineering Series of WSEAS (see details, contents, author indices and editors below) with ISBN and ISSN indexed by the major Citation Indices (ISI ranked): www.worldses.org/indexes (B) CD-ROM Proceedings with pages' numbers with ISBN and ISSN indexed by the major Citation Indexes: www.worldses.org/indexes (C) E-Library: http://www.wseas.org/online and possible, for a very small number of papers: (D) JOURNAL PUBLICATION: Expanded and enhanced versions of papers published in the conference proceedings also going to be considered for possible publication in one of the WSEAS journals that participate in the major International Scientific Indices (Elsevier, Scopus, EI, Compendex, INSPEC, CSA .... see: www.worldses.org/indexes ). 2) WSEAS gave a very strong and important tool to all the participants: A new username and password without expiry date for on- line access in the WSEAS Conference proceedings FOR EVER. 3) The Participants received 6 very rich coffee-breaks (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences), 1 Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences) and 1 Gala Dinner with the high quality of the WSEAS 4) Cultural and social part as usual in WSEAS events. 5) The conference Books (Hard-Copy Proceedings), CD-ROM proceedings and Journals (with selected papers) published by WSEAS Press continue to sell for a long time after the meeting has taken place. This is another demonstration of the prestige the scientific community attribute to the meetings organized by the WSEAS. .: BOOK (hard-copy of the Proceedings): Editors: Balswaroop Bhatt (Trinidad and Tobago), Bhoendradatt Tewarie (Trinidad and Tobago), Athina Lazakidou (Greece), Konstantinos Siasiakos (Greece). Pages : 506, price: 80 EUR [Contents], [Order], [Full PDF of the Papers], [Help] .: JOURNALS: .: What is the Permanent Procedure for additional Journal publication for a very small number of High-Quality Papers presented in the WSEAS Conferences in China (after the recommendation of Chairmen). So, the authors with accepted & presented papers received the following e- mail: We have started now the procedure for the evaluation of the extended versions of your papers for possible inclusion in the WSEAS journals after new rounds of review. INTRODUCTION: You know that our goal is to maintain very strong international journals, to increase the impact of our beloved WSEAS Transactions, really top journals as they really are. To this end, we need only high quality papers, breakthrough works of archival value, i.e. papers that are well written from any point of view, completed studies (with their numerical examples or experiments that must be compared with the previous results in the literature), excellent english language and of course correct WSEAS format. The papers also must be substantially extended version of the paper that was presented in the conference (with more than 40% new material). We need papers that will attract the attention of other scholars citing them increasing our impact. In the next few years, the WSEAS transactions must be in every academic library, in every corner of the earth. To this end, we need your high quality contribution. HOW TO PROCEED: a) Check very carefully if your idea is really important, breakthrough in your field and can appear in a Journal of the quality and the level of the WSEAS Transactions. If you doubt, do not send it so easily. Your paper must not be only a good idea. It must be a complete study with theoretical background, complete bibliographical references; without grammatical and syntactical errors. For theoretical works: full comparison with previous published papers is necessary. We need numerical examples, applicability of the method, originality, novelty and directions for future research. For experimental or computational works: full comparison with previous published papers is necessary. We need real experiments with the necessary documentation, while for computational work, we need full benchmarks. Of course along discussions for the applicability of the method, originality, novelty and directions for future research. b) Complete the extended version of your paper until December 31, 2007 and upload it via http://............... (the full web address was given only to authors that presented a paper) until December 31, 2007 c) If your extended version fulfills the paragraph a), then our Editors will send it to 3 independent Reviewers outside your country. If not, our Editors are entitled to reject it from this early stage informing you properly. The positive answer of the 3 reviewers is necessary (attention: 2 yes and 1 no implies NO, i.e. rejection). d) Our Editors will collect the reviewers' remarks and will send them again to you for acceptance/ acceptance after minor revision / acceptance after major revision / rejection e) Possibly new rounds of review will be needed. f) No additional fee is needed in case of acceptance. After all this procedure, the accepted papers that come from WSEAS Conferences in Canada will be published in the various WSEAS Transactions. IF you miss the deadline of December 31, 2007 , or if your paper was not presented in the WSEAS Conferences, THEN: you can upload it quite independently as regular paper from the WSEAS Site for the Journals: http://www.worldses.org/journals/index.html The final list of the papers must have the approval of our Editors and 3 Reviewers, and of course the Editor-in-Chief of the particular Journal. We want only authors that presented their papers to complete this web form: http://............... (the full web address was given only to authors that presented a paper) So, in this form you will need a password (the password was given only to the authors that presented a paper). .: BEST STUDENT PAPERS: The Organizing Committee received the forms that the Session Chairmen filled in after the end of their Sessions and after additional evaluation and discussion decided the following. The Criteria were: a) Originality and scientific impact b) Good presentation c) Paper presented by a student The results of this evaluation will be announced soon in the web page: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html .: INDICES: PROCEEDINGS: The Proceedings related to the Conference are covered by: 1. ISI (ISINET) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 6. ULRICH 9. Directory of Published Proceedings 10. Computer Science Bibliography Administrator 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Engineering Information 15. SCOPUS 16. EBSCO 17. EMBASE 18. Compendex (CPX) 19. GEOBASE 20. BIOBASE 21. BIOTECHNOBASE 22. FLUIDEX 23. OceanBase 24. BEILSTEIN Abstracts 25. World Textiles 26. MEDLINE 27. British Library 28. National Library of Greece 29. German National Library of Science and Technology 30. IARAS Index JOURNALS: The WSEAS journals are covered by: 1. ISI through the INSPEC (IEE) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 7. ULRICH 9. Computer Science Bibliography Administrator 10. British Library 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Swets Information Services 15. Engineering Information 16. SCOPUS 17. EBSCO 18. EMBASE 19. Compendex (CPX) 20. Geobase 21. BIOBASE 22. BIOTECHNOBASE 23. FLUIDEX 24. OceanBase 25. BEILSTEIN Abstracts 26. World Textiles 27. MEDLINE 28. Mayersche 29. Index of Information Systems Journals 30. National Library of Greece 31. IARAS Index .: SOCIAL PART (Coffee-Breaks, Banquet, Excursions) 6 very rich coffee-breaks with Coffee, Tea, Milk, Sweets, Cakes, Pastries, Juices and Sandwiches (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Excellent Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Gala Dinner. Participants enjoyed a wonderful night. .: Some Excursions took place after the conference. See the pictures: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html === Subject: Re: Regarding solution manual for Introduction to Algorithm. Thomas H. Cormen. posting-account=T7fhkAoAAADh6aLufWf8lNSXnUk_5MhJ CLR 1.1.4322),gzip(gfe),gzip(gfe) Did you find the soultions manual? If you do, could you please send it to me. I would appreciate it a lot! === Subject: I need Solution manual posting-account=2Ao9ggkAAAB1JcOMWiDDOjkHclbisJtt Gecko/20061010 Firefox/2.0,gzip(gfe),gzip(gfe) (squid/2.5.STABLE9) I am studying Engineering Electromagnetics. In the Course Some problem I am encountering. I need a Solution Manual of ENGINEERING ELECTROMAGNETICS (7/E) BY HAYT AND BUCK mail this solution of masaddique_159@yahoo.com THIANK YOU === Subject: Re: I need Solution manual Bye! === Subject: Much Help Needed on Difficult Calculus Problems Can anyone offer me any advice on how to work and answer any of the following questions? 1) Find the limit of the sequence x = n square root of n! as n tends to ¡. 2) Determine whether the series ¡ á (n!)^(-1/n) is convergent or divergent. n=1 3) Find the sum of the series ¡ á (1/2^n) tan (x/2^n) for every value of x. n=1 -Drew === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. That's as n tends to infinity. Or you could say informally that n becomes infinite. The problem as stated is pretty trivial since n sqrt(n!) > n for n > 1. --Lynn === Subject: Re: Much Help Needed on Difficult Calculus Problems in alt.math.undergrad: > Can anyone offer me any advice on how to work and answer > any of the following questions? > 1) Find the limit of the sequence x = n square root of n! > as n tends to ¡. Is there a typo in this one? > 2) Determine whether the series > ¡ > á (n!)^(-1/n) is convergent or divergent. > n=1 The denominator of the n-th term is the geometric mean of 1, 2, ..., n. Use the arithmetic mean - geometric mean inequality to compare with a familiar series. [...] Brian === Subject: helpppp pleasee!! whats is the antiderivative of 4x^-1 ?? === Subject: Re: helpppp pleasee!! in alt.math.undergrad: > whats is the antiderivative of 4x^-1 ?? The derivative of ln(x) with respect to x is 1/x, so the derivative of 4 ln(x) is 4/x. Brian === Subject: helpppp mee pleasee i need help using the substitution process to find... the antiderivative of r(radical r^2+2) dr help pleaseee === Subject: Re: helpppp mee pleasee >i need help using the substitution process to find... >the antiderivative of r(radical r^2+2) dr >help pleaseee If that's r sqrt(r^2 + 2) dr u = r^2 + 2 du = 2 r dr, so 1/2 du = r dr Antiderivative of 1/2 sqrt(u) du = 1/2 u^(1/2) du = ? === Subject: sub.. substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this === Subject: Re: sub.. >substitution process to find antiderivative of r(e^-r^2) dr >pleaseee help me with this Your turn. What do you think? === Subject: Re: sub.. > substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this Your turn. What do you think? > think. That appears to be the entire difficulty. === Subject: help with substitution i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee === Subject: Re: help with substitution ok, but my answer has to have a +c in it i think === Subject: Re: help with substitution >i need help using the substitution process to find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. === Subject: Re: help with substitution i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to > learn how to use complicated rules like mathematics has and consequently > consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar lessons? Dave === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar > lessons? Especially *wrong* ones. in rebellion to?? Wonton to flout?? His math is wrong (or wong), too. sqrt -1 doesn't mean anything: sqrt is a function, and one can't subtract a numberfrom it. Maybe he means sqrt(-1). -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com> i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. Yet alas you're not the OP to call me on that. do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar > lessons? > I offer full service help. Why can't they learn English? Do they have a learning disability? Math has even more rules and they're harder rules. What help can be given to those who detest rules? ---- === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. > Yet alas you're not the OP to call me on that. > > do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar lessons? > I offer full service help. > Why can't they learn English? > Do they have a learning disability? > Math has even more rules and they're harder rules. > What help can be given to those who detest rules? ---- Not all OP's are speaking english by nature, have pity with them. -- Vooruit mensen, achteruit! (Elimineer x voor een e-mail) Hou-du. === Subject: Re: help with substitution > >i need help using the substitution process to > find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you > haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always > s capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > consider you unable to > learn how to use complicated rules like mathematics > has and consequently > consider it meaningless to help you. === Subject: [] help with substitution <25173561.1197114231915.JavaMail.jakarta@nitrogen.mathforum.org> help pleaseee I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always s capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > Help. I'm needing help substituting 'eggroll' with a word that coheres your sentence. consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. > === Subject: substitution????? substtution to find antiderivative of (5e^(-3g)) dg === Subject: Re: substitution????? >substtution to find antiderivative of (5e^(-3g)) dg u = -3 g du = -3 dg, so dg = ? === Subject: hellppp me out use the substitution to find the indefinite integral antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please === Subject: Re: hellppp me out <1432039.1197079325702.JavaMail.jakarta@nitrogen.mathforum.org>, The best help we can offer is to advise you to pay more attention in class, and read the assigned sections of the text. === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please cant be done, your hosed! (try dividing first) === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt > > helppp me please >cant be done, your hosed! (try dividing first) > A joke of some sort? === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please If you are going to post all your homework questions, why not group them together in one post so we can keep straight which homework we are doing for you? --Lynn === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please Hint: the derivative of t^3 + 6 t + 3 is 3 t^2 + 6 = 3 (t^2 + 2) === Subject: sorry i just dont get the substitution and... i dont get the substitution process.. can somebody xplain it to me, for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for === Subject: Re: sorry i just dont get the substitution and... >i dont get the substitution process.. can somebody xplain it to me, >for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for The basic idea is that you want to put the given expession in one of the forms that you know an antiderivative for, such as Int u^a du = u^(a+1) / (a + 1) + C for all a except a = -1 Int e^u du = e^u + C So let's look at 6x^2 dx / (2 x^3 + 7)^(3/2) You see that there's an x^3 in the denominator, and an x^2 in the numerator. That's promising, because if we substitute for the x^3 in the denominator, the derivative of x^3 is 2x^2 and so we may have something easy to substitute in the numerator as well (including the dx of course). Looking more closely, we see that we have 2 x^3, whose derivative is 6 x^2. Now that's VERY good, because that's exactly what's in the numerator. So, say we try u = 2 x^3 du = 6 x^2 dx Our expression becomes du / (u + 7)^(3/2) But wait! Now we realize that if we had made the substitution u = 2 x^3 + 7, then du still equals 6 x^2 dx and the resulting expression is even simpler, namely du / u^(3/2) Now *that* is an expression we know an antiderivative for! So, let's do the problem from the beginning. Find an antiderivative for 6x^2 dx / (2 x^3 + 7)^(3/2) Let u = 2 x^3 + 7 Then du = 6 x^2 dx Substituting into the original expression gives du / u^(3/2) = u^(-3/2) du for which an antiderivative is u^(-3/2 + 1) / (-3/2 + 1) = u^(-1/2) / (-1/2) = -2 u^(-1/2) = -2 / u^(1/2) = -2 / sqrt(u) Now, we want to get the answer back in terms of x, so we substitute for u [remember, u = 2 x^3 + 7] and get -2 / (2 x^3 + 7)^(1/2) or -2 / sqrt(2 x^3 + 7) Putting the problem in the form of an indefinite integral, we can now write Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / (2 x^3 + 7)^(1/2) + C or Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / sqrt(2 x^3 + 7) + C The C is the so-called 'constant of integration', which I assume has been discussed in conjunction with antiderivatives and indefinite integrals. === Subject: Complicated Differential Equation Sorry all I made a mistake in the first differential equation post. The equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, and V are all known constants. Is there any way to approximate this expression for i(t)? In my original post the expression didn't have the last term so some suggested using the Lambert W-Function, and another suggested using Newton's method. Would I still be able to use these methods, and if so how would I use them? === Subject: Re: Complicated Differential Equation <30569604.1197093354146.JavaMail.jakarta@nitrogen.mathforum.org>, > Sorry all I made a mistake in the first differential equation post. The > equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, > and V are all known constants. Is there any way to approximate this > expression for i(t)? In my original post the expression didn't have the last > term so some suggested using the Lambert W-Function, and another suggested > using Newton's method. Would I still be able to use these methods, and if so > how would I use them? V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2 gives i(t)/[V-b*i(t)-c*i(t)^2]*i'(t) = 1/a Now use partial fractions to split up i(t)/[V-b*i(t)-c*i(t)^2] At which point integration is possible, and one can solve for i(t). === Subject: =?windows-1256?B?Ljo6IFsgwt7c5uwgyNHk3MfjzCDt3tzm4yDIytPR?= =?windows-1256?B?7dogzOXH0t/cIMjU39zhIOPHysrV3ObRIObH4ePdx8w=?= =?windows-1256?B?3Mfl3CDH5OUg38fj3OEgXSA6Oi4=?= posting-account=OEMLPAoAAAD96Le1WgD9Upxh2I266gSV SIMBAR={94AA8A13-642B-404A-B4A4-C4EFD1151A5B}; Alexa Toolbar),gzip(gfe),gzip(gfe) === Subject: read plz posting-account=Yt8G1goAAACz_ktFECg3NbvAf5VVNJ0C Gecko/2007080210 GranParadiso/3.0a7,gzip(gfe),gzip(gfe) donot mail at hotkid_1@hotmail.com for solution manuals i donot have any === Subject: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, or just write a bit about the topic, it would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics (Well, you would probably still need logic...). === Subject: Re: Foundations of Mathematics, help? > mathematics, what I mean by that is the things that > define mathematics, and which it is based on. Much in > the same was that mathematics defines much of physics > (I think...) I disagree very sharply with that, by the way. Physics is 'defined' by what we observe in experiments, not by mathematics! > Anyway, I am posting here because I don't have much > of an idea of where to start. If anyone could advise > there, or just write a bit about the topic, it would > be greatly appreciated. > Oh, and if there is anyone out there who wouldn't > mind me asking them some questions that will > undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and > formal logic, and I will. But it also occurred to me > that these cannot be the only ways to define the > basis of mathematics (Well, you would probably still > need logic...). === Subject: Re: Foundations of Mathematics, help? mathematics, what I mean by that is the things > that define mathematics, and which it is based on. Much > in the same was that mathematics defines much of > physics (I think...) > I disagree very sharply with that, by the way. > way. Physics is 'defined' by what we observe in > experiments, not by mathematics! > I figured someone would say something like that... And I agree mostly, but it helped express the idea I was trying to, so I used it :) Anyway, I am posting here because I don't have > much of an idea of where to start. If anyone could > advise there, or just write a bit about the topic, it > would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me > know. P.S. I have been told before to study set theory > and formal logic, and I will. But it also occurred to > me that these cannot be the only ways to define the basis of mathematics (Well, you would probably > still need logic...). > ics and got a lot of intersting hits. Have you tried > that? Yup... === Subject: Re: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, You could read Fraenkel, Bar-Hillel and Levy, _Foundations of Set Theory_ which covers more than its title suggests; and Feferman _The Number Systems_ the subtitle of which is _Foundations of Algebra and Analysis_. > or just write a bit about the topic, it would be greatly appreciated. > Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. sci.logic might be good for that. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics You could try Mac Lane _Categories for Working Mathematicians_ > (Well, you would probably still need logic...). -- How unlike the home life of our own dear Queen. === Subject: Re: Foundations of Mathematics, help? === Subject: hey guys posting-account=vz_6QQoAAABOxomOXgeWKt9p9p4FZ-ez SV1),gzip(gfe),gzip(gfe) people join this new group and make it an interactive place !! === Subject: solutions manuals posting-account=m06QOgkAAACFEdunwVichFUaRyeknXjQ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Can I get the manuals for: 1) Linear Algebra with Applications, Otto Bretscher,( Pearson Custom Publishing) 2) Fundamentals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Edward B. Saff, Arthur David Snider, (Pearson Custom Publishing) Are they the complete set? You can e-mail me at === Subject: implementation of simplex method in C language hi, I am looking for an implementation of simplex method in C language. === Subject: Re: implementation of simplex method in C language : > I am looking for an implementation of simplex method in C language. Just by any wild chance, could this be a homework assignment? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: implementation of simplex method in C language >hi, >I am looking for an implementation of simplex method in >C language. http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html === Subject: Re: implementation of simplex method in C language posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > hi, > I am looking for an implementation of simplex method in C language. Why C? What difference does the language make? Or have you been asked to implement it yourself in C as part of an assignment???? I can suggest a number of commercially available LP packages. What are you willing to pay? === Subject: Water Treatment: Principles and Design, 2nd Edition posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) Can you send me Water Treatment: Principles and Design, 2nd Edition thank you very much liew168@sina.com === Subject: Re: Water Treatment: Principles and Design, 2nd Edition Can you send me Water Treatment: Principles and Design, 2nd Edition > thank you very much The answer is of course no. (If someone reading your post has the book and wishes to give it away, they would not know how to get it to you.) May I ask you a question? Why don't you go to a book shop and buy it like any normal person? (If you do so, do remember to mention the author and publisher.) -- How unlike the home life of our own dear Queen. === Subject: Re: List of solutions manual (thousands) posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) BERGH .8eæ.93.b9.81F > My List of Solutions Manual > contact me to : newbergh123@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. > This list (not links) is available from : > http://rapidshare.com/files/59002351/List of solutions manual.txt > > - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files > converted to pdf, real instructor sol. manual > Principles of Statics (10th Ed., Hibbeler) > Engineering Mechanics : Dynamics (11th Ed., Hibbeler)-Not mathcad > files converted to pdf, real instructor sol. manual > Principles of Dynamics (10th Ed., Hibbeler) > Mechanics of Materials (4th Ed, Hibbeler) > Mechanics of Materials (6th Ed, Hibbeler) > Mechanics of Materials (7th Ed, Hibbeler) > Statics and Mechanics of Materials (2nd Ed., Hibbeler) > Energy Principles and Variational Methods in Applied Mechanics (2nd > Ed., Reddy) > Theory of Vibrations with Applications (5th Ed., Thomson & Dahleh) > Engineering Vibrations (2nd Ed., Inman) > Engineering Vibrations (3rd Ed., Inman) > Theory of Vibration: An Introduction (2nd Ed., A.A. Shabana) > Vibration of Discrete and Continuous Systems (2nd Ed., Ahmed Shabana) > Introduction to Finite Element Vibration Analysis (Maurice Petyt) > Vibrations and Stability: Advanced Theory, Analysis, and Tools (2nd > Ed., Jon J. Thomsen) > Mechanical Vibrations (4th Ed., Rao) > Mechanical Vibration (William J. Palm, III) > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Finite Element Analysis Theory and Application with ANSYS (2nd Ed., > Moaveni) > Finite Element Analysis Theory and Application with ANSYS (3rd Ed., > Moaveni) > The Finite Element Method and Applications in Engineering Using ANSYS > (Madenci & Guven) + original Ebook > Modeling and Analysis of Dynamic Systems (3rd Ed, Close, Frederick & > Newell) > System Dynamics (1st Ed., William J Palm III) > System Dynamics: Modeling and Simulation of Mechatronic Systems (4th > Ed., Karnopp, Margolis & Rosenberg) > Concepts and Applications of Finite Element Analysis (4th Ed., Cook, > Malkus, Plesha & Witt) > Finite Element Modeling for Stress Analysis (Robert Cook) > Advanced Strength and Applied Elasticity (4th Ed., Ugural) > Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) + > original Ebook > Fracture Mechanics (2nd Ed., Anderson) > Mechanical Behavior of Materials (2nd Ed. Dowling) > Mechanical Behavior of Materials (3rd Ed. Dowling) > Mechanical Behavior of Materials (W.F. Hosford) + original Ebook > Mechanical Behavior of Materials (Keith Bowman) > Theory and Design for Mechanical Measurements (4th Ed, Figliola & > Beasley) > Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Principles of Metal Manufacturing Processes (Beddoes & Bibby) > Materials Selection in Mechanical Design (3rd Ed., Michael Ashby) > Introduction to Manufacturing Processes (3rd Ed., Schey) > Manufacturing Processes for Engineering Materials (5th Ed. Kalpakjian > & Smith) > Manufacturing, Engineering & Technology (4th Ed. Kalpakjian & Smith) > Manufacturing, Engineering & Technology (5th Ed. Kalpakjian & Smith) > Automation, Production Systems, and Computer-Integrated Manufacturing > (2nd Ed., Groover) > Introduction to Robotics: Mechanics and Control (3rd Ed, Craig) > Applied Manufacturing Process Planning: With Emphasis on Metal Forming > and Machining (Nelson, Schneider) > Linear State-Space Control Systems (Robert L. Williams, II & Douglas > A. Lawrence) > Rocket Propulsion Elements (7th Ed., George P. Sutton & Oscar Biblarz) > Mechanics of Flight (Warren F. Phillips) > Fundamentals of Airplane Flight Mechanics (David G. Hull) > Flight Performance of Fixed and Rotary Wing Aircraft (Antonio > Filippone) > Aircraft Structures for Engineering Students (3rd Ed., T.H.G. Megson) > + original ebook > Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson) > + original ebook > Mechanics of Aircraft Structures (2nd Ed, C. T. Sun) > Principles of Helicopter Aerodynamics (2nd Ed., Leishman) > Interactive Aerospace Engineering and Design (Dava Newman) > Fundamentals of Aerodynamics (3th Ed., Anderson) > Fundamentals of Aerodynamics (4th Ed., Anderson) > Introduction to Flight (5th Ed., Anderson) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Mechatronics (Sabri Cetinkunt) > Introduction to Mechatronics and Measurement Systems (3rd Ed., David > G. Alciatore & Michael B. Histand) > Introduction to Engineering Experimentation (2nd Ed., Wheeler & Ganji) > Gas Dynamics (3rd Ed., John & Keith) > Fundamentals of Gas Dynamics (2nd Ed, Robert D. Zucker) + original > Ebook > Internal Combustion Engines: Applied Thermosciences (2nd Ed., Ferguson > & Kirkpatrick) > Automotive Engines (8th Ed., Crouse) > Automotive Brake Systems Package (4th Ed., Rehkopf) > Automotive Engine Performance (2nd Ed., Halderman) > Automotive Mathematics (Jason C. Rouvel) > Blueprint Reading for the Machine Trades (6th Ed., Schultz & Smith) > Modern Welding Technology (6th Ed., Cary & Helzer) > Theory of Ground Vehicles (3rd Ed., J. Y. Wong) > Hydraulic Control Systems (Noah Manring) > Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. > Dixon) + original Ebook > Principles of Turbomachinery in Air-Breathing Engines (Baskharone) > Fundamentals of Jet Propulsion with Applications (Ronald D. Flack) > Fundamentals of Robotic Mechanical Systems: Theory, Methods, and > Algorithms (3rd Ed., Jorge Angeles) > Tissue Mechanics (Cowin, Doty) > BTEC First Engineering Curriculum Support Pack (Mike Tooley) > BTEC First Engineering (Mike Tooley) > Exploring Engineering: An Introduction for Freshmen to Engineering and > to the Design Process (Philip Kosky, George Wise, Robert Balmer & > William Keat) > Engineering Science (5th Ed., W. Bolton) > Fundamentals of Renewable Energy Processes (Aldo da Rosa) + original > Ebook > Renewable Energy (3rd Ed., SÀrensen or Sorensen) + original Ebook > Power Generation Technologies (Paul Breeze) + original Ebook > Concepts in Engineering (Holtzapple & Reece) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Autodesk Inventor (James M. Leake) > Foundations of Engineering (2nd Ed, Holtzapple & Dan Reece) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) - Electrical, Electronics & Computer Engineering > > Electrical Engineering: Principles and Applications (4th Ed., Allan R. > Hambley) > Electric Circuits (8th Ed., James W Nilsson & Susan Riedel) > Electric Circuits (7th Ed., James W Nilsson & Susan Riedel) > Introductory Circuits for Electrical and Computer Engineering (James > W. Nilsson, Susan A. Riedel) > Applied Electromagnetics: Early Transmission Lines Approach (Stuart M. > Wentworth) > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Introduction to Electric Circuits (6th Ed., Richard Dorf & James > Svoboda) > Introduction to Electric Circuits (7th Ed., Richard Dorf & James > Svoboda) > Modern Control Systems (11th Ed., Dorf) > System Dynamics (1st Ed., William J Palm III) > Electric Machines Analysis and Design Applying MatLab (Cathey) > Principles and Applications of Electrical Engineering (4th Ed, > Rizzoni) > Principles and Applications of Electrical Engineering (5th Ed, > Rizzoni) > Fundamentals of Electric Circuits (2nd Ed., Charles Alexander & > Matthew Sadiku) > Fundamentals of Electric Circuits (3rd Ed., Charles Alexander & > Matthew Sadiku) > Microelectronic Circuit Design (2nd Ed., Richard Jaeger & Travis > Blalock) > Microelectronic Circuit Design (3rd Ed., Richard Jaeger & Travis > Blalock) > Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with VHDL Design (2nd Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (1st Ed., Stephen > Brown & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (2nd Ed., Stephen > Brown & Zvonko Vranesic) > Continuous and Discrete Control Systems (Dorsey) > Design with Operational Amplifiers and Analog Integrated Circuits (3rd > Ed., Sergio Franco) > Engineering Circuit Analysis (6th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Circuit Analysis (7th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Electromagnetics (7th Ed., William H. Hayt & John A. Buck) > Principles of Electronic Materials and Devices (2nd Ed, Safa O. Kasap) > Principles of Electronic Materials and Devices (3rd Ed, Safa O. Kasap) > A First Lab in Circuits and Electronics (Yannis Tsividis) > Power Electronic Circuits (Issa Batarseh) > Power Electronics: Converters, Applications, and Design (3rd Ed., Ned > Mohan, Tore Undeland & William Robbins) > An Introduction to Digital and Analog Communications (2nd Ed., Simon > Haykin & Michael Moher) > Communication Systems (4th Ed., Simon Haykin) > Signals and Systems (2nd Ed., Simon Haykin & Barry Van Veen) > Programming in Haskell (Graham Hutton) > Logic in Computer Science: Modelling and Reasoning about Systems > (Michael Huth & Mark Ryan) > Introduction to Distributed Algorithms (2nd., Gerard Tel) > Information Theory, Inference and Learning Algorithms (David J. C. > MacKay) > Digital Systems Engineering (William J. Dally & John W. Poulton) > Concepts in Programming Languages (by John C. Mitchell) > Simulation Modeling and Analysis with Expertfit Software (4th Ed., > Averill Law) > Measurement Systems (5th Ed, Ernest Doebelin) > Wireless Communications (Andrea Goldsmith) > Testing of Digital Systems (N. K. Jha & S. Gupta) > Space-Time Coding (Hamid Jafarkhani) > Space-Time Block Coding for Wireless Communications (Erik G. Larsson & > Petre Stoica) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Radio-Frequency Electronics: Circuits and Applications (Jon B. Hagen) > Photonic Devices (Jia-ming Liu) > Networking Wireless Sensors (Bhaskar Krishnamachari) > Mobile Wireless Communications (Mischa Schwartz) > Introduction to Color Imaging Science (Hsien-Che Lee) > Fundamentals of Wireless Communication (David Tse & Pramod Viswanath) > Fundamentals of Modern VLSI Devices (Yuan Taur & Tak H. Ning) > Electronic and Optoelectronic Properties of Semiconductor Structures > (Jasprit Singh) > Digital Signal Processing System Analysis and Design (Paulo S. R. > Diniz) > An Introduction to Statistical Signal Processing (Robert M. Gray) > An Introduction to Radio Frequency Engineering (Christopher Coleman) > Algebraic Codes for Data Transmission (Richard E. Blahut) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Fundamentals of Semiconductor Fabrication (Gary S. May, Simon M. Sze) > Semiconductor Devices: Physics and Technology (2nd Ed, Simon M. Sze) > Electric Machinery (6th Ed., Fitzgerald) + Ebook > Electric Machinery Fundamentals (4th Ed., Chapman) > Electric Machinery and Power System Fundamentals (Chapman) > Local Area Networks (2nd Ed., Keiser) > Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka) > Introduction to Signals and Systems (Lindner) > Digital Signal Processing (3rd Ed., Mitra) > Semiconductor Physics and Devices (3rd Ed., Donald A. Neamen) > Design for Electrical and Computer Engineers (1st Ed., Ralph Ford & > Chris Coulston) > Fundamentals of Modeling and Analyzing Engineering Systems (Cha, > Rosenberg, Dym) > Principles of Linear Systems (Philip E. Sarachik) > Power Systems Harmonics: Fundamentals, Analysis and Filter Design > (George J. Wakileh) > Principles of Adaptive Filters and Self-learning Systems (Anthony > Zaknich) > Control of Robot Manipulators in Joint Space (R. Kelly, V. Santib.87.96ez, > A. Lor.92a) > Modelling and Control of Robot Manipulators (2nd Ed., Lorenzo > Sciavicco, Bruno Siciliano) > Algebraic Methods for Nonlinear Control Systems (2nd Ed., Giuseppe > Conte, Claude H. Moog, Anna Maria Perdon) > Modern Control Engineering - Problems B (3rd Ed. K.OGATA) + Ebook > Modern Control Engineering (4th Ed. K.OGATA) > LabVIEW 8 Student Edition (Bishop) > Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami- > Naeini) > Modeling and Simulation of Dynamic Systems (Woods, Lawrence) > Computer Numerical Control: Operation and Programming (3rd Ed., > Stenerson & Curran) > Engineering Problem Solving with C (3rd Ed., Etter) > Process Control Instrumentation Technology (8th Ed., Johnson) > Electrical Power and Controls (2nd Ed., Skvarenina & DeWitt) > Electronics and Computer Math (8th Ed., Deem & Zannini) > Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based > Introduction (John Semmlow) > Aircraft Digital Electronic and Computer Systems: Principles, > Operation and Maintenance (Mike Tooley) > VLSI Test Principles and Architectures: Design for Testability (Chen, > Cheng, Eklow et al.) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Machine Vision: Theory, Algorithms, Practicalities (3rd Ed., E. R. > Davies) > Instrumentation and Control Systems (W. Bolton) > Essential Java for Scientists and Engineers (Brian D Hahn & Katherine > M Malan) > Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Ed., > Bernard V. Liengme) > Electric Motors and Drives : Fundamentals, Types and Applications (3rd > Ed., Austin Hughes) > 10-Key Touch Key: Developing Speed and Accuracy (Burton) > Introduction to C++ Programming, Brief (Y. Daniel Liang) > C++ for Business Programmers (2nd Ed., John C. Molluzzo) > Introduction to Java Programming-Comprehensive Version (6th Ed., Y. > Daniel Liang) > Introduction to Java Programming: Fundamentals First (6th Ed., Y. > Daniel Liang) > Objects First With Java: A Practical Introduction Using BlueJ (3rd > Ed., David J. Barnes & Michael Kolling) > Java: An Introduction to Problem Solving and Programming (4th Ed., > Walter Savitch) > Simply Java Programming: An Application-Driven» Tutorial Approach > (Deitel) > Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & > Jeffrey Nyhoff) > Advanced Java» 2 Platform How to Program (Deitel & Santry) > SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) > Introduction to Programming Using Visual Basic 2005 (6th Ed., David I. > Schneider) > Simply Visual Basic 2005 (2nd Ed., Harvey & Paul Deitel & Associates) > Visual Basic 2005 How to Program (3rd Ed., Deitel & Associates) > Introduction to Programming with Visual Basic 6.0 (4th Ed., David I. > Schneider) > Visual Basic.Net Programming (2nd Ed., Jeffrey Tsay) > Simply Visual Basic .NET (Deitel & Nieto) > Mechatronics (Sabri Cetinkunt) > Introduction to Linear Programming (Leonid N. Vaserstein) > Science of Electronics, The: DC/AC (David M. Buchla, Thomas L. Floyd) > Introductory Circuit Analysis (11th Ed., Robert L. Boylestad) > Principles of Electric Circuits: Conventional Current Version (8th > Ed., Thomas Floyd) > Contemporary Electric Circuits: Insights and Analysis (2nd ed., > Strangeway, Petersen, Gassert & Lokken) > Electronics Technology Fundamentals - Conventional Flow (2nd Ed., > Robert T. Paynter & Toby Boydell) > Electronics Fundamentals: Circuits, Devices and Applications (7th Ed., > Thomas L. Floyd) > Principles of Electric Circuits: Electron Flow Version (8th Ed., > Thomas L. Floyd) > Electronics Technology Fundamentals - Electron Flow (2nd Ed., Robert > T. Paynter, Toby Boydell) > Introductory DC/AC Circuits (6th Ed., Nigel P. Cook) > Introductory DC/AC Electronics (6th Ed., Nigel P. Cook) > Electronic Devices - Conventional Current Version (7th Ed., Thomas L. > Floyd) > Electronic Devices - Conventional Current Version (8th Ed., Thomas L. > Floyd) > Electronic Devices - Electron Flow Version (8th, Thomas L. Floyd) > Electronic Devices and Circuit Theory (9th Ed., Robert L. Boylestad, > Louis Nashelsky) > Introductory Electronic Devices and Circuits: Electron Flow Version > (7th Ed., Robert T. Paynter) > Introductory Electronic Devices and Circuits: Conventional Flow > Version (7th Ed., Robert T. Paynter) > Electronic Devices - Electron Flow Version (5th, Thomas L. Floyd) > Science of Electronics, The: Digital (Thomas L. Floyd & David M. > Buchla) > Science of Electronics, The: Analog Devices (Thomas L. Floyd, David M. > Buchla) > Digital Electronics: A Practical Approach (7th Ed., William Kleitz) > Digital Electronics: A Practical Approach (8th Ed., William Kleitz) > Digital Systems: Principles and Applications (10th Ed., Ronald Tocci, > Neal Widmer, Greg Moss) > Digital Electronics with VHDL - Quartus II Version (William Kleitz) > Digital Fundamentals (9th Ed., Thomas L. Floyd) > Digital Fundamentals with PLD Programming (Thomas L. Floyd) > The 8051 Microcontroller (4th Ed., I. Scott MacKenzie, Raphael Chung- > Wei Phan) > The 8051 Microcontroller and Embedded Systems (2nd Ed., Muhammad Ali > Mazidi, Janice Mazidi & Rolin McKinlay) > INTEL Microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486, > Pentium, Prentium ProProcessor, Pentium II, III, 4, (7th Ed., Barry B. > Brey) > Microcontroller Technology: The 68HC11, 5/E (Peter Spasov) > PIC Microcontroller (Muhammad Ali Mazidi, Rolin McKinlay & Danny > Causey) > Industrial Electronics (James A. Rehg, Glenn J. Sartori) > Programmable Controllers Using the Allen-Bradley SlC-500 Family (2nd > Ed., Dave Geller) > Programmable Logic Controllers (James A. Rehg, Glenn J. Sartori) > Fundamentals of Programmable Logic Controllers, Sensors, and > Communications (3rd Ed., Jon Stenerson) > An Introduction to Programming with Visual Basic 6.0, Update Edition > (4th Ed., Schneider) > C++ Programming Today (Barbara Johnston) > Introduction to Data Communications and Networking (Wayne Tomasi) > Introduction to Telecommunications (2nd Ed., Martha Rosengrant) > Network Security Essentials: Applications and Standards (3rd Ed., > William Stallings) > Information Security: Principles and Practices (Mark Merkow, James > Breithaupt) > Principles and Practice of Information Security (Linda Volonino, > Stephen R. Robinson) > Modern Electronic Communication (8th Ed., Jeff Beasley, Gary M. > Miller) > Modern Electronic Communication (9th Ed., Jeff Beasley, Gary M. > Miller) > Electronic Communications for Technicians (2nd ed., Tom Wheeler) > Concepts In Systems and Signals (2nd Ed., John D. Sherrick) > Understanding Fiber Optics (5th Ed., Jeff Hecht) > Understanding UNIX/LINUX Programming: A Guide to Theory and Practice > (Bruce Molay) > Applying PIC18 Microcontrollers: Architecture, Programming, and > Interfacing using C and Assembly (Barry B. Brey) > Electrical Power and Controls (2nd Ed., Timothy L. Skvarenina, William > E. DeWitt) > Process Control Instrumentation Technology (8th Ed., Curtis Johnson) > Electrical Machines, Drives and Power Systems (6th Ed., Theodore > Wildi) > Introduction to Vacuum Technology (David M. Hata) > Electronic Project Design and Fabrication (6th Ed., Ronald A. Reis) > Technology and Society (3rd Ed., Linda Hjorth, Barbara A. Eichler, > Ahmed S. Khan, John Morello) > Solid State Electronic Devices (6th Ed., Ben Streetman, Sanjay > Banerjee) > Approaching Quantum Computing (Dan C. Marinescu & Gabriela M. > Marinescu) > Foundations of MEMS (Chang Liu) > Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby) > Elements of Engineering Electromagnetics (6th Ed., Nannapaneni > Narayana Rao) > Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti) > Digital Design: Principles and Practices Package (4th Ed., John F. > Wakerly) > VHDL: A Starter's Guide (2nd Ed., Sudhakar Yalamanchili) > Computer Organization and Architecture: Designing for Performance (7th > Ed., William Stallings) > Parallel Programming: Techniques and Applications Using Networked > Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & > Michael Allen) > Fundamentals of Parallel Processing (Harry F. Jordan & Gita Alaghband) > Feedback Control of Dynamic Systems (5th Ed., Gene Franklin, J.D. > Powell, Abbas Emami-Naeini) > Digital & Analog Communication Systems (7th Ed., Leon W. Couch) > Fundamentals of Communication Systems (John G. Proakis, Masoud Salehi) > Modern Wireless Communications (Simon Haykin, Michael Moher) > Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud > Salehi) > Data and Computer Communications (8th Ed., William Stallings) > Cryptography and Network Security (4th Ed., William Stallings) > Computer Networking with Internet Protocols (William Stallings) > Probabilistic Systems and Random Signals (Abraham H Haddad) > Error Control Coding (2nd Ed., Shu Lin & Daniel J. Costello) > Wireless Communications & Networks (2nd ed., William Stallings) > Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) > Detection and Estimation:Theory; and Its Applications (Thomas > Schonhoff & Arthur Giordano) > Signals, Systems, and Transforms (3rd Ed., Charles L. Phillips, John > M. Parr & Eve A. Riskin) > Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., > Edward W. Kamen & Bonnie S Heck) > Digital Signal Processing (4th Ed., John G. Proakis, Dimitris K > Manolakis) > Adaptive Filter Theory (4th Ed., Simon Haykin) > Spectral Analysis of Signals (Petre Stoica & Randolph L. Moses) > Fluency with Information Technology: Skills, Concepts, and > Capabilities (2nd Ed., Lawrence Snyder) > Fluency with Information Technology, Brief Edition (Lawrence Snyder) > Jolly) > Comprehensive Excel 2002 for Office XP (4th Ed., Karen J. Jolly) > Ethics for the Information Age (2nd Ed., Michael J. Quinn) > Computer Science: An Overview (8th Ed., J. Glenn Brookshear) > Computer Science: An Overview (9th Ed., J. Glenn Brookshear) > Concise Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Concise Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Extended Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Extended Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Logic and Design of Computer Programs (Jim Messinger) > Absolute C++ (2nd Ed., Walter Savitch) > Absolute C++ (3rd Ed., Walter Savitch) > Starting Out with C++: Early Objects (6th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > Problem Solving with C++: The Object of Programming (5th Ed., Walter > Savitch) > Problem Solving with C++ (6th Ed., Walter Savitch) > Problem Solving, Abstraction, and Design using C++ (4th Ed., Frank L. > Friedman & Elliot B. Koffman) > Problem Solving, Abstraction & Design Using C++ (5th Ed., Frank L. > Friedman & Elliot B. Koffman) > Ed., Tony Gaddis) > Starting out with C++ Brief Version Updated (4th Ed., Tony Gaddis & > Barret Krupnow) > Starting out with C++ Brief Version (5th Ed., Tony Gaddis & Barret > Krupnow) > Starting Out with C++: Brief Version Update, Visual C++ .NET (4th Ed., > Tony Gaddis & Barret Krupnow) > Starting Out with C++: Early Objects (5th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > C++ By Dissection (Ira Pohl) > Essential C++ for Engineers and Scientists (2nd Ed., Jeri R. Hanly) > C++ Coach: Essentials for Introductory Programming (Jeff Salvage) > C++ Primer (4th Ed., Stanley B. Lippman, Jos.8ee Lajoie & Barbara E. > Moo) > Engineering Computation with MATLAB (David Smith) > Absolute Java with Student Resource Disk (2nd Ed., Walter Savitch) > Absolute Java (3rd Ed., Walter Savitch) > The Art and Science of Java (Eric Roberts) > Building Java Programs: A Back to Basics Approach (Stuart Reges & > Martin Stepp) > Introduction to Programming in Java: An Interdisciplinary Approach > (Robert Sedgewick & Kevin Wayne) > Java Foundations: Introduction to Program Design and Data Structures > (John Lewis, Peter DePasquale & Joe Chase) > Starting Out with Java: Early Objects (3rd Ed., Tony Gaddis) > Ed., Tony Gaddis) > Java Software Solutions (Java 5.0 version): Foundations of Program > Design (4th Ed., John Lewis & William Loftus) > Java Software Solutions: Foundations of Program Design (5th Ed., John > Lewis & William Loftus) > Structures (Tony Gaddis & Godfrey Muganda) > Object of Java, The: Introduction to Programming Using Software > Engineering Principles (2nd Ed, David D. Riley) > Object-Oriented Programming in Java: A Graphical Approach, Preliminary > Edition (Kathryn E. Sanders & Andy van Dam) > Starting Out with Java 5: Control Structures to Objects (Tony Gaddis) > Starting Out with Java 5: Early Objects (Tony Gaddis) > Introduction to Programming Using Java: An Object-Oriented Approach > (2nd Ed., David Arnow, Scott Dexter & Gerald Weiss) > Computing with Java (2nd Ed., Art Gittleman) > Problem Solving with Java, Update (2nd Ed., Elliot B. Koffman & Ursula > Wolz) > Starting Out with Alice: A Visual Introduction to Programming (Tony > Gaddis) > Problem Solving and Program Design in C (4th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Problem Solving and Program Design in C (5th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Starting Out with Visual Basic 2005 (3rd Ed., Tony Gaddis & Kip > Irvine) > Starting Out with Visual Basic 6 (Tony Gaddis, Kip Irvine & Bruce > Denton) > Starting Out with Visual Basic.Net (2nd Ed., Tony Gaddis, Kip Irvine & > Bruce Denton) > Computer Programming Fundamentals with Applications in Visual Basic¬ > 6.0 (Mitchell C. Kerman & Ronald L. Brown) > Advanced VB.NET Alternate with VB.Net CD's (3rd Ed., Kip Irvine & Tony > Gaddis) > Advanced Visual Basic 2005 (4th Ed., Kip Irvine & Tony Gaddis) > C# Software Solutions: Foundations of Program Design (John Lewis) > Problem Solving, Abstraction and Design Using C++, Visual C++.NET > Edition (Frank L. Friedman & Elliot B. Koffman) > Ada 95: Problem Solving and Program Design (3rd Ed., Michael B. > Feldman & Elliot B. Koffman) > Programming and Problem Solving with Delphi (Mitchell C. Kerman) > C Program Design for Engineers (2nd Ed., Jeri R. Hanly & Elliot B. > Koffman) > Data Abstraction & Problem Solving with C++ (5th ed., Frank M. > Carrano) > Data Structures and Algorithm Analysis in C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in C++ (3rd Ed., Mark Allen > Weiss) > Data Abstraction and Problem Solving with C++: Walls and Mirrors (4th > Ed., Frank M. Carrano) > Data Structures and Other Objects Using C++ (3rd Ed., Michael Main & > Walter Savitch) > Data Structures and Problem Solving Using C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in Java (2nd Ed., Mark Allen > Weiss) > Collections Framework (Simon Gray) > Data Abstraction and Problem Solving with Java (2nd Ed., Frank M. > Carrano & Janet J. Prichard) > Data Structures and Other Objects Using Java (3rd Ed., Michael Main) > Data Structures and Problem Solving Using Java (3rd Ed., Mark Allen > Weiss) > Java Software Structures: Designing and Using Data Structures (2nd > Ed., John Lewis, Joseph Chase) > The Object of Data Abstraction and Structures (using Java) (David > Riley) > Classic Data Structures in Java (Timothy Budd) > Data Structures in Java (Thomas A. Standish) > Introduction to the Design and Analysis of Algorithms (1st Ed., Anany > V. Levitin) > Introduction to the Design and Analysis of Algorithms (2nd Ed., Anany > V. Levitin) > Algorithm Design (Jon Kleinberg & .83va Tardos) > Data Structures and Algorithm Analysis in C (2nd Ed., Mark Allen > Weiss) > Computer Algorithms: Introduction to Design and Analysis (3rd Ed., > Sara Baase & Allen Van Gelder) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (4th Ed., George F. Luger) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (5th Ed., George F. Luger) > The Complete A+ Guide to PC Repair (3rd Ed., Cheryl A. Schmidt) > The Complete A+ Guide to PC Repair (4th Ed., Cheryl A. Schmidt) > Complete Computer Repair Textbook (4th Ed., Cheryl A. Schmidt) > Computer Systems Organization and Architecture (John D. Carpinelli) > CMOS VLSI Design: A Circuits and Systems Perspective (3rd Ed., Neil > H.E. Weste & David Harris) > Interactive Computer Graphics: A Top-Down Approach Using OpenGL (4th > Ed., Edward Angel) > File Structures: An Object-Oriented Approach with C++ (3rd Ed., > Michael J. Folk, Bill Zoellick & Greg Riccardi) > Oracle 10g Programming: A Primer (Rajshekhar Sunderraman) > Darwen) > Fundamentals of Database Systems (5th Ed., Ramez Elmasri & Shamkant B. > Navathe) > Database Systems: An Application Oriented Approach, Compete Version > (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > DataBase Systems: A Practical Approach to Design, Implementation and > Management (4th Ed., Thomas M. Connolly & Carolyn E. Begg) > Database Systems: An Application-Oriented Approach, Introductory > Version (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > Fundamentals of Database Systems/Oracle 9i Programming (4th Ed., Ramez > Elmasri, Shamkant B. Navathe & Rajshekhar Sunderraman) > Oracle 9i Programming: A Primer (Rajshekhar Sunderraman) > Principles of Database Systems with Internet and Java Applications > (Greg Riccardi) > Introduction to Data Mining (Pang-Ning Tan, Michael Steinbach & Vipin > Kumar) > Data Mining: A Tutorial Based Primer (Richard Roiger & Michael Geatz) > Learning SQL: A Step-by-Step Guide Using Access (Sikha Bagui & Richard > Earp) > Access 2007 Guidebook (6th Ed., Maggie Trigg & Phyllis Dobson) > Dobson) > Implementing Databases in Oracle 9i (John Day & Craig Van Slyke) > Web 101: Making the Net Work for You (2nd Ed., Wendy G. Lehnert) > Web 101 (3rd Ed., Wendy G. Lehnert & Richard L. Kopec) > Web Developer Foundations: Using XHTML (2nd Ed., Terry Felke-Morris) > Web Development & Design Foundations With XHTML (3rd Ed., Terry Felke- > Morris) > Internet Effectively: A Beginner's Guide to the World Wide Web (Tyrone > Adams & Sharon Scollard) > Light on the Web: Essentials to Making the 'Net Work for You (Wendy G. > Lehnert) > Programming the World Wide Web (3rd Ed., Robert W. Sebesta) > Programming the World Wide Web (4th Ed., Robert W. Sebesta) > XML: Language Mechanics and Applications (Dwight Peltzer) > Practical Perl with CGI Applications (Elizabeth Chang) > Developing Web Applications with Active Server Pages (Thom Luce) > Structure and Interpretation of Signals and Systems (Edward A. Lee & > Pravin Varaiya) > Languages and Machines: An Introduction to the Theory of Computer > Science (3r Ed., Thomas A. Sudkamp) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) > Galin) > Object Oriented Software Development Using Java (2nd Ed., Xiaoping > Jia) > Introduction to the Team Software Process (Watts S. Humphrey) > Software Project Management: A Real-World Guide to Success (Joel > Henry) > Software Engineering (8th Ed., Ian Sommerville) > Object-Oriented Programming featuring Graphical Applications in Java > (Michael J. Laszlo) > Project-Based Software Engineering: An Object-Oriented Approach > (Evelyn Stiller & Cathie LeBlanc) > Engineering of Software, The: A Technical Guide for the Individual > (Dick Hamlet & Joe Maybee) > Concepts of Programming Languages (7th Ed., Robert W. Sebesta) > Concepts of Programming Languages (8th Ed., Robert W. Sebesta) > Advanced Java: Internet Applications (2nd Ed., Art Gittleman) > Objects to Components with Java 2 Platform (Art Gittleman) > C for Java Programmers (Tomasz Muldner) > Pointers on C (Kenneth Reek) > C++ Programming with Design Patterns Revealed (Tomasz Muldner) > The C++ Programming Language (3rd Ed., Bjarne Stroustrup) > Operating Systems: A Systematic View (6th Ed., William S. Davis & T.M. > Rajkumar) > Unix: The Textbook (2nd Ed., Syed Mansoor Sarwar, Robert Koretsky & > Syed Aqeel Sarwar) > Operating Systems (3rd Ed., Gary Nutt) > LINUX & UNIX Programming Tools: A Primer for Software Developers (Syed > Mansoor Sarwar & Khaled H. Al-Saqabi) > Addison-Wesley's Interactive Linux Tutorial and Reference (Edutrends, > Inc.) > Linux: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel > Sarwar) > Kernel Projects for Linux (Gary Nutt) > OSP: An Environment for Operating System Projects (Michael Kifer & > Scott A. Smolka) > Distributed Computing: Principles and Applications (M.L. Liu) > Distributed Operating Systems and Algorithm Analysis (Randy Chow & > Theodore Johnson) > Mastering Networks: An Internet Lab Manual (Jorg Liebeherr & Magda El > Zarki) > Computer Networking: A Top-Down Approach Featuring the Internet (3rd > Ed., James F. Kurose & Keith W. Ross) > Computer Networking: A Top-Down Approach (4th Ed., James F. Kurose & > Keith W. Ross) > Computer Networking Complete Package (3rd Ed., James F. Kurose & Keith > W. Ross) > Network Management: Principles and Practice (Mani Subramanian) > Computer Security: Art and Science (Matt Bishop) > Introduction to Computer Security (Matt Bishop) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) - Math, Statistics & Probability > > Advanced Engineering Mathematics (8th Ed., Erwin Kreyszig) > Advanced Engineering Mathematics (9th Ed., Erwin Kreyszig) > Elementary Differential Equations (7th Ed., Boyce) > Elementary Differential Equations (8th Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (7th > Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (8th > Ed., Boyce & Diprima) > Differential Equations: An Introduction to Modern Methods and > Applications (James Brannan & William Boyce) > Introduction to the Finite Element Method: Theory, Programming and > Applications (Erik G. Thompson) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Elementary Linear Algebra (9th Ed., Anton) > Elementary Linear Algebra with Applications (9th Ed., Howard Anton & > Chris Rorres) > Applied Statistics and Probability for Engineers (3rd Ed., Douglas > Montgomery & George Runger) > Applied Statistics and Probability for Engineers (4th Ed., Douglas > Montgomery & George Runger) > Engineering Statistics (3rd Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Engineering Statistics (4th Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Probability and Statistics in Engineering (4th Ed., William W. Hines, > Douglas Montgomery, David Goldsman & Connie Borror) > Design and Analysis of Experiments (6th Ed., Douglas Montgomery) > Spreadsheet Tools for Engineers using Excel (2nd Ed. Byron S > Gottfried) > Spreadsheet Tools for Engineers using Excel (3rd Ed. Byron S > Gottfried) > Numerical Methods for Engineers (4th Ed. Steven C. Chapra) > Numerical Methods for Engineers (5th Ed. Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (1st Ed., Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (2nd Ed., Steven C. Chapra) > Statistics for Engineers and Scientists (1st Ed, William C. Navidi) > Statistics for Engineers and Scientists (2nd Ed, William C. Navidi) > Probability (Jim Pitman) > Numerical Methods with Matlab (Amos Gilat & Vish Subramaniam) > MATLAB: An Introduction with Applications (2nd Ed., Amos Gilat) > Discrete and Combinatorial Mathematics (5th ed., Ralph P. Grimaldi) > Discrete Mathematics (Sherwood Washburn, Thomas Marlowe & Charles T. > Ryan) > Discrete Mathematics (5th ed., John Dossey, Albert Otto, Lawrence > Spence & Charles Vanden Eynden) > Mathematics for New Technologies (Don Hutchison & Mark Yannotta) > An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy) > Fundamentals of Finite Element Analysis (1st Ed., David V. Hutton) > The Finite Element Method: Its Basis and Fundamentals (6th Ed., > Zienkiewicz, R. L. Taylor & J.Z. Zhu) > Differential Equations (A. King, J. Billingham, S. Otto) > Regression Methods in Biostatistics: Linear, Logistic, Survival, and > Repeated Measures Models (Eric Vittinghoff, David Glidden, Stephen > Shiboski, Charles McCulloch) > A Modern Introduction to Probability and Statistics: Understanding Why > and How (F.M. Dekking, C. Kraaikamp, H.P. Lopuha.8a, L.E. Meester) > Statistical Methods for the Analysis of Repeated Measurements (Charles > S. Davis) > Bayesian Core: A Practical Approach to Computational Bayesian > Statistics (Jean-Michel Marin, Christian Robert) > Essentials of Stochastic Processes (Rick Durrett) > Regression Analysis: Theory, Methods, and Applications (Ashish Sen & > Muni Srivastava) > Applied Probability and Statistics (Mario Lefebvre) > Foundations of Hyperbolic Manifolds (2nd Ed., John Ratcliffe) > Fourier and Laplace Transforms (R. J. Beerends , H. G. ter Morsche) > Infinite-Dimensional Dynamical Systems (James C. Robinson) > Mathematical Methods for Physics and Engineering, (3rd Ed., Riley, > Hobson & Bence) + original Ebook > Numerical Methods in Engineering with MATLAB (Jaan Kiusalaas) + > original Ebook > Numerical Methods in Engineering with Python (Jaan Kiusalaas) + > original Ebook > An Introduction to Numerical Analysis (Endre Suli and David Mayers) + > original Ebook > Fundamentals of Engineering Numerical Analysis (Parviz Moin) > Monte Carlo Statistical Methods (2nd Ed., Christian P. Robert, George > Casella) > Introduction to Mathematical Structures and Proofs (Larry J. Gerstein) > Analyzing Categorical Data (Jeffrey S. Simonoff) > Fundamentals of Complex Analysis with Applications to Engineering, > Science, and Mathematics (3rd Ed., E. Saff & Arthur Snider) > Probability & Statistics for Engineers & Scientists (8th Ed., Walpole, > Myers, Ye) > Statistics for Engineering and the Sciences (5th Ed., Mendenhall & > Sincich) > Miller & Freund's Probability and Statistics for Engineers (7th Ed., > Johnson, Miller, Freund) > Applied Numerical Analysis Using MATLAB (2nd Ed., Fausett) > Numerical Methods Using Matlab (4th Ed., Mathews & Fink) > Applied Numerical Methods for Engineers and Scientists (Rao) > Applied Numerical Analysis Using MATLAB (2nd Ed., Laurene v. Fausett) > Friendly Introduction to Numerical Analysis (Bradie) > Elementary Linear Algebra (2nd Ed., Spence, Insel & Friedberg) > Elementary Linear Algebra with Applications (9th Ed., Kolman & Hill) > Introductory Linear Algebra: An Applied First Course (8th Ed., Kolman > & Hill) > Linear Algebra with Applications (7th Ed., S. Leon) > Linear Algebra for Engineers and Scientists Using Matlab (Hardy) > Linear Algebra with Applications (3rd Ed., Bretscher) > Modern Matrix Algebra (Hill & Kolman) > Partial Differential Equations and Boundary Value Problems with > Fourier Series (2nd ed., Asmar) > Applied Partial Differential Equations (4th Ed., Haberman) > Technical Calculus (5th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics (2th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics with Calculus (2th Ed., Dale Ewen, Joan S. Gary > & James E. Trefzger) > Introductory Mathematics (4th Ed., Cook) > Mathematics for the Technical Trades (Cook) > College Mathematics (7th Ed., Cleaves & Hobbs) > Fundamentals of Statistics (2nd Ed., Michael III Sullivan) > Statistics: Informed Decisions Using Data (2nd Ed., Michael III > Sullivan) > Modern Elementary Statistics (12th Ed., John E. Freund, Benjamin M. > Perles) > Franklin) > Elementary Statistics: Picturing the World (3rd Ed., Larson & Farber) > First Course in Statistics (9th Ed., James T. McClave & Terry Sincich) > Statistics (10th Ed., McClave & Terry Sincich) > Interactive Statistics (3rd Ed., Martha Aliaga & Brenda Gunderson) > Statistics for the Life Sciences (3rd Ed., Samuels & Witmer) > Applied Statistics and the SAS Programming Language (5th Ed., Cody & > Smith) > Biostatistics for the Health Sciences (R. Clifford Blair & Richard > Taylor) > Biostatistics: How It Works (Steve Selvin) > Business Statistics: First Course and Student CD (4th Ed., David M. > Levine, Timothy C. Krehbiel & Mark L. Berenson) > Course in Business Statistics with CD-ROM (4th Ed., Groebner, Shannon, > Fry & Smith) > Business Statistics: Decision Making and Student CD Package (7th Ed., > Groebner) > Business Statistics: A Decision-Making Approach and Student CD Update > Package (6th Ed., Groebner, Shannon, Fry & Smith) > Statistics for Business & Economics (10th Ed., McClave, Benson & > Sincich) > Statistics for Managers Using Excel and Student CD Package (5th Ed., > Levine) > Statistics for Managers Using Microsoft Excel and Student CD Package > (4th Ed., Levine, Stephan, Krehbiel & Berenson) > Statistics for Business and Economics and Student CD (6th Ed., > Newbold, Carlson & Thorne) > Statistics for Business and Economics and Student CD-ROM (5th Ed., > Newbold, Carlson & Thorne) > Basic Business Statistics: Concepts and Applications and CD package > (10th Ed., Berenson, Krehbiel & Levine) > John E. Freund's Mathematical Statistics with Applications (7th Ed., > Miller) > Probability and Statistical Inference (7th Ed., Hogg & Tanis) > Introduction to Mathematical Statistics (6th Ed., Hogg, Craig & > McKean) > Introduction to Mathematical Statistics and Its Applications (4th Ed., > Larsen & Marx) > Brief Course in Mathematical Statistics (Hogg & Tanis) > Fundamentals of Probability, with Stochastic Processes (3rd Ed., Saeed > Ghahramani) > First Course in Probability (7th Ed., Sheldon Ross) > Applied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern) > Multivariate Data Analysis (6th Ed., Hair, Black, Babin, Anderson & > Tatham) > Essential MATLAB for Engineers and Scientists (3rd Ed., Brian D Hahn & > Dan Valentine) > Introduction to Applied Statistical Signal Analysis: Guide to > Biomedical and Electrical Engineering Applications (3rd Ed. Richard > Shiavi) > Construction Mathematics (Surinder Virdi & Roy Baker) > Numerical Methods in Biomedical Engineering (Stanley Dunn, Alkis > Constantinides & Prabhas Moghe) > Probability and Statistics with Integrated Software Routines (Ronald > Deep) > Boundary Value Problems and Partial Differential Equations (5th Ed., > David Powers) > Finite Element Analysis with Error Estimators : An Introduction to the > FEM and Adaptive Error Analysis for Engineering Students (J. Akin) > Basic Engineering Mathematics (4th Ed., John Bird) > Engineering Mathematics (4th Ed., John Bird) > Higher Engineering Mathematics (5th Ed., John Bird) > Mathematics for Electrical Engineering and Computing (Mary > Attenborough) > Introductory Statistics for Engineering Experimentation (Peter Nelson, > Karen Copeland & Marie Coffin) > Understanding Engineering Mathematics (Bill Cox) > Statistics And Probability For Engineering : Applications With > Microsoft Excel (Decoursey) > Business Math Using Calculators: With 10-Key Computer Assisted > Instruction (Burton) > Mathematics for Economics and Business (5th Ed., Ian Jacques) > Business Math, Brief w/CD & Study Guide & Tutor Center Access Card Pkg > (7th Ed., Cleaves & Hobbs) > Math for Merchandising: A Step-by-Step Approach (3rd Ed., Moore) > Mathematics for Business (7th Ed., Salzman , Miller & Clendenen) > Mathematics for Business (8th Ed., Salzman , Miller & Clendenen) > Advanced Engineering Mathematics (2nd Ed, Michael Greenberg) > Basic College Mathematics with Early Integers (K. Elayn Martin-Gay) > Developmental Mathematics (K. Elayn Martin-Gay) > Essentials of Basic College Mathematics (John Jr Tobey, Jr., Jeffrey > Slater) > Basic College Mathematics (5th Ed., John Tobey & Jeffrey Slater) > Prealgebra (5th Ed., K. Elayn Martin-Gay) > Prealgebra & Introductory Algebra (2nd Ed., K. Elayn Martin-Gay) > Prealgebra (3rd Ed., Jamie Blair, John Tobey & Jeffrey Slater) > Elementary Algebra Early Graphing for College Students (3rd Ed., Allen > R. Angel) > Elementary Algebra (Michael Sullivan III, Katherine R. Struve & Janet > Mazzarella) > Elementary Algebra for College Students (7th Ed., Allen R. Angel) > Experiencing Introductory and Intermediate Algebra Through Functions > and Graphs (3rd Ed., JoAnne Thomasson & Robert Pesut) > Introductory Algebra (3rd Ed., K. Elayn Martin-Gay) > Beginning Algebra (6th Ed., John Jr Tobey & Jeffrey Slater) > Beginning Algebra: Early Graphing (Jamie Blair, John Tobey & Jeffrey > Slater) > Beginning and Intermediate Algebra (2nd Ed., Jamie Blair, John Tobey & > Jeffrey Slater) > Introductory Algebra (4th Ed., Robert F Blitzer) > Introductory and Intermediate Algebra (2nd Ed., Robert F Blitzer) > Intermediate Algebra for College Students (7th Ed., Allen R. Angel) > Intermediate Algebra (Michael Sullivan III & Katherine R. Struve) > Intermediate Algebra (3rd Ed., K. Elayn Martin-Gay) > Essentials of Intermediate Algebra for College Students (Robert F. > Blitzer) > Intermediate Algebra (4th Ed., Robert F Blitzer) > Algebra A Combined Approach (3rd Ed., K. Elayn Martin-Gay) > Elementary & Intermediate Algebra (Michael Sullivan III, Katherine R. > Struve & Janet Mazzarella) > Essentials of Introductory and Intermediate Algebra for College > Students (Robert F. Blitzer) > Algebra for College Students (3rd Ed., Allen R. Angel) > Algebra for College Students (5th Ed., Robert F Blitzer) > College Geometry: A Problem Solving Approach with Applications (2nd > Ed., Gary L. Musser, Lynn Trimpe & Vikki R. Maurer) > College Algebra (8th Ed., Michael Sullivan) > College Algebra Essentials (8th Ed., Michael Sullivan) > College Algebra (4th Ed., Robert F. Blitzer) > College Algebra Essentials (2nd Ed., Robert F. Blitzer) > College Algebra: An Early Functions Approach (Robert F. Blitzer) > College Algebra: Concepts Through Functions (Michael Sullivan III & > Michael Sullivan) > College Algebra Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Essentials of College Algebra: Enhanced with Graphing Utilities (4th > Ed., Michael Sullivan III & Michael Sullivan) > Algebra and Trigonometry (8th Ed., Michael Sullivan) > Algebra and Trigonometry (3rd Ed., Robert F. Blitzer) > Algebra and Trigonometry: An Early Functions Approach (Robert F. > Blitzer) > Precalculus: Concepts Through Functions, A Right Triangle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Algebra & Trigonometry (7th Ed., Michael Sullivan) > Algebra and Trigonometry Enhanced With Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Trigonometry (7th Ed., Michael Sullivan) > Trigonometry (8th Ed., Michael Sullivan) > Trigonometry Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus (8th Ed., Michael Sullivan) > Precalculus (3rd Ed., Robert F. Blitzer) > Precalculus Essentials (2nd Ed., Robert F. Blitzer) > Precalculus: Concepts Through Functions, A Unit Circle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Precalculus Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus Essentials: Enhanced with Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Thinking Mathematically (4th Ed., Robert F. Blitzer) > Excursions in Modern Mathematics (5th Ed., Peter Tannenbaum) > Excursions In Modern Mathematics with Mini-Excursions (6th Ed., Peter > Tannenbaum) > Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) > Fundamentals of Mathematics (10th Ed., William M Setek & Michael A > Gallo) > Learning Math in Elementary and Middle School & IMAP Package (4th Ed., > George Cathcart, Yvonne M. Pothier, James H. Vance & Nadine S. Bezuk) > Understanding the Math You Teach: Content and Methods for > Prekindergarten Through Grade 4 (Anita C. Burris) > Algebra Connections (Ira J. Papick & UMO University of Missouri) > Calculus Connections (Asma Harcharras, Dorina Mitrea) > Data Analysis and Probability Connections: Mathematics for Middle > School Teachers (Debra A. Perkowski & Michael Perkowski) > Geometry Connections (John K. Beem) > Elementary Math Modeling Updated (2nd Ed., Mary Ellen Davis & C. Henry > Edwards) > Additional Calculus Topics (11th Ed., Raymond Barnett, Michael Ziegler > & Karl Byleen) > Finite Math and Its Application (9th Ed., Larry J Goldstein, David I > Schneider & Martha J. Siegel) > Introductory Mathematical Analysis for Business, Economics and the > Life and social Sciences (11th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Introductory Mathematical Analysis for Business, Economics and the > Life and Social Sciences (12th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Additional Calculus Topics (9th Ed., Raymond A. Barnett, Michael R. > Ziegler & Karl E. Byleen) > College Mathematics for Business, Economics, Life Sciences and Social > Sciences (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. > Byleen) > Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, > David I Schneider, David I. Lay & Nakhle Asmar) > Calculus and its Applications (11th Ed., Larry J Goldstein, David I > Schneider, David I. Lay & Nakhle Asmar) > Calculus for Business, Economics, Life Sciences and Social Sciences > (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) > Calculus, Early Transcendentals (6th Ed., C. Henry Edwards & David E. > Penney) > Calculus, Early Transcendentals (7th Ed., C. Henry Edwards & David E. > Penney) > Calculus (9th Ed., Dale Varberg, Edwin Purcell & Steve Rigdon) > Calculus Early Transcendentals (Dale Varberg, Edwin Purcell & Steve > Rigdon) > Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley & Karl J. > Smith) > Calculus (6th Ed., Henry Edwards & David E. Penney) > Single Variable Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley > & Karl J. Smith) > Vector Calculus (3rd Ed., Susan J. Colley) > Applied Linear Algebra (Peter J. Olver & Cheri Shakiban) > Introductory Linear Algebra: An Applied First Course (8th Ed., Bernard > Kolman & David R. Hill) > Differential Equations and Linear Algebra (2nd Ed., Jerry Farlow, > James E. Hall, Jean Marie McDill & Beverly H. West) > Differential Equations and Linear Algebra (2nd Ed., C. Henry Edwards & > David E. Penney) > Differential Equations (2nd Ed., John Polking, Al Boggess & David > Arnold) > Differential Equations with Boundary Value Problems (2nd ed., John > Polking, Al Boggess & David Arnold) > Discrete Mathematics with Graph Theory (3rd Ed., Edgar G. Goodaire & > Michael M. Parmenter) > Discrete Mathematics (6th Ed., Richard Johnsonbaugh) > Essential Discrete Mathematics (Todd Feil & Joan Krone) > Business Mathematics, 10th Ed. (Charles D. Miller, Stanley A. Salzman > & Gary Clendenen) > Elementary Statistics (6th Ed., Neil A. Weiss) > Elementary Statistics (7th Ed., Neil A. Weiss) > Elementary Statistics Using the Graphing Calculator: For the TI-83/84 > Plus (Mario F. Triola) > Elementary Statistics Using the TI-83/84 Plus Calculator (2nd Ed., > Mario F. Triola) > Elementary Statistics Update (9th Ed., Mario F. Triola) > Elementary Statistics (10th Ed., Mario F. Triola) > Elementary Statistics With Multimedia Study Guide (10th Ed., Mario F. > Triola) > Essentials of Statistics (2nd Ed., Mario F. Triola) > Essentials of Statistics (3rd Ed., Mario F. Triola) > Introductory Statistics (7th Ed., Neil A. Weiss) > Introductory Statistics (8th Ed., Neil A. Weiss) > Intro Stats (2nd Ed., Richard D. De Veaux, Paul F. Velleman & David E. > Bock) > Stats: Data and Models, (Richard D. De Veaux, Paul F. Velleman & David > E. Bock) > Stats: Data and Models, (2nd ed., Richard D. De Veaux, Paul F. > Velleman & David E. Bock) > Elementary Statistics Using Excel (2nd Ed., Mario F. Triola) > Elementary Statistics Using Excel (3rd Ed., Mario F. Triola) > Stats: Modeling the World (2nd Ed., David E. Bock, Paul F. Velleman & > Richard D. De Veaux) > Statistical Reasoning for Everyday Life (2nd Ed., Jeffrey O. Bennett, > William L. Briggsr & Mario F. Triola) > Business Statistics (Mario F. Triola & LeRoy A. Franklin) > Biostatistics for the Biological and Health Sciences with Statdisk > (Marc M. Triola & Mario F. Triola) > A Course in Probability (Neil A. Weiss) > Probability and Statistics (3rd Ed., Morris H. DeGroot & Mark J. > Schervish) > Statistics for Science and Engineering (John Kinney) > Developmental Mathematics (7th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Mathematical Proofs: A Transition to Advanced Mathematics (Gary > Chartrand, Albert D. Polimeni & Ping Zhang) > Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Ed., > Carol Schumacher) > Elementary Number Theory (5th Ed., Kenneth H. Rosen) > History of Mathematics: Brief Version (Victor J. Katz) > College Geometry: A Discovery Approach (2nd Ed., David Kay) > Geometry: An Investigative Approach (2nd Ed., Phares G. O'Daffer & > Stanley R. Clemens) > A First Course in Abstract Algebra (7th Ed., John B. Fraleigh) > Complex Variables with Applications (3rd Ed., David A. Wunsch) > Numerical Analysis with CD-ROM (Timothy Sauer) > Numerical Analysis and Scientific Computation (Jeffery J. Leader) > Linear Algebra and Differential Equations (Gary L. Peterson & James S. > Sochacki) > Elementary Differential Equations Bound with IDE CD Package (2nd Ed., > Werner E. Kohler & Lee W. Johnson) > Elementary Differential Equations with Boundary Value Problems with > IDE CD Package (2nd Ed., Werner E. Kohler & Lee W. Johnson) > Fundamentals of Differential Equations (6th Ed., Kent B. Nagle, Late, > Edward B. Saff & Arthur David Snider) > Fundamentals of Differential Equations and Boundary Value Problems > (4th Ed., Kent B. Nagle, Late, Edward B. Saff & Arthur David Snider) > Linear Algebra and Its Applications with CD-ROM, Update (3rd Ed., > David C. Lay) > Introduction to Linear Algebra (5th ed., Lee W. Johnson, R. Dean Riess > & Jimmy T. Arnold) > Calculus for the Life Sciences (Marvin L. Bittinger, Neal Brand & John > Quintanilla) > Calculus with Applications for the Life Sciences (Raymond N. > Greenwell, Nathan P. Ritchey & Margaret L. Lial) > Calculus: An Integrated Approach to Functions and Their Rates of > Change, Preliminary Edition (Robin J. Gottlieb) > Calculus (9th Ed., George B. Thomas, Jr. & Ross L. Finney) > Thomas' Calculus, Alternate Edition (9th Ed., George B. Thomas, Jr. & > Ross L. Finney) > Calculus: A Complete Course (2nd Ed., Ross L. Finney, Franklin D. > Demana, Bert K. Waits & Daniel Kennedy) > Calculus (Elgin H. Johnston & Jerry Mathews) > Thomas' Calculus, Updated (10th Ed., George B. Thomas, Jr., Ross L. > Finney, Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus (11th Ed., George B. Thomas, Jr., Maurice D. Weir, > Joel D. Hass & Frank R. Giordano) > Thomas' Calculus Early Transcendentals (11th Ed., George B. Thomas, > Jr., Maurice D. Weir, Joel D. Hass & Frank R. Giordano) > University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, > Jr.) > University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir > & George B. Thomas, Jr.) > Thomas' Calculus, Media Upgrade (11th Ed., George B. Thomas, Jr., > Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Ed., > George B. Thomas, Jr., Maurice D. Weir, Joel D. Hass & Frank R. > Giordano) > Calculus with Applications (8th Ed., Margaret L. Lial, Raymond N. > Greenwell & Nathan P. Ritchey) > Calculus with Applications, Brief Version (8th Ed., Margaret L. Lial, > Raymond N. Greenwell & Nathan P. Ritchey) > Finite Math with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics (8th Ed., Margaret L. Lial, Raymond N. Greenwell & > Nathan P. Ritchey) > Mathematics with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics and Calculus with Applications (7th Ed., Margaret > L. Lial, Raymond N. Greenwell & Nathan P. Ritchey) > Mathematical Ideas (10th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas (11th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas Expanded Edition (10th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Mathematical Ideas Expanded Edition (11th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (3rd Ed., Jeffrey O. Bennett & William L. Briggs) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (4th Ed., Jeffrey O. Bennett & William L. Briggs) > A Problem Solving Approach to Mathematics (9th Ed., Rick Billstein, > Shlomo Libeskind & Johnny W. Lott) > A Survey of Mathematics with Applications (7th Ed., Allen R. Angel, > Christine D. Abbott & Dennis C. Runde) > A Survey of Mathematics with Applications: Expanded Edition (7th Ed., > Allen R. Angel, Christine D. Abbott & Dennis C. Runde) > Mathematics All Around (3rd Ed., Tom Pirnot) > Mathematics for Elementary School Teachers (3rd Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary School Teachers (4th Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary Teachers with Activities (Sybilla > Beckmann) > Mathematics for Elementary Teachers plus Activities Manual (2nd Ed., > Sybilla Beckmann) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (8th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (9th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > Mathematical Reasoning for Elementary Teachers (4th Ed., Calvin T. > Long & Duane W. DeTemple) > Essentials of Using and Understanding Mathematics: A Quantitative > Reasoning Approach (Jeffrey O. Bennett & William L. Briggs) > Technical Calculus with Analytic Geometry (4th Ed., Allyn J. > Washington) > Basic Technical Mathematics (8th Ed., Allyn J. Washington) > Basic Technical Mathematics with Calculus (8th Ed., Allyn J. > Washington) > Basic Technical Mathematics with Calculus Metric Version (8th Ed., > Allyn J. Washington) > Introduction to Technical Mathematics (5th Ed., Allyn J. Washington, > Mario F. Triola & Ellena E. Reda) > A Graphical Approach to Precalculus (4th Ed., John Hornsby, Margaret > L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits (3rd Ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits: A Unit Circle > Approach (4th Ed., John Hornsby, Margaret L. Lial & Gary K. Rockswold) > Precalculus: Functions and Graphs (5th Ed., Franklin Demana, Bert K. > Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphical, Numerical, Algebraic (7th Ed., Franklin > Demana, Bert K. Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphs and Models Graphing Calculator Manual Package (3rd > Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & > Judith A. Penna) > Functioning in the Real World: A Precalculus Experience (2nd Ed., > Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker & Martha J. > Siegel) > Precalculus with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Precalculus (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Mark Dugopolski) > Precalculus (4th Ed., Mark Dugopolski) > Precalculus (3rd Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Precalculus: Functions and Graphs (2nd Ed., Mark Dugopolski) > Fundamentals of Precalculus (Mark Dugopolski) > Trigonometry (Mark Dugopolski) > Trigonometry (2nd Ed., Mark Dugopolski) > Trigonometry (8th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Trigonometry: A Circular Function Approach (Marie Aratari) > A Graphical Approach to Algebra and Trigonometry (4th ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > Algebra and Trigonometry: Graphs and Models Graphing Calculator Manual > Package (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. > Ellenbogen & Judith A. Penna) > Algebra and Trigonometry (2nd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > Algebra and Trigonometry (3rd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > College Algebra and Trigonometry (J. S. Ratti & Marcus S. McWaters) > College Algebra and Trigonometry (3rd Ed., Mark Dugopolski) > College Algebra and Trigonometry (4th Ed., Mark Dugopolski) > Algebra and Trigonometry with Modeling and Visualization (3rd Ed., > Gary K. Rockswold) > College Algebra and Trigonometry (3rd Ed., Margaret L. Lial, John > Hornsby & David I. Schneider) > A Graphical Approach to College Algebra (4th Ed., John Hornsby, > Margaret L. Lial & Gary K. Rockswold) > College Algebra: Graphs and Models Graphing Calculator Manual Package > (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen > & Judith A. Penna) > College Algebra (J. S. Ratti & Marcus S. McWaters) > College Algebra with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Essentials of College Algebra with Modeling and Visualization (3rd > Ed., Gary K. Rockswold) > Essentials of College Algebra (Margaret L. Lial, John Hornsby & David > I. Schneider) > Essentials of College Algebra, Alternate Edition (Margaret L. Lial, > John Hornsby & David I. Schneider) > College Algebra (3rd Ed., Mark Dugopolski) > College Algebra (4th Ed., Mark Dugopolski) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (2nd Ed., Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin > L. Bittinger) > College Algebra (9th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Essentials of Geometry for College Students (2nd Ed., Margaret L. > Lial, Barbara A. Brown, Arnold R. Steffenson & L. Murphy Johnson) > Algebra for College Students (5th Ed., Margaret L. Lial, John Hornsby > & Terry McGinnis) > Introductory and Intermediate Algebra (3rd Ed., argaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (3rd Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (4th Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Elementary and Intermediate Algebra (1st Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Elementary and Intermediate Algebra (2nd Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Introductory and Intermediate Algebra: A Combined Approach (2nd Ed., > Marvin L. Bittinger & Judith A. Beecher) > Introductory and Intermediate Algebra (3rd Ed., Marvin L. Bittinger & > Judith A. Beecher) > Elementary and Intermediate Algebra (George Woodbury) > Elementary and Intermediate Algebra: Concepts and Applications (4th > Ed., Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Beginning and Intermediate Algebra with Applications and Visualization > (Gary K. Rockswold & Terry A. Krieger) > Elementary and Intermediate Algebra: Graphs & Models (2nd Ed., Marvin > L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Foundations of Mathematics (Marvin L. Bittinger & Judith A. Penna) > Intermediate Algebra (9th Ed., Marvin L. Bittinger) > Intermediate Algebra (10th Ed., Marvin L. Bittinger) > Intermediate Algebra: Graphs & Models (2nd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra: Graphs & Models (3rd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra with Applications and Visualization (2nd Ed., > Gary K. Rockswold & Terry A. Krieger) > Intermediate Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Intermediate Algebra (Tom Carson, Ellyn Gillespie & Bill E. Jordan) > Intermediate Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Intermediate Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Beginning Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Developmental Mathematics: Basic Mathematics and Algebra (Margaret L. > Lial, John Hornsby, Terry McGinnis, Stanley A. Salzman & Diana L. > Hestwood) > Prealgebra and Introductory Algebra (Marvin L. Bittinger & David J. > Ellenbogen) > Prealgebra and Introductory Algebra (2nd Ed., Marvin L. Bittinger & > David J. Ellenbogen) > Elementary Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Introductory Algebra (9th Ed., Marvin L. Bittinger) > Introductory Algebra (10th Ed., Marvin L. Bittinger) > Prealgebra and Introductory Algebra (2nd Ed., Margaret L. Lial, John > Hornsby, Terry McGinnis & Diana L. Hestwood) > Elementary Algebra with Early Systems of Equations (Tom Carson & Ellyn > Gillespie) > Elementary Algebra: Concepts and Applications (6th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Elementary Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Introductory Algebra (Richelle M. Blair) > Introductory Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Beginning Algebra with Applications and Visualization (Gary K. > Rockswold & Terry A. Krieger) > Integrated Arithmetic and Basic Algebra (3rd Ed., Bill E. Jordan & > William P. Palow) > Introductory Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Developmental Mathematics (6th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Prealgebra (3rd Ed., Margaret L. Lial & Diana L. Hestwood) > Prealgebra (4th Ed., Marvin L. Bittinger & David J. Ellenbogen) > Prealgebra (5th Ed., Marvin L. Bittinger, David J. Ellenbogen & > Barbara L. Johnson) > Prealgebra (2nd Ed., Tom Carson) > Basic Mathematics (9 th Ed., Marvin L. Bittinger) > Basic Mathematics (10 th Ed., Marvin L. Bittinger) > Basic Mathematics Preliminary Edition (Robert Prior) > Basic Mathematics with Early Integers (Marvin L. Bittinger & Judith A. > Penna) > Basic College Mathematics (7th Ed., Margaret L. Lial, Stanley A. > Salzman & Diana L. Hestwood) > Basic Mathematics through Applications (3rd Ed., Geoffrey Akst & Sadie > Bragg) > Fundamental Mathematics through Applications (3rd Ed., Geoffrey Akst & > Sadie Bragg) > Wave Motion (J. Billingham & A. C. King) > Solving ODEs with MATLAB (L. F. Shampine, I. Gladwell & S. Thompson) > Numerical Solution of Partial Differential Equations: An Introduction > (2nd Ed., K. W. Morton & D. F. Mayers) > Measure Theory and Filtering: Introduction and Applications (Lakhdar > Aggoun & Robert J. Elliott) > Mathematical Models in Biology: An Introduction (Elizabeth S. Allman & > John A. Rhodes) > Insurance Risk and Ruin (David C. M. Dickson) > Data Analysis and Graphics Using R: An Example-based Approach (2nd > Ed., John Maindonald & John Braun) > Convex Optimization (Stephen Boyd & Lieven Vandenberghe) > Lauritzen) > Calculus: Concepts and Methods (Ken Binmore & Joan Davies) > An Introduction to Partial Differential Equations (Yehuda Pinchover & > Jacob Rubinstein) > An Introduction to Ordinary Differential Equations (James C. Robinson) > An Introduction to Mathematical Physiology and Biology (2nd Ed., J. > Mazumdar) > An Introduction to Financial Option Valuation: Mathematics, > Stochastics and Computation (Desmond Higham) > An Interactive Introduction to Mathematical Analysis (Jonathan Lewin) > An Elementary Introduction to Mathematical Finance: Options and other > Topics (2nd Ed., Sheldon M. Ross) > A Course in Financial Calculus (Alison Etheridge) - Physics & Astronomy : > > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Fundamentals of Physics (8th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (6th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (7th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > An Introduction to Thermodynamics and Statistical Mechanics (2nd Ed, > Keith Stowe) > Equilibrium and Non-Equilibrium Statistical Thermodynamics (Michel Le > Bellac, Fabrice Mortessagne & G. George Batrouni) > Elements of Statistical Mechanics: With an Introduction to Quantum > Field Theory and Numerical Simulation (Ivo Sachs & Siddhartha Sen) > Quantum Transport (2nd Ed., Supriyo Datta) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Applied Quantum Mechanics (1st Ed., A. F. J. Levi) + original Ebook > Applied Quantum Mechanics (2nd Ed., A. F. J. Levi) > Astronomy A Physical Perspective (2nd Ed., Marc L. Kutner) + original > Ebook > Classical Mechanics (Douglas Gregory) + original Ebook > Electromagnetic Field Theory Fundamentals (2nd Ed., Singh Guru & > Hiziroglu) > Fundamentals of Quantum Mechanics (C.L. Tang) + original Ebook > Special Relativity (P.M. Schwarz & J.H. Schwarz) > Statistical Thermodynamics (Normand Laurendeau) > Statistical Thermodynamics and Microscale Thermophysics (Van P. Carey) > Thermal Physics (Ralph Baierlein) > Topics in Atomic Physics (Charles E. Burkhardt, Jacob J. Leventhal) > Applied Physics (8th Ed., Dale Ewen, Ronald Nelson, Neill Schurter & > Erik Gundersen) > Orbital Mechanics for Engineering Students (Howard Curtis) > Diagnostic Ultrasound Imaging: Inside Out (Thomas Szabo) > Astronomy: A Beginner's Guide to the Universe (5th Ed., Eric Chaisson > & Steve McMillan) > The Cosmic Perspective Media Update with MasteringAstronomy» and > Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with MasteringAstronomy» > and Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. > Bennett, Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with Astronomy Place > website, Skygazer Planetarium Software (3rd Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective (3rd Ed., Jeffrey O. Bennett, Megan > Donahue, Nicholas Schneider & Mark Voit) > Astronomy Today (5th Ed., Eric Chaisson & Steve McMillan) > An Introduction to Modern Astrophysics (2nd Ed., Bradley W. Carroll & > Dale A. Ostlie) > Conceptual Physical Science (3rd Ed., Paul G. Hewitt, John A. Suchocki > & Leslie Hewitt) > Conceptual Integrated Science (Paul G. Hewitt, Suzanne Lyons, John A. > Suchocki & Jennifer Yeh) > Physics: Concepts & Connections (4th Ed., Art Hobson) > Conceptual Physics (10th Ed., Paul G. Hewitt) > College Physics (6th Ed., Jerry D Wilson, Anthony J Buffa & Bo Lou) > Physics with Mastering Physics (3rd Ed., James S. Walker) > Active Learning Guide (Alan Van Heuvelen & Eugenia Etkina) > E&M TIPERs: Electricity & Magnetism Tasks (C. J. Hieggelke, D. P. > Maloney, T. L. O'Kuma & Steve Kanim) > Physics: Principles with Applications (6th Ed., Douglas C. Giancoli) > Physlet¬ Physics: Interactive Illustrations, Explorations and Problems > for Introductory Physics (Wolfgang Christian & Mario Belloni) > University Physics with Modern Physics with Mastering Physics (11th > Ed., Hugh D. Young & Roger A. Freedman) > Physics for Scientists and Engineers (3rd Ed., Douglas C. Giancoli) > Physics for Scientists and Engineers with Modern Physics (3rd Ed., > Douglas C. Giancoli) > Physlet¬ Quantum Physics: An Interactive Introduction (Mario Belloni, > Wolfgang Christian & Anne Cox) > Introduction to Electrodynamics (3rd Ed., David J. Griffiths) > Introduction to Optics (3rd Ed., Frank L Pedrotti, Leno M Pedrotti & > Leno S Pedrotti) > Introduction to Quantum Mechanics (2nd Ed., David J. Griffiths) > Quantum Mechanics: An Accessible Introduction (Robert Scherrer) > The Physics of Sound (3rd Ed., Richard E Berg & David G Stork) > Classical Electromagnetism (Jerrold Franklin) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Introduction to Color Imaging Science (Hsien-Che Lee) > An Introduction to Astrobiology (Iain Gilmour & Mark A. Sephton) > An Introduction to Galaxies and Cosmology (Mark H. Jones & Robert J. > Lambourne) > An Introduction to the Solar System (Neil McBride & Iain Gilmour) > Quantum Physics (Michel Le Bellac) > Laser Fundamentals (2nd Ed., William T. Silfvast) > Introductory Quantum Optics (Christopher Gerry & Peter Knight) > Introduction to Plasma Physics: With Space and Laboratory Applications > (D. A. Gurnett & A. Bhattacharjee) > A Short Introduction to Quantum Information and Quantum Computation > (Michel Le Bellac) > A Quantum Approach to Condensed Matter Physics (Philip L. Taylor & > Olle Heinonen) > A First Course in String Theory (Barton Zwiebach) > A First Course in Computational Physics and Object-Oriented > Programming with C++ (David Yevick) > A Course in Modern Mathematical Physics: Groups, Hilbert Space and > Differential Geometry (Peter Szekeres) > Time Series Analysis and Its Applications: With R Examples (2nd Ed., > Robert Shumway & David Stoffer) > Introduction to Time Series and Forecasting (Peter Brockwell & Richard > Davis) > Ultrasonic Nondestructive Evaluation Systems: Models and Measurements > (Lester W. Schmerr & Sung-Jin Song) - Civil Engineering : > > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Fundamentals of Structural Analysis, (1st Ed., Leet & Uang) > Fundamentals of Structural Analysis, (2nd Ed., Leet & Uang) > Fundamentals of Structural Analysis, (3rd Ed., Leet & Uang) > Structural and Stress Analysis (2nd Ed., Megson) + Ebook > Statics and Strength of Materials for Architecture and Building > Construction (3rd Ed., Onouye & Kane) > Open Channel Hydraulics (A. Osman Akan) > Fundamentals of Structural Stability (George Simitses & Dewey Hodges) > Introduction to Naval Architecture : Formerly Muckle's Naval > Architecture for Marine Engineers (4th Ed., E C Tupper) > The Management of Construction: A Project Lifecycle Approach (F. > Lawrence Bennett) > Advanced Topics in Finite Element Analysis of Structures: With > Mathematica and MATLAB Computations (Asghar Bhatti) > Elementary Structures for Architects and Builders (5th Ed., Ronald E. > Shaeffer) > Surveying with Construction Applications (6th Ed., Barry F. Kavanagh) > Structural Analysis (6th Ed., Hibbeler) > Dynamics of Structures (3rd Ed., Chopra) > Structures (6th Ed., Daniel Lewis Schodek & Martin Bechthold) > Concrete Structures (Mehdi Setareh & Robert M. Darvas) > Reinforced Concrete Design (6th Ed., Chu-Kia Wang, Charles G. Salmon) > Reinforced Concrete Design (7th Ed., Chu-Kia Wang, Charles G. Salmon & > Jos.8e A. Pincheira) > Reinforced Concrete Design (6th Ed., George F. Limbrunner & Abi > Aghayere) > Reinforced Concrete: Mechanics and Design (4th Ed., James G. MacGregor > & James K. Wight) > Structural Steel Design (4th Ed., Jack C. McCormac) > Design of Reinforced Concrete (6th Ed., Jack C. McCormac & James K. > Nelson) > Design of Reinforced Concrete (7th Edition, ACI 318-05 Code Edition, > by Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (3rd Ed., > James K. Nelson, Jr., Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (4th Ed., Jack > C. McCormac) > Surveying (5th Ed., Jack C. McCormac) > Introduction to Structural Analysis & Design (S. D. Rajan) > Soil Mechanics and Foundations (2nd Ed., Muniram Budhu) > Soils and Foundations (7th Ed., Liu & Evett) > Essentials of Soil Mechanics and Foundations: Basic Geotechnics (7th > Ed., David F. McCarthy) > Building Construction: Principles, Materials, and Systems (Madan > Mehta, Diane Armpriest & Walter Scarborough) > Construction Methods and Management (7th Ed., Stephens W. Nunnally) > Construction Project Administration (8th Ed., Ed Fisk Wayne Reynolds) > Construction Accounting and Financial Management (Steven J. Peterson) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Construction Estimating Using Excel (Stephen J. Peterson) > Heating and Cooling of Buildings: Design for Efficiency (2nd Ed., Jan > F. Kreider, Peter S. Curtiss & Ari Rabl) > Steel Structures: Behavior and LRFD (1st Ed., Ramulu S Vinnakota) > The Engineering of Foundations (1st Ed., Rodrigo Salgado) > Introduction to Transportation Engineering (2nd Ed., Banks) > Construction Contracts (2nd Ed., Hinze) > Urban Transportation Planning (2nd Ed., Meyer & Miller) > Construction Planning, Equipment, and Methods (6th Ed., Peurifoy & > Schexnayder) > Construction Planning, Equipment, and Methods (7th Ed., Peurifoy, > Schexnayder & Aviad Shapira) > Open Channel Hydraulics (Terry Sturm) > Construction Management Fundamentals (Schexnayder & Mayo) > Fundamentals of Structural Dynamics (2nd Ed., Roy R. Craig & Andrew J. > Kurdila) > Structural Concrete: Theory and Design (3rd Ed., M. Nadim Hassoun & > Akthem Al-Manaseer) > Principles of Highway Engineering and Traffic Analysis (3rd Ed., Fred > Mannering, Walter Kilareski & Scott Washburn) - Environmental Engineering, Earth and Environmental Sciences : > > Principles of Environmental Engineering and Science (Mackenzie L Davis > & Susan J Masten) > Introduction to Environmental Engineering (4th Ed., MacKenzie L. Davis > & David A. Cornwell) > Introduction to Environmental Engineering and Science (2nd Ed., > Gilbert M. Masters) > Introduction to Environmental Engineering and Science (3rd Ed., > Gilbert M. Masters & Wendell P. Ela) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) > Introduction to Engineering and the Environment (1st Ed., Edward S. > Rubin) > Basic Environmental Technology: Water Supply, Waste Management & > Pollution Control (5th Ed., Jerry A. Nathanson) > Small and Decentralized Wastewater Management Systems (1st Ed, Crites > & Tchobanoglous) > Water Resources Engineering (R. Wurbs, W. James) > Water and Wastewater Technology (6th Ed., Mark J. Hammer, Sr. & Mark > J. Hammer, Jr.) > Principles of Sequence Stratigraphy (Octavian Catuneanu) > Atmospheric Science: An Introductory Survey (2nd Ed., John Wallace, > Peter Hobbs) > Plant Pathology (5th Ed., George Agrios) > Environmental Engineering (4th Ed., Ruth F Weiner & Robin Matthews) > Groundwater Hydrology (3rd Ed., David Keith Todd & Larry W. Mays) > Groundwater Science (Charles Fitts) > Agriculture's Ethical Horizon (Robert Zimdahl) > Environmental Contaminants: Assessment and Control (Daniel Vallero) > Water Resources Engineering 2005 Edition (Larry W. Mays) > Water-Resources Engineering (2nd Ed., Chin) > Water Chemistry (Benjamin) > Hazardous Waste Management (2nd Ed., Michael D. LaGrega, Phillip L > Buckingham & Jeffrey C Evans) > Environmental Biotechnology: Principles and Applications (1st Ed., > Bruce E. Rittmann & Perry L. McCarty) > Chemistry for Environmental Engineering and Science (5th Ed., Clair N > Sawyer, Perry L. McCarty & Gene F. Parkin) > Geology for Engineers and Environmental Scientists (3rd Ed., Alan E. > Kehew) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Water Treatment: Principles and Design (2nd Ed., by MWH) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & > Baxter Vieux) - Chemistry and Chemical Engineering : > > Mass Transfer Operations (3rd Ed., Treybal) > Mass Transfer in Multicomponent Mixtures (J.A. Wesseling & R. Krishna) > + original Ebook > Principles and Modern Applications of Mass Transfer Operations (Jaime > Benitez) > Diffusion - Mass Transfer in Fluid Systems (2nd Ed., Cussler) > Separation Process Principles (1st Ed, Seader & Henley) > Separation Process Principles (2nd Ed, Seader & Henley) > Equilibrium Staged Separations (Wankat) > Principles of Chemical Separations with Environmental Applications > (Richard D. Noble) > Product and Process Design Principles: Synthesis, Analysis, and > Evaluation (2nd Ed., Seider & Seader) + Ebook > Principles and Practices of Automatic Process Control (3rd Ed., Smith > & Corripio) + Ebook > Process Dynamics and Control (2nd Ed., Seborg & Edgard) > Process Control - A First Course with MATLAB (P.C. Chau) + Ebook > Process Dynamics: Modeling, Analysis and Simulation (Wayne Bequette) > Plant Design and Economics for Chemical Engineers, (5th Ed., Peters & > Timmerhaus) + Ebook > Basic Principles and Calculations in Chemical Engineering (6th Ed., > Himmelblau) > Basic Principles and Calculations in Chemical Engineering (7th Ed., > Himmelblau) > Unit Operations of Chemical Engineering (6th Ed., McCabe & Smith) > Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) > Advanced Transport Phenomena (John C. Slattery) > Introduction to Transport Phenomena (W. Thomson) > Transport Phenomena: A Unified Aprroach (Robert S. Brodkey & Harry C. > Hershey) + Ebook > Transport Phenomena in Multiphase Systems (Faghri & Zhang) > Modeling in Transport Phenomena: A Conceptual Approach (2nd Ed., > Ismail Tosun) + original Ebook > Transport Phenomena (2nd Ed., Bird & Stewart) + Ebook > Solutions to Class 1&2 - Transport Phenomena (Bird) > Chemical Engineering Design (Coulson & Richardson's Chemical > Engineering - Volume 6) - (4th Ed., Sinnott) + original Ebook > Chemical Engineering Design and Analysis - An Introduction (Duncan & > Reimer) > Chemical Reaction Engineering (3rd Ed., Levenspiel) + Ebook > Chemical Reactor Analysis and Design Fundamentals (Rawlings & Ekerdt) > + Ebook > Fundamentals of Chemical Reaction Engineering (1st Ed., Davis) > Conceptual Design of Distillation Systems (1st Ed., Doherty & Malone) > Distillation Theory and its Application to Optimal Design of > Separation Units (F.B. Petlyuk) + original Ebook > Batch Distillation: Simulation, Optional Design and Control (Diwekar) > + Ebook > Fluid Mechanics for Chemical Engineers, (3rd Ed., Noel de Nevers) > Introduction to Chemical Processes: Principles, Analysis, Synthesis > (1st Ed., Regina M. Murphy) > Optimization of Chemical Processes (2nd Ed., Edgar & Himmelblau) + > Ebook > Chemical and Engineering Thermodynamics (3rd Ed., Stanley I. Sandler) > Chemical, Biochemical, and Engineering Thermodynamics (4th Ed., > Stanley I. Sandler) > Introduction to Chemical Engineering Thermodynamics (6th Ed., Smith & > Van Ness) > Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & > Van Ness) > Introductory Chemical Engineering Thermodynamics (J. Elliott, C. Lira) > Engineering and Chemical Thermodynamics (Koretsky) > Phase Equilibria, Phase Diagrams and Phase Transformations - Their > Thermodynamic Basis (2nd Ed., Mats Hillert) > Introduction to Chemical Kinetics and Chemical Reaction Engineering > (Missen, Mims) + original Ebook > Principles of Chemical Kinetics (James House) > Transport Processes and Unit Operations (3rd Ed., Christie J. > Geankoplis) > Transport Processes and Separation Process Principles (4th Ed., > Christie J. Geankoplis) > Elementary Principles of Chemical Processes (3rd Ed., Felder & > Rousseau) + Ebook > Chemical Process Safety: Fundamentals with Applications (2nd Ed., > Crowl & Louvar) + Ebook > Elements of Chemical Reaction Engineering (3rd Ed., Fogler) > Elements of Chemical Reaction Engineering (4th Ed., Fogler) > Group Theory with Applications in Chemical Physics (Patrick Jacobs) > Food Analysis (3rd Ed., Suzanne Nielsen) > Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, > v2.5, 3rd Ed. (Brian F. Woodfield & Matthew C. Asplund) > Introductory Chemistry and CW+ GradeTracker Access Card Package, 2nd > Ed. (Nivaldo J. Tro) > Introductory Chemistry: Concepts and Connections, 4th Ed. (Charles H > Corwin) > Prentice Hall Lab Manual Introductory Chemistry, 4th Ed. (Charles H > Corwin) > General, Organic and Biological Chemistry: Structures of Life with > Student Access Kit for MasteringGOBChemistry», 2nd ed. (Karen C. > Timberlake) > Chemistry: An Introduction to General, Organic, and Biological > Chemistry with The Chemistry Place CD-ROM, 9th Ed (Karen C. > Timberlake) > Conceptual Chemistry, 3rd Ed (John A. Suchocki) > Explorations in Conceptual Chemistry: A Student Activity Manual > (Jeffrey Paradis) > Criminalistics: An Introduction to Forensic Science (9th Ed., Richard > Saferstein) > Physical Chemistry with Spartan Student Physical Chemistry Software > (Thomas Engel & Philip Reid) > Quantum Chemistry and Spectroscopy with Spartan Student Physical > Chemistry Software (Thomas Engel & Philip Reid) > Themodynamics, Statistical Thermodynamics, and Kinetics (Thomas Engel > & Philip Reid) > Physical Chemistry (7th. Ed., Peter Atkins & Julio de Paula) > Chemistry An Introduction to Organic, Inorganic and Physical Chemistry > (3rd Ed., Catherine E. Housecroft & Edwin Constable) > General Chemistry: The Essential Concepts (4th Ed., Raymond Chang) > Chemistry: The Molecular Nature of Matter and Change (3rd Ed., Martin > Silberberg) > Chemistry: The Molecular Nature of Matter and Change (4th Ed., Martin > Silberberg) > General, Organic and Biochemistry (3rd ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (4th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (5th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > Fundamentals of Chemistry (3rd Ed., David E Goldberg) > Fundamentals of Chemistry (4th Ed., David E Goldberg) > Fundamentals of Chemistry (5th Ed., David E Goldberg) > Modern Analytical Chemistry (Harvey) > General Chemistry Lab Manual (Petra A. M. van Koppen) > Practical Interfacing in the Laboratory: Using a PC for > Instrumentation, Data Analysis and Control (Stephen E. Derenzo) > Bioprocess Engineering Principles (Pauline M. Doran) - Industrial Engineering, Business, Economics and Finance : > > Engineering Economy (5th Ed., Leland T Blank & Anthony Tarquin) > Engineering Economy (6th Ed., Leland T Blank & Anthony Tarquin) + > original Ebook > Contemporary Engineering Economics (4th Ed., Chan Park) > Engineering Economy (13th Ed, Sullivan) > Introduction to Statistical Quality Control (5th Ed., Douglas C. > Montgomery) > Managing Engineering and Technology (4th, Morse & Babcock) > (4th Ed, Gryna) > Juran's Quality Planning and Analysis for Enterprise Quality (5th Ed., > Gryna, Chua & DeFeo) > Quality (4th Ed., Summers) > Quality Management (5th Ed., Goetsch & Davis) > Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) > Value Driven Product Planning and Systems Engineering (H. E. Cook & L. > A. Wissmann) > Work Systems: The Methods, Measurement & Management of Work (Mikell P. > Groover) > Occupational Safety and Health for Technologists, Engineers, and > Managers (5th Ed., Goetsch) > Occupational Safety and Health for Technologists, Engineers, and > Managers (6th Ed., Goetsch) > Introduction to Engineering Technology (6th Ed., Robert J. Pond) > Manufacturing Facilities Design and Material Handling (3rd Ed., Meyers > & Stephens) > Fundamentals of Forensic Science (Max Houck & Jay Siegel) > Introduction to Optimum Design (2nd Ed., Jasbir Arora) > Project Management for Business and Engineering : Principles and > Practice (2nd Ed., John Nicholas) > ISO 9001:2000 Quality Registration Step-by-Step (3rd Ed., Fred Dobb) > Systems for Planning and Control in Manufacturing (D. K. Harrison & D. > J. Petty) > Planning and Control of Manufacturing Operations (John Kenworthy) > Professionalism: Real Skills for Workplace Success (Anderson & Bolt) > Customer Service: Career Success Through Customer Loyalty (4th Ed., > Timm) > Customer Service: A Practical Approach (3rd Ed., Harris) > Customer Service: A Practical Approach (4th Ed., Harris) > Serving Internal and External Customers (Anne Swartzlander) > Customer Relationship Management: The Bottom Line to Optimizing Your > ROI (Anton & Petouhoff) > Engineering Economy and the Decision-Making Process (Joseph C. > Hartman) > Engineering Management: Challenges in the New Millennium (C M Chang) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Supply Chain Management (3rd Ed., Sunil Chopra & Peter Meindl) > Industrial Safety and Health Management (5th Ed., C. Ray Asfahl) > Computer Numerical Control: Operation and Programming (3rd Ed., Jon S. > Stenerson & Kelly Curran) > Introduction to Management Science and Student CD Package (8th Ed., > Bernard W. Taylor) > Introduction to Management Science with Student CD (9th Ed., Bernard > W. Taylor) > Operations Research: An Introduction (8th Ed., Taha) > Decision Support Systems and Intelligent Systems (7th Ed., Turban, > Aronson, Ting-Peng Liang) > Decision Support and Business Intelligence Systems (8th Ed., Turban, > Aronson, Ting-Peng Liang & Sharda) > Operations Management and Student CD Package (7th Ed., Krajewski, > Ritzman) > Operations Management: Process and Value Chains (8th Ed., Krajewski, > Ritzman & Malhotra) > Operations Management (8th Ed., Jay Heizer & Render) > Introduction to Operations and Supply Chain Management with Advanced > Decision Support Tools (Cecil Bozarth) > Managing Business Process Flows: Principles of Operations Management > (2nd Ed., Anupind, Chopra, Deshmukh, et al) > Operations Management & Student CD Package (8th Ed., Heizer & Render) > Principles Of Operations Management and Student CD (6th Ed., Heizer & > Render) > Foundations of Operations Management (Ritzman & Krajewski) > Decision Modeling with Microsoft¬ Excel (6th Ed., Moore & Weatherford) > Managing Quality: Integrating The Supply Chain (3rd Ed., S. Thomas > Foster) > Six Sigma: Basic Tools and Techniques (Donna C.S. Summers) > First Course in Quality Engineering (KS Krishnamoorthi) > Statistical Quality Design and Control (2nd Ed., DeVor, Chang & > Sutherland) > Economics: A Tool for Critically Understanding Society (7th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Economics: A Tool for Critically Understanding Society (8th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Introduction to Economic Reasoning (6th Ed., William D. Rohlf, Jr.) > Introduction to Economic Reasoning (7th Ed., William D. Rohlf, Jr.) > Essential Foundations of Economics (3rd Ed., Robin Bade & Michael > Parkin) > Understanding Modern Economics (Roger LeRoy Miller) > The Economics of Macro Issues (3rd Ed., Roger LeRoy Miller & Daniel K. > Benjamin) > Foundations of Economics (3rd Ed., Robin Bade & Michael Parkin) > Economics Today (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (14th Ed., Roger LeRoy Miller) > Economics (Michael A. Leeds, Peter von Allmen & Richard C. Schiming) > Economics: Private Markets and Public Choice (7th Ed., Robert B. > Ekelund, Jr., Rand W. Ressler & Robert D. Tollison) > Principles of Economics, 7th Ed. (Roy J. Ruffin & Paul R. Gregory) > The Economics of Public Issues (14th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > The Economics of Public Issues (15th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > Macroeconomics (7th Ed., Michael Parkin) > Macroeconomics (8th Ed., Michael Parkin) > Foundations of Microeconomics (3rd Ed., Robin Bade & Michael Parkin) > Foundations of Macroeconomics (3rd Ed., Robin Bade & Michael Parkin) > Microeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Macroeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Economics Today: The Micro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Micro View (14th Ed., Roger LeRoy Miller) > Microeconomics (7th Ed., Michael Parkin) > Microeconomics (8th Ed., Michael Parkin) > Macroeconomics (2nd Ed., Stephen D. Williamson) > Macroeconomics (3rd Ed., Stephen D. Williamson) > Macroeconomics Update Edition (5th Ed., Andrew B. Abel, Ben S. > Bernanke) > Macroeconomics (6th Ed., Andrew B. Abel, Ben S. Bernanke & Dean > Croushore) > Macroeconomics (10th Ed., Robert J. Gordon) > Economic Growth (David N. Weil) > Money, the Financial System, and the Economy (5th Ed., R. Glenn > Hubbard) > Money, the Financial System, and the Economy (6th Ed., R. Glenn > Hubbard) > The Economics of Money, Banking and Financial Markets (8th Ed., > Frederic S. Mishkin) > Principles of Money, Banking, and Financial Markets (11th Ed., > Lawrence S. Ritter, William L. Silber & Gregory F. Udell) > International Economics (3rd Ed., James Gerber) > International Economics (4th Ed., James Gerber) > International Economics (7th Ed., Steven Husted & Michael Melvin) > World Trade and Payments: An Introduction (9th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > World Trade and Payments: An Introduction (10th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > International Economics: Theory and Policy (7th Ed., Paul R. Krugman & > Maurice Obstfeld) > International Money and Finance (7th Ed., Michael Melvin) > Economic Development (9th Ed., Michael P. Todaro & Stephen C. Smith) > Microeconomics (4th Ed., Jeffrey M. Perloff) > Microeconomics (Don E. Waldman) > Microeconomics: Theory and Applications with Calculus (Jeffrey M. > Perloff) > Environmental Economics and Policy (5th Ed., Tom Tietenberg) > Environmental and Natural Resource Economics (7th Ed., Tom Tietenberg) > Health Economics (3rd Ed., Charles E. Phelps) > & Elizabeth J. Jensen) > Modern Industrial Organization (4th Ed., Dennis W. Carlton & Jeffrey > M. Perloff) > Modern Labor Economics: Theory and Public Policy (9th Ed., Ronald G. > Ehrenberg & Robert S. Smith) > Law and Economics (4th Ed., Robert Cooter & Thomas Ulen) > Law and Economics (5th Ed., Robert Cooter & Thomas Ulen) > Market Regulation (Roger Sherman) > Public Finance and the American Economy (2nd Ed., Neil Bruce) > The Economics of Sports (2nd Ed., Michael A. Leeds & Peter von Allmen) > The Economics of Sports (3rd Ed., Michael A. Leeds & Peter von Allmen) > Introduction to Econometrics, Brief Edition (James H. Stock & Mark W. > Watson) > Introduction to Econometrics (2nd ed., James H. Stock & Mark W. > Watson) > Econometrics: A Modern Introduction (Michael P. Murray) > Using Econometrics: A Practical Guide (5th Ed., A.H. Studenmund) > Mathematical Methods for Economics (2nd Ed., Michael Klein) > Personal Finance with Financial Planning Software (3rd Ed., Jeff > Madura) > Finance: Investments, Institutions, and Management - Update (2nd Ed., > Stanley G. Eakins) > Introduction to Finance (Lawrence J. Gitman & Jeff Madura) > Principles of Managerial Finance Brief plus MyFinanceLab Student > Access Kit (4th Ed., Lawrence J. Gitman) > Principles of Managerial Finance plus MyFinanceLab Student Access Kit > (11th Ed., Lawrence J. Gitman) > Corporate Finance plus MyFinanceLab Student Access Kit (Jonathan Berk > & Peter DeMarzo) > Risk Takers: Uses and Abuses of Financial Derivatives (John > Marthinsen) > Theory of Asset Pricing (George Pennacchi) > Multinational Business Finance (11th Ed., David K. Eiteman, Arthur I. > Stonehill & Michael H. Moffett) > Fundamentals of Multinational Finance (2nd Ed., Michael H. Moffett, > Arthur I. Stonehill & David K. Eiteman) > Cases in International Finance (2nd Ed., Gunter Dufey & Ian H. Giddy) > Fundamentals of Investing plus MyFinanceLab Student Access Kit and > OTIS Student Access Kit (10th Ed., Lawrence J. Gitman & Michael D. > Joehnk) > Fundamentals of Investing & Wharton's OTIS Student Access Kit Package > (9th Ed., Lawrence J. Gitman & Michael D. Joehnk) > OTIS: Online Trading and Investment Simulator Student Access Kit > (Wharton Learning Lab) > Derivatives Markets (2nd Ed., Robert L. McDonald) > Principles of Risk Management and Insurance (9th Ed., George E. Rejda) > Principles of Risk Management and Insurance (10th Ed., George E. > Rejda) > Financial Markets and Institutions (5th Ed., Frederic S. Mishkin & > Stanley G. Eakins) > Statistical Analysis of Financial Data in S-PLUS (Rene A. Carmona) > Statistics and Finance: An Introduction (David Ruppert) > Mathematical Statistics for Economics and Business (Ron C. > Mittelhammer) - Materials Engineering : > > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials Science and Engineering: An Introduction (6th Ed., William > D. Callister, Jr.) > Materials Science and Engineering: An Introduction (7th Ed., William > D. Callister, Jr.) > Fundamentals of Materials Science and Engineering : Integrated > Approach (2nd Ed., William D. Callister, Jr.) > Science and Design of Engineering Materials (2nd Ed., Schaffer, > Saxena, et al) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Foundations of Materials Science and Engineering (3rd Ed, Smith) > Foundations of Materials Science and Engineering (4th Ed, Smith) > Plastics: Materials and Processing (3rd Ed., Strong) > Engineering Materials: Properties and Selection (8th Ed., Budinski) > Introduction to Materials Science for Engineers (6th Ed., Shackelford) > Materials: Engineering, Science, Processing and Design (Michael Ashby, > Dr Hugh Shercliff & David Cebon) > Principles of Corrosion Engineering and Corrosion Control (Zaki Ahmad) > Analysis and Performance of Fiber Composites (3rd Ed., Bhagwan > Agarwal, Lawrence Broutman & K. Chandrashekhara) > Basic Engineering Plasticity: An Introduction with Engineering and > Manufacturing Applications (David Rees) > Steels: Microstructure and Properties (3rd Ed. Bhadeshia & Honeycombe) > Theory of Plasticity (3rd Ed. Jagabanduhu Chakrabarty) > Engineering Materials Vol. 1 : An Introduction to Properties, > Applications and Design (3rd Ed., Michael Ashby & David R H Jones) > Engineering Materials Vol. 2 : An Introduction to Microstructures, > Processing and Design (3rd Ed., Michael Ashby & David R H Jones) > Plastics: Microstructure and Engineering Applications (3rd Ed., Nigel > Mills) > Laser Processing of Engineering Materials : Principles, Procedure and > Industrial Application (John Ion) > Sintering : Densification, Grain Growth and Microstructure (Suk-Joong > Kang) > Biomaterials Science : An Introduction to Materials in Medicine (2nd > Ed., Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Laminar Composites (by George Staab) + original Ebook > contact me to : newbergh123@yahoo.com > Water Treatment: Principles and Design, 2nd Edition for me. thank you very much! liew168@sina.com > === Subject: Re: List of solutions manual (thousands) posting-account=U0LgTAoAAACT3plNs1Bj32A1VT9Tz6dl 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; InfoPath.2),gzip(gfe),gzip(gfe) > My List of Solutions Manual > contact me to : newbergh...@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. This list (not links) is available from : http://rapidshare.com/files/59002351/List of solutions manual.txt - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files ... read more > I Am in possesion of the following Solution Manuals and will give them for free!!!!!!!!!!!!!!!!!!!!!! just email me at mickeydizzle@gmail.com -Engineering Mechanics Statics 10th & 11th by Hibbeler -Engineering Mechanics Dynamics 11th by Hibbeler -Engineering Mechanics Dynamics 4th Bedford === Subject: mike lalonde posting-account=3isBZgoAAADJM-2G3Oc0CRLy9Sk4yeg_ 5.0),gzip(gfe),gzip(gfe) 42434 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle bacini sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde 4 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde michael lalonde mike lalonde temagami henry merchant tammy dubriel gerry dubriel victor dubriel yvan tonge yvan steve tonge 3 === Subject: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=nsrQxAoAAACDkV1_uYvq7QQjzxtFXYoo Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Do you have this one available? How can I get it? Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton please email me if you have it. I only need solution for ch 9 to 13 I have the rest if you're interested let me know student482@gmail.com alt.history.british, alt.guitar.amps === Subject: See the accepted papers, keynote lecture, plenary lectures, the contents of the Book of the Proceedings (i.e. accepted papers). WSEAS Post-Conference Report for the Conferences MACMESE '07 and DNCOCO '07 (124 images) posting-account=KWYMKQoAAAArfstGv6VUH6u1SaWpz4Xi 5.1),gzip(gfe),gzip(gfe) Click on the link below and see the accepted papers, the keynote and Plenary Speeches, the contents of the Book of the Proceedings as well as nice photos from an MACMESE '07 and DNCOCO '07 excellent conferences in Trinidad and Tobago Islands , co-organized by the University of West Indies and WSEAS ------------------------------------- http://www.wseas.com/wseas/reports/trinidadandtobago/index.html Post-Conference Report for the WSEAS Conferences: MACMESE '07 and DNCOCO '07 Trinidad and Tobago Islands (Caribbean Sea), November 5-7, 2007 http://www.wseas.com/wseas/reports/trinidadandtobago/index.html * This report contains 124 images copyrighted by the WSEAS. All rights reserved. * If you need some image with high resolution please click on the images below * If you need some image with extremely high resolution, contact us by email The University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences, Department of Mathematics and Computer Science, St. Augustine, Trinidad (W. I.) http://www.wseas.com/wseas/reports/trinidadandtobago/index.html and the WSEAS Society (http://www.wseas.org) , coorganized the following two parallel conferences: * 9th WSEAS Int. Conf. on MATHEMATICAL and COMPUTATIONAL METHODS in SCIENCE and ENGINEERING (MACMESE'07) (This conference was part of the MMACTEE international conference until 2006) * 6th WSEAS Int. Conf. on DATA NETWORKS, COMMUNICATIONS, COMPUTERS (DNCOCO '07), (The name of this conference was ISCOCO until 2005) OPENING, KEYNOTE, PLENARY SPEECHES: The two parallel Conferences were opened by Professor Bal Bhatt, who is director of the Department of Mathematics and Computer Science of the University of West Indies and he was the chairman of the conference and Professor Winston Mellowes, who is the Chairman, Professor Dyer Narinesingth, who is the Dean of the University of West Indies, the Campus Principal Professor Bridget Brereton, Mr. John Roopchan of the Ministry of Education and Dr. Bhoendradatt Tewarie, Director of the Institute of Critical Thinking, where the conference was held. After the opening ceremony the first keynote speaker was Professor Biswa N. Datta (Distinguished Research Professor at the Northern Illinois University, USA), who has presented the recent advances on computational methods for active vibration control and model updating in vibrating structures. Professor Eyad H. Abed (Institute for Systems Research, Electrical and Computer Engineering, University of Maryland, USA) who was PLENARY SPEAKER also presented new results on selective modal analysis of dynamic systems On Tuesday, 6th November 2007 (2nd day of the conference), Professor Imre J. Rudas (Institute of Intelligent Engineering Systems John von Neumann Faculty of Informatics Budapest Tech, Budapest, Hungary) who was PLENARY SPEAKER also described interesting aggregation procedures in intelligent systems. http://www.wseas.com/wseas/reports/trinidadandtobago/index.html On Tuesday evening was the cocktail party for all participants of the WSEAS Conference, who were invited at the office of the Campus Principal Professor Bridget Brereton (See pictures below) Both of the WSEAS Conferences in Trinidad were characterized by their friendly atmosphere (see photos below) as well as the high quality of the presentations and discussions. A variety of topics constituted the focus of paper submissions. In regular sessions papers addressed several interesting topics. Prominent lectures provided key-note and plenary speeches for the conference. Moreover, special sessions were organized, and invited lectures were given by well-known researchers. With pride, the WSEAS received the following Important Contributions and upgraded them as Keynote and Plenary Lectures.: KEYNOTE LECTURE: Recent Advances on Computational Methods for Active Vibration Control and Model Updating in Vibrating Structures : Linking Control to Industry by Prof. Biswa N. Datta, Northern Illinois University, USA. PLENARY LECTURE 1: New Results on Selective Modal Analysis of Dynamic Systems by Prof. Eyad H. Abed, University of Maryland, Maryland, USA. PLENARY LECTURE 2: Polynomial Optimization via Sums of Squares Relaxations by Prof. Mihai Putinar, University of California at Santa Barbara, CA, USA. PLENARY LECTURE 3: Aggregation procedures in intelligent systems by Prof. Imre J. Rudas, Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Hungary. PLENARY LECTURE 4: Selection Problems and Multi-criteria Decision Making by Dr. Alexey L Sadovski, Texas A&M University-Corpus Christi, USA. BENEFITS FOR THE PARTCIPANTS: WSEAS, http://www.wseas.org gave a very strong and important tool to all the participants: A new username and password without expiry date for on-line access in the WSEAS Conference proceedings FOR EVER. Conference Statistics Submitted papers: 335 Accepted papers: 147 acceptance ratio = (Number of accepted papers / Number of Submitted)*100 = 43.88% Remark: Two withdrawn accepted papers are considered as accepted papers in our Statistics. .: REVIEW PROCESS: Each paper was reviewed at least by 3 independent reviewers. The WSEAS Secretariat sent each paper to 5 reviewers. Some papers received reviews from 5 different referees. The WSEAS Secretariat forwarded these comments by personalized emails to the responsible for the correspondence author. The full list of the reviewers will be available in the web page: http://www.worldses.org/reviewers.htm The additional features of these 2 conferences 1) Publication of the Proceedings in 3 media: hard-copy, CD, E-Library (A) One Book in the Electrical and Computer Engineering Series and Energy and Environmental Engineering Series of WSEAS (see details, contents, author indices and editors below) with ISBN and ISSN indexed by the major Citation Indices (ISI ranked): www.worldses.org/indexes (B) CD-ROM Proceedings with pages' numbers with ISBN and ISSN indexed by the major Citation Indexes: www.worldses.org/indexes (C) E-Library: http://www.wseas.org/online and possible, for a very small number of papers: (D) JOURNAL PUBLICATION: Expanded and enhanced versions of papers published in the conference proceedings also going to be considered for possible publication in one of the WSEAS journals that participate in the major International Scientific Indices (Elsevier, Scopus, EI, Compendex, INSPEC, CSA .... see: www.worldses.org/indexes ). 2) WSEAS gave a very strong and important tool to all the participants: A new username and password without expiry date for on- line access in the WSEAS Conference proceedings FOR EVER. 3) The Participants received 6 very rich coffee-breaks (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences), 1 Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences) and 1 Gala Dinner with the high quality of the WSEAS 4) Cultural and social part as usual in WSEAS events. 5) The conference Books (Hard-Copy Proceedings), CD-ROM proceedings and Journals (with selected papers) published by WSEAS Press continue to sell for a long time after the meeting has taken place. This is another demonstration of the prestige the scientific community attribute to the meetings organized by the WSEAS. .: BOOK (hard-copy of the Proceedings): Editors: Balswaroop Bhatt (Trinidad and Tobago), Bhoendradatt Tewarie (Trinidad and Tobago), Athina Lazakidou (Greece), Konstantinos Siasiakos (Greece). Pages : 506, price: 80 EUR [Contents], [Order], [Full PDF of the Papers], [Help] .: JOURNALS: .: What is the Permanent Procedure for additional Journal publication for a very small number of High-Quality Papers presented in the WSEAS Conferences in China (after the recommendation of Chairmen). So, the authors with accepted & presented papers received the following e- mail: We have started now the procedure for the evaluation of the extended versions of your papers for possible inclusion in the WSEAS journals after new rounds of review. INTRODUCTION: You know that our goal is to maintain very strong international journals, to increase the impact of our beloved WSEAS Transactions, really top journals as they really are. To this end, we need only high quality papers, breakthrough works of archival value, i.e. papers that are well written from any point of view, completed studies (with their numerical examples or experiments that must be compared with the previous results in the literature), excellent english language and of course correct WSEAS format. The papers also must be substantially extended version of the paper that was presented in the conference (with more than 40% new material). We need papers that will attract the attention of other scholars citing them increasing our impact. In the next few years, the WSEAS transactions must be in every academic library, in every corner of the earth. To this end, we need your high quality contribution. HOW TO PROCEED: a) Check very carefully if your idea is really important, breakthrough in your field and can appear in a Journal of the quality and the level of the WSEAS Transactions. If you doubt, do not send it so easily. Your paper must not be only a good idea. It must be a complete study with theoretical background, complete bibliographical references; without grammatical and syntactical errors. For theoretical works: full comparison with previous published papers is necessary. We need numerical examples, applicability of the method, originality, novelty and directions for future research. For experimental or computational works: full comparison with previous published papers is necessary. We need real experiments with the necessary documentation, while for computational work, we need full benchmarks. Of course along discussions for the applicability of the method, originality, novelty and directions for future research. b) Complete the extended version of your paper until December 31, 2007 and upload it via http://............... (the full web address was given only to authors that presented a paper) until December 31, 2007 c) If your extended version fulfills the paragraph a), then our Editors will send it to 3 independent Reviewers outside your country. If not, our Editors are entitled to reject it from this early stage informing you properly. The positive answer of the 3 reviewers is necessary (attention: 2 yes and 1 no implies NO, i.e. rejection). d) Our Editors will collect the reviewers' remarks and will send them again to you for acceptance/ acceptance after minor revision / acceptance after major revision / rejection e) Possibly new rounds of review will be needed. f) No additional fee is needed in case of acceptance. After all this procedure, the accepted papers that come from WSEAS Conferences in Canada will be published in the various WSEAS Transactions. IF you miss the deadline of December 31, 2007 , or if your paper was not presented in the WSEAS Conferences, THEN: you can upload it quite independently as regular paper from the WSEAS Site for the Journals: http://www.worldses.org/journals/index.html The final list of the papers must have the approval of our Editors and 3 Reviewers, and of course the Editor-in-Chief of the particular Journal. We want only authors that presented their papers to complete this web form: http://............... (the full web address was given only to authors that presented a paper) So, in this form you will need a password (the password was given only to the authors that presented a paper). .: BEST STUDENT PAPERS: The Organizing Committee received the forms that the Session Chairmen filled in after the end of their Sessions and after additional evaluation and discussion decided the following. The Criteria were: a) Originality and scientific impact b) Good presentation c) Paper presented by a student The results of this evaluation will be announced soon in the web page: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html .: INDICES: PROCEEDINGS: The Proceedings related to the Conference are covered by: 1. ISI (ISINET) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 6. ULRICH 9. Directory of Published Proceedings 10. Computer Science Bibliography Administrator 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Engineering Information 15. SCOPUS 16. EBSCO 17. EMBASE 18. Compendex (CPX) 19. GEOBASE 20. BIOBASE 21. BIOTECHNOBASE 22. FLUIDEX 23. OceanBase 24. BEILSTEIN Abstracts 25. World Textiles 26. MEDLINE 27. British Library 28. National Library of Greece 29. German National Library of Science and Technology 30. IARAS Index JOURNALS: The WSEAS journals are covered by: 1. ISI through the INSPEC (IEE) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 7. ULRICH 9. Computer Science Bibliography Administrator 10. British Library 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Swets Information Services 15. Engineering Information 16. SCOPUS 17. EBSCO 18. EMBASE 19. Compendex (CPX) 20. Geobase 21. BIOBASE 22. BIOTECHNOBASE 23. FLUIDEX 24. OceanBase 25. BEILSTEIN Abstracts 26. World Textiles 27. MEDLINE 28. Mayersche 29. Index of Information Systems Journals 30. National Library of Greece 31. IARAS Index .: SOCIAL PART (Coffee-Breaks, Banquet, Excursions) 6 very rich coffee-breaks with Coffee, Tea, Milk, Sweets, Cakes, Pastries, Juices and Sandwiches (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Excellent Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Gala Dinner. Participants enjoyed a wonderful night. .: Some Excursions took place after the conference. See the pictures: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html === Subject: Re: Regarding solution manual for Introduction to Algorithm. Thomas H. Cormen. posting-account=T7fhkAoAAADh6aLufWf8lNSXnUk_5MhJ CLR 1.1.4322),gzip(gfe),gzip(gfe) Did you find the soultions manual? If you do, could you please send it to me. I would appreciate it a lot! === Subject: I need Solution manual posting-account=2Ao9ggkAAAB1JcOMWiDDOjkHclbisJtt Gecko/20061010 Firefox/2.0,gzip(gfe),gzip(gfe) (squid/2.5.STABLE9) I am studying Engineering Electromagnetics. In the Course Some problem I am encountering. I need a Solution Manual of ENGINEERING ELECTROMAGNETICS (7/E) BY HAYT AND BUCK mail this solution of masaddique_159@yahoo.com THIANK YOU === Subject: Re: I need Solution manual Bye! === Subject: Much Help Needed on Difficult Calculus Problems Can anyone offer me any advice on how to work and answer any of the following questions? 1) Find the limit of the sequence x = n square root of n! as n tends to ¡. 2) Determine whether the series ¡ á (n!)^(-1/n) is convergent or divergent. n=1 3) Find the sum of the series ¡ á (1/2^n) tan (x/2^n) for every value of x. n=1 -Drew === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. That's as n tends to infinity. Or you could say informally that n becomes infinite. The problem as stated is pretty trivial since n sqrt(n!) > n for n > 1. --Lynn === Subject: Re: Much Help Needed on Difficult Calculus Problems in alt.math.undergrad: > Can anyone offer me any advice on how to work and answer > any of the following questions? > 1) Find the limit of the sequence x = n square root of n! > as n tends to ¡. Is there a typo in this one? > 2) Determine whether the series > ¡ > á (n!)^(-1/n) is convergent or divergent. > n=1 The denominator of the n-th term is the geometric mean of 1, 2, ..., n. Use the arithmetic mean - geometric mean inequality to compare with a familiar series. [...] Brian === Subject: helpppp pleasee!! whats is the antiderivative of 4x^-1 ?? === Subject: Re: helpppp pleasee!! in alt.math.undergrad: > whats is the antiderivative of 4x^-1 ?? The derivative of ln(x) with respect to x is 1/x, so the derivative of 4 ln(x) is 4/x. Brian === Subject: helpppp mee pleasee i need help using the substitution process to find... the antiderivative of r(radical r^2+2) dr help pleaseee === Subject: Re: helpppp mee pleasee >i need help using the substitution process to find... >the antiderivative of r(radical r^2+2) dr >help pleaseee If that's r sqrt(r^2 + 2) dr u = r^2 + 2 du = 2 r dr, so 1/2 du = r dr Antiderivative of 1/2 sqrt(u) du = 1/2 u^(1/2) du = ? === Subject: sub.. substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this === Subject: Re: sub.. >substitution process to find antiderivative of r(e^-r^2) dr >pleaseee help me with this Your turn. What do you think? === Subject: Re: sub.. > substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this Your turn. What do you think? > think. That appears to be the entire difficulty. === Subject: help with substitution i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee === Subject: Re: help with substitution ok, but my answer has to have a +c in it i think === Subject: Re: help with substitution >i need help using the substitution process to find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. === Subject: Re: help with substitution i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to > learn how to use complicated rules like mathematics has and consequently > consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar lessons? Dave === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar > lessons? Especially *wrong* ones. in rebellion to?? Wonton to flout?? His math is wrong (or wong), too. sqrt -1 doesn't mean anything: sqrt is a function, and one can't subtract a numberfrom it. Maybe he means sqrt(-1). -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com> i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. Yet alas you're not the OP to call me on that. do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar > lessons? > I offer full service help. Why can't they learn English? Do they have a learning disability? Math has even more rules and they're harder rules. What help can be given to those who detest rules? ---- === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. > Yet alas you're not the OP to call me on that. > > do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar lessons? > I offer full service help. > Why can't they learn English? > Do they have a learning disability? > Math has even more rules and they're harder rules. > What help can be given to those who detest rules? ---- Not all OP's are speaking english by nature, have pity with them. -- Vooruit mensen, achteruit! (Elimineer x voor een e-mail) Hou-du. === Subject: Re: help with substitution > >i need help using the substitution process to > find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you > haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always > s capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > consider you unable to > learn how to use complicated rules like mathematics > has and consequently > consider it meaningless to help you. === Subject: [] help with substitution <25173561.1197114231915.JavaMail.jakarta@nitrogen.mathforum.org> help pleaseee I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always s capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > Help. I'm needing help substituting 'eggroll' with a word that coheres your sentence. consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. > === Subject: substitution????? substtution to find antiderivative of (5e^(-3g)) dg === Subject: Re: substitution????? >substtution to find antiderivative of (5e^(-3g)) dg u = -3 g du = -3 dg, so dg = ? === Subject: hellppp me out use the substitution to find the indefinite integral antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please === Subject: Re: hellppp me out <1432039.1197079325702.JavaMail.jakarta@nitrogen.mathforum.org>, The best help we can offer is to advise you to pay more attention in class, and read the assigned sections of the text. === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please cant be done, your hosed! (try dividing first) === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt > > helppp me please >cant be done, your hosed! (try dividing first) > A joke of some sort? === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please If you are going to post all your homework questions, why not group them together in one post so we can keep straight which homework we are doing for you? --Lynn === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please Hint: the derivative of t^3 + 6 t + 3 is 3 t^2 + 6 = 3 (t^2 + 2) === Subject: sorry i just dont get the substitution and... i dont get the substitution process.. can somebody xplain it to me, for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for === Subject: Re: sorry i just dont get the substitution and... >i dont get the substitution process.. can somebody xplain it to me, >for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for The basic idea is that you want to put the given expession in one of the forms that you know an antiderivative for, such as Int u^a du = u^(a+1) / (a + 1) + C for all a except a = -1 Int e^u du = e^u + C So let's look at 6x^2 dx / (2 x^3 + 7)^(3/2) You see that there's an x^3 in the denominator, and an x^2 in the numerator. That's promising, because if we substitute for the x^3 in the denominator, the derivative of x^3 is 2x^2 and so we may have something easy to substitute in the numerator as well (including the dx of course). Looking more closely, we see that we have 2 x^3, whose derivative is 6 x^2. Now that's VERY good, because that's exactly what's in the numerator. So, say we try u = 2 x^3 du = 6 x^2 dx Our expression becomes du / (u + 7)^(3/2) But wait! Now we realize that if we had made the substitution u = 2 x^3 + 7, then du still equals 6 x^2 dx and the resulting expression is even simpler, namely du / u^(3/2) Now *that* is an expression we know an antiderivative for! So, let's do the problem from the beginning. Find an antiderivative for 6x^2 dx / (2 x^3 + 7)^(3/2) Let u = 2 x^3 + 7 Then du = 6 x^2 dx Substituting into the original expression gives du / u^(3/2) = u^(-3/2) du for which an antiderivative is u^(-3/2 + 1) / (-3/2 + 1) = u^(-1/2) / (-1/2) = -2 u^(-1/2) = -2 / u^(1/2) = -2 / sqrt(u) Now, we want to get the answer back in terms of x, so we substitute for u [remember, u = 2 x^3 + 7] and get -2 / (2 x^3 + 7)^(1/2) or -2 / sqrt(2 x^3 + 7) Putting the problem in the form of an indefinite integral, we can now write Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / (2 x^3 + 7)^(1/2) + C or Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / sqrt(2 x^3 + 7) + C The C is the so-called 'constant of integration', which I assume has been discussed in conjunction with antiderivatives and indefinite integrals. === Subject: Complicated Differential Equation Sorry all I made a mistake in the first differential equation post. The equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, and V are all known constants. Is there any way to approximate this expression for i(t)? In my original post the expression didn't have the last term so some suggested using the Lambert W-Function, and another suggested using Newton's method. Would I still be able to use these methods, and if so how would I use them? === Subject: Re: Complicated Differential Equation <30569604.1197093354146.JavaMail.jakarta@nitrogen.mathforum.org>, > Sorry all I made a mistake in the first differential equation post. The > equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, > and V are all known constants. Is there any way to approximate this > expression for i(t)? In my original post the expression didn't have the last > term so some suggested using the Lambert W-Function, and another suggested > using Newton's method. Would I still be able to use these methods, and if so > how would I use them? V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2 gives i(t)/[V-b*i(t)-c*i(t)^2]*i'(t) = 1/a Now use partial fractions to split up i(t)/[V-b*i(t)-c*i(t)^2] At which point integration is possible, and one can solve for i(t). === Subject: =?windows-1256?B?Ljo6IFsgwt7c5uwgyNHk3MfjzCDt3tzm4yDIytPR?= =?windows-1256?B?7dogzOXH0t/cIMjU39zhIOPHysrV3ObRIObH4ePdx8w=?= =?windows-1256?B?3Mfl3CDH5OUg38fj3OEgXSA6Oi4=?= posting-account=OEMLPAoAAAD96Le1WgD9Upxh2I266gSV SIMBAR={94AA8A13-642B-404A-B4A4-C4EFD1151A5B}; Alexa Toolbar),gzip(gfe),gzip(gfe) === Subject: read plz posting-account=Yt8G1goAAACz_ktFECg3NbvAf5VVNJ0C Gecko/2007080210 GranParadiso/3.0a7,gzip(gfe),gzip(gfe) donot mail at hotkid_1@hotmail.com for solution manuals i donot have any === Subject: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, or just write a bit about the topic, it would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics (Well, you would probably still need logic...). === Subject: Re: Foundations of Mathematics, help? > mathematics, what I mean by that is the things that > define mathematics, and which it is based on. Much in > the same was that mathematics defines much of physics > (I think...) I disagree very sharply with that, by the way. Physics is 'defined' by what we observe in experiments, not by mathematics! > Anyway, I am posting here because I don't have much > of an idea of where to start. If anyone could advise > there, or just write a bit about the topic, it would > be greatly appreciated. > Oh, and if there is anyone out there who wouldn't > mind me asking them some questions that will > undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and > formal logic, and I will. But it also occurred to me > that these cannot be the only ways to define the > basis of mathematics (Well, you would probably still > need logic...). === Subject: Re: Foundations of Mathematics, help? mathematics, what I mean by that is the things > that define mathematics, and which it is based on. Much > in the same was that mathematics defines much of > physics (I think...) > I disagree very sharply with that, by the way. > way. Physics is 'defined' by what we observe in > experiments, not by mathematics! > I figured someone would say something like that... And I agree mostly, but it helped express the idea I was trying to, so I used it :) Anyway, I am posting here because I don't have > much of an idea of where to start. If anyone could > advise there, or just write a bit about the topic, it > would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me > know. P.S. I have been told before to study set theory > and formal logic, and I will. But it also occurred to > me that these cannot be the only ways to define the basis of mathematics (Well, you would probably > still need logic...). > ics and got a lot of intersting hits. Have you tried > that? Yup... === Subject: Re: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, You could read Fraenkel, Bar-Hillel and Levy, _Foundations of Set Theory_ which covers more than its title suggests; and Feferman _The Number Systems_ the subtitle of which is _Foundations of Algebra and Analysis_. > or just write a bit about the topic, it would be greatly appreciated. > Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. sci.logic might be good for that. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics You could try Mac Lane _Categories for Working Mathematicians_ > (Well, you would probably still need logic...). -- How unlike the home life of our own dear Queen. === Subject: Re: Foundations of Mathematics, help? === Subject: hey guys posting-account=vz_6QQoAAABOxomOXgeWKt9p9p4FZ-ez SV1),gzip(gfe),gzip(gfe) people join this new group and make it an interactive place !! === Subject: solutions manuals posting-account=m06QOgkAAACFEdunwVichFUaRyeknXjQ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Can I get the manuals for: 1) Linear Algebra with Applications, Otto Bretscher,( Pearson Custom Publishing) 2) Fundamentals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Edward B. Saff, Arthur David Snider, (Pearson Custom Publishing) Are they the complete set? You can e-mail me at === Subject: implementation of simplex method in C language hi, I am looking for an implementation of simplex method in C language. === Subject: Re: implementation of simplex method in C language : > I am looking for an implementation of simplex method in C language. Just by any wild chance, could this be a homework assignment? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: implementation of simplex method in C language >hi, >I am looking for an implementation of simplex method in >C language. http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html === Subject: Re: implementation of simplex method in C language posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > hi, > I am looking for an implementation of simplex method in C language. Why C? What difference does the language make? Or have you been asked to implement it yourself in C as part of an assignment???? I can suggest a number of commercially available LP packages. What are you willing to pay? === Subject: Water Treatment: Principles and Design, 2nd Edition posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) Can you send me Water Treatment: Principles and Design, 2nd Edition thank you very much liew168@sina.com === Subject: Re: Water Treatment: Principles and Design, 2nd Edition Can you send me Water Treatment: Principles and Design, 2nd Edition > thank you very much The answer is of course no. (If someone reading your post has the book and wishes to give it away, they would not know how to get it to you.) May I ask you a question? Why don't you go to a book shop and buy it like any normal person? (If you do so, do remember to mention the author and publisher.) -- How unlike the home life of our own dear Queen. === Subject: Re: List of solutions manual (thousands) posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) BERGH .8eæ.93.b9.81F > My List of Solutions Manual > contact me to : newbergh123@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. > This list (not links) is available from : > http://rapidshare.com/files/59002351/List of solutions manual.txt > > - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files > converted to pdf, real instructor sol. manual > Principles of Statics (10th Ed., Hibbeler) > Engineering Mechanics : Dynamics (11th Ed., Hibbeler)-Not mathcad > files converted to pdf, real instructor sol. manual > Principles of Dynamics (10th Ed., Hibbeler) > Mechanics of Materials (4th Ed, Hibbeler) > Mechanics of Materials (6th Ed, Hibbeler) > Mechanics of Materials (7th Ed, Hibbeler) > Statics and Mechanics of Materials (2nd Ed., Hibbeler) > Energy Principles and Variational Methods in Applied Mechanics (2nd > Ed., Reddy) > Theory of Vibrations with Applications (5th Ed., Thomson & Dahleh) > Engineering Vibrations (2nd Ed., Inman) > Engineering Vibrations (3rd Ed., Inman) > Theory of Vibration: An Introduction (2nd Ed., A.A. Shabana) > Vibration of Discrete and Continuous Systems (2nd Ed., Ahmed Shabana) > Introduction to Finite Element Vibration Analysis (Maurice Petyt) > Vibrations and Stability: Advanced Theory, Analysis, and Tools (2nd > Ed., Jon J. Thomsen) > Mechanical Vibrations (4th Ed., Rao) > Mechanical Vibration (William J. Palm, III) > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Finite Element Analysis Theory and Application with ANSYS (2nd Ed., > Moaveni) > Finite Element Analysis Theory and Application with ANSYS (3rd Ed., > Moaveni) > The Finite Element Method and Applications in Engineering Using ANSYS > (Madenci & Guven) + original Ebook > Modeling and Analysis of Dynamic Systems (3rd Ed, Close, Frederick & > Newell) > System Dynamics (1st Ed., William J Palm III) > System Dynamics: Modeling and Simulation of Mechatronic Systems (4th > Ed., Karnopp, Margolis & Rosenberg) > Concepts and Applications of Finite Element Analysis (4th Ed., Cook, > Malkus, Plesha & Witt) > Finite Element Modeling for Stress Analysis (Robert Cook) > Advanced Strength and Applied Elasticity (4th Ed., Ugural) > Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) + > original Ebook > Fracture Mechanics (2nd Ed., Anderson) > Mechanical Behavior of Materials (2nd Ed. Dowling) > Mechanical Behavior of Materials (3rd Ed. Dowling) > Mechanical Behavior of Materials (W.F. Hosford) + original Ebook > Mechanical Behavior of Materials (Keith Bowman) > Theory and Design for Mechanical Measurements (4th Ed, Figliola & > Beasley) > Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Principles of Metal Manufacturing Processes (Beddoes & Bibby) > Materials Selection in Mechanical Design (3rd Ed., Michael Ashby) > Introduction to Manufacturing Processes (3rd Ed., Schey) > Manufacturing Processes for Engineering Materials (5th Ed. Kalpakjian > & Smith) > Manufacturing, Engineering & Technology (4th Ed. Kalpakjian & Smith) > Manufacturing, Engineering & Technology (5th Ed. Kalpakjian & Smith) > Automation, Production Systems, and Computer-Integrated Manufacturing > (2nd Ed., Groover) > Introduction to Robotics: Mechanics and Control (3rd Ed, Craig) > Applied Manufacturing Process Planning: With Emphasis on Metal Forming > and Machining (Nelson, Schneider) > Linear State-Space Control Systems (Robert L. Williams, II & Douglas > A. Lawrence) > Rocket Propulsion Elements (7th Ed., George P. Sutton & Oscar Biblarz) > Mechanics of Flight (Warren F. Phillips) > Fundamentals of Airplane Flight Mechanics (David G. Hull) > Flight Performance of Fixed and Rotary Wing Aircraft (Antonio > Filippone) > Aircraft Structures for Engineering Students (3rd Ed., T.H.G. Megson) > + original ebook > Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson) > + original ebook > Mechanics of Aircraft Structures (2nd Ed, C. T. Sun) > Principles of Helicopter Aerodynamics (2nd Ed., Leishman) > Interactive Aerospace Engineering and Design (Dava Newman) > Fundamentals of Aerodynamics (3th Ed., Anderson) > Fundamentals of Aerodynamics (4th Ed., Anderson) > Introduction to Flight (5th Ed., Anderson) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Mechatronics (Sabri Cetinkunt) > Introduction to Mechatronics and Measurement Systems (3rd Ed., David > G. Alciatore & Michael B. Histand) > Introduction to Engineering Experimentation (2nd Ed., Wheeler & Ganji) > Gas Dynamics (3rd Ed., John & Keith) > Fundamentals of Gas Dynamics (2nd Ed, Robert D. Zucker) + original > Ebook > Internal Combustion Engines: Applied Thermosciences (2nd Ed., Ferguson > & Kirkpatrick) > Automotive Engines (8th Ed., Crouse) > Automotive Brake Systems Package (4th Ed., Rehkopf) > Automotive Engine Performance (2nd Ed., Halderman) > Automotive Mathematics (Jason C. Rouvel) > Blueprint Reading for the Machine Trades (6th Ed., Schultz & Smith) > Modern Welding Technology (6th Ed., Cary & Helzer) > Theory of Ground Vehicles (3rd Ed., J. Y. Wong) > Hydraulic Control Systems (Noah Manring) > Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. > Dixon) + original Ebook > Principles of Turbomachinery in Air-Breathing Engines (Baskharone) > Fundamentals of Jet Propulsion with Applications (Ronald D. Flack) > Fundamentals of Robotic Mechanical Systems: Theory, Methods, and > Algorithms (3rd Ed., Jorge Angeles) > Tissue Mechanics (Cowin, Doty) > BTEC First Engineering Curriculum Support Pack (Mike Tooley) > BTEC First Engineering (Mike Tooley) > Exploring Engineering: An Introduction for Freshmen to Engineering and > to the Design Process (Philip Kosky, George Wise, Robert Balmer & > William Keat) > Engineering Science (5th Ed., W. Bolton) > Fundamentals of Renewable Energy Processes (Aldo da Rosa) + original > Ebook > Renewable Energy (3rd Ed., SÀrensen or Sorensen) + original Ebook > Power Generation Technologies (Paul Breeze) + original Ebook > Concepts in Engineering (Holtzapple & Reece) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Autodesk Inventor (James M. Leake) > Foundations of Engineering (2nd Ed, Holtzapple & Dan Reece) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) - Electrical, Electronics & Computer Engineering > > Electrical Engineering: Principles and Applications (4th Ed., Allan R. > Hambley) > Electric Circuits (8th Ed., James W Nilsson & Susan Riedel) > Electric Circuits (7th Ed., James W Nilsson & Susan Riedel) > Introductory Circuits for Electrical and Computer Engineering (James > W. Nilsson, Susan A. Riedel) > Applied Electromagnetics: Early Transmission Lines Approach (Stuart M. > Wentworth) > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Introduction to Electric Circuits (6th Ed., Richard Dorf & James > Svoboda) > Introduction to Electric Circuits (7th Ed., Richard Dorf & James > Svoboda) > Modern Control Systems (11th Ed., Dorf) > System Dynamics (1st Ed., William J Palm III) > Electric Machines Analysis and Design Applying MatLab (Cathey) > Principles and Applications of Electrical Engineering (4th Ed, > Rizzoni) > Principles and Applications of Electrical Engineering (5th Ed, > Rizzoni) > Fundamentals of Electric Circuits (2nd Ed., Charles Alexander & > Matthew Sadiku) > Fundamentals of Electric Circuits (3rd Ed., Charles Alexander & > Matthew Sadiku) > Microelectronic Circuit Design (2nd Ed., Richard Jaeger & Travis > Blalock) > Microelectronic Circuit Design (3rd Ed., Richard Jaeger & Travis > Blalock) > Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with VHDL Design (2nd Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (1st Ed., Stephen > Brown & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (2nd Ed., Stephen > Brown & Zvonko Vranesic) > Continuous and Discrete Control Systems (Dorsey) > Design with Operational Amplifiers and Analog Integrated Circuits (3rd > Ed., Sergio Franco) > Engineering Circuit Analysis (6th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Circuit Analysis (7th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Electromagnetics (7th Ed., William H. Hayt & John A. Buck) > Principles of Electronic Materials and Devices (2nd Ed, Safa O. Kasap) > Principles of Electronic Materials and Devices (3rd Ed, Safa O. Kasap) > A First Lab in Circuits and Electronics (Yannis Tsividis) > Power Electronic Circuits (Issa Batarseh) > Power Electronics: Converters, Applications, and Design (3rd Ed., Ned > Mohan, Tore Undeland & William Robbins) > An Introduction to Digital and Analog Communications (2nd Ed., Simon > Haykin & Michael Moher) > Communication Systems (4th Ed., Simon Haykin) > Signals and Systems (2nd Ed., Simon Haykin & Barry Van Veen) > Programming in Haskell (Graham Hutton) > Logic in Computer Science: Modelling and Reasoning about Systems > (Michael Huth & Mark Ryan) > Introduction to Distributed Algorithms (2nd., Gerard Tel) > Information Theory, Inference and Learning Algorithms (David J. C. > MacKay) > Digital Systems Engineering (William J. Dally & John W. Poulton) > Concepts in Programming Languages (by John C. Mitchell) > Simulation Modeling and Analysis with Expertfit Software (4th Ed., > Averill Law) > Measurement Systems (5th Ed, Ernest Doebelin) > Wireless Communications (Andrea Goldsmith) > Testing of Digital Systems (N. K. Jha & S. Gupta) > Space-Time Coding (Hamid Jafarkhani) > Space-Time Block Coding for Wireless Communications (Erik G. Larsson & > Petre Stoica) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Radio-Frequency Electronics: Circuits and Applications (Jon B. Hagen) > Photonic Devices (Jia-ming Liu) > Networking Wireless Sensors (Bhaskar Krishnamachari) > Mobile Wireless Communications (Mischa Schwartz) > Introduction to Color Imaging Science (Hsien-Che Lee) > Fundamentals of Wireless Communication (David Tse & Pramod Viswanath) > Fundamentals of Modern VLSI Devices (Yuan Taur & Tak H. Ning) > Electronic and Optoelectronic Properties of Semiconductor Structures > (Jasprit Singh) > Digital Signal Processing System Analysis and Design (Paulo S. R. > Diniz) > An Introduction to Statistical Signal Processing (Robert M. Gray) > An Introduction to Radio Frequency Engineering (Christopher Coleman) > Algebraic Codes for Data Transmission (Richard E. Blahut) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Fundamentals of Semiconductor Fabrication (Gary S. May, Simon M. Sze) > Semiconductor Devices: Physics and Technology (2nd Ed, Simon M. Sze) > Electric Machinery (6th Ed., Fitzgerald) + Ebook > Electric Machinery Fundamentals (4th Ed., Chapman) > Electric Machinery and Power System Fundamentals (Chapman) > Local Area Networks (2nd Ed., Keiser) > Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka) > Introduction to Signals and Systems (Lindner) > Digital Signal Processing (3rd Ed., Mitra) > Semiconductor Physics and Devices (3rd Ed., Donald A. Neamen) > Design for Electrical and Computer Engineers (1st Ed., Ralph Ford & > Chris Coulston) > Fundamentals of Modeling and Analyzing Engineering Systems (Cha, > Rosenberg, Dym) > Principles of Linear Systems (Philip E. Sarachik) > Power Systems Harmonics: Fundamentals, Analysis and Filter Design > (George J. Wakileh) > Principles of Adaptive Filters and Self-learning Systems (Anthony > Zaknich) > Control of Robot Manipulators in Joint Space (R. Kelly, V. Santib.87.96ez, > A. Lor.92a) > Modelling and Control of Robot Manipulators (2nd Ed., Lorenzo > Sciavicco, Bruno Siciliano) > Algebraic Methods for Nonlinear Control Systems (2nd Ed., Giuseppe > Conte, Claude H. Moog, Anna Maria Perdon) > Modern Control Engineering - Problems B (3rd Ed. K.OGATA) + Ebook > Modern Control Engineering (4th Ed. K.OGATA) > LabVIEW 8 Student Edition (Bishop) > Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami- > Naeini) > Modeling and Simulation of Dynamic Systems (Woods, Lawrence) > Computer Numerical Control: Operation and Programming (3rd Ed., > Stenerson & Curran) > Engineering Problem Solving with C (3rd Ed., Etter) > Process Control Instrumentation Technology (8th Ed., Johnson) > Electrical Power and Controls (2nd Ed., Skvarenina & DeWitt) > Electronics and Computer Math (8th Ed., Deem & Zannini) > Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based > Introduction (John Semmlow) > Aircraft Digital Electronic and Computer Systems: Principles, > Operation and Maintenance (Mike Tooley) > VLSI Test Principles and Architectures: Design for Testability (Chen, > Cheng, Eklow et al.) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Machine Vision: Theory, Algorithms, Practicalities (3rd Ed., E. R. > Davies) > Instrumentation and Control Systems (W. Bolton) > Essential Java for Scientists and Engineers (Brian D Hahn & Katherine > M Malan) > Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Ed., > Bernard V. Liengme) > Electric Motors and Drives : Fundamentals, Types and Applications (3rd > Ed., Austin Hughes) > 10-Key Touch Key: Developing Speed and Accuracy (Burton) > Introduction to C++ Programming, Brief (Y. Daniel Liang) > C++ for Business Programmers (2nd Ed., John C. Molluzzo) > Introduction to Java Programming-Comprehensive Version (6th Ed., Y. > Daniel Liang) > Introduction to Java Programming: Fundamentals First (6th Ed., Y. > Daniel Liang) > Objects First With Java: A Practical Introduction Using BlueJ (3rd > Ed., David J. Barnes & Michael Kolling) > Java: An Introduction to Problem Solving and Programming (4th Ed., > Walter Savitch) > Simply Java Programming: An Application-Driven» Tutorial Approach > (Deitel) > Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & > Jeffrey Nyhoff) > Advanced Java» 2 Platform How to Program (Deitel & Santry) > SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) > Introduction to Programming Using Visual Basic 2005 (6th Ed., David I. > Schneider) > Simply Visual Basic 2005 (2nd Ed., Harvey & Paul Deitel & Associates) > Visual Basic 2005 How to Program (3rd Ed., Deitel & Associates) > Introduction to Programming with Visual Basic 6.0 (4th Ed., David I. > Schneider) > Visual Basic.Net Programming (2nd Ed., Jeffrey Tsay) > Simply Visual Basic .NET (Deitel & Nieto) > Mechatronics (Sabri Cetinkunt) > Introduction to Linear Programming (Leonid N. Vaserstein) > Science of Electronics, The: DC/AC (David M. Buchla, Thomas L. Floyd) > Introductory Circuit Analysis (11th Ed., Robert L. Boylestad) > Principles of Electric Circuits: Conventional Current Version (8th > Ed., Thomas Floyd) > Contemporary Electric Circuits: Insights and Analysis (2nd ed., > Strangeway, Petersen, Gassert & Lokken) > Electronics Technology Fundamentals - Conventional Flow (2nd Ed., > Robert T. Paynter & Toby Boydell) > Electronics Fundamentals: Circuits, Devices and Applications (7th Ed., > Thomas L. Floyd) > Principles of Electric Circuits: Electron Flow Version (8th Ed., > Thomas L. Floyd) > Electronics Technology Fundamentals - Electron Flow (2nd Ed., Robert > T. Paynter, Toby Boydell) > Introductory DC/AC Circuits (6th Ed., Nigel P. Cook) > Introductory DC/AC Electronics (6th Ed., Nigel P. Cook) > Electronic Devices - Conventional Current Version (7th Ed., Thomas L. > Floyd) > Electronic Devices - Conventional Current Version (8th Ed., Thomas L. > Floyd) > Electronic Devices - Electron Flow Version (8th, Thomas L. Floyd) > Electronic Devices and Circuit Theory (9th Ed., Robert L. Boylestad, > Louis Nashelsky) > Introductory Electronic Devices and Circuits: Electron Flow Version > (7th Ed., Robert T. Paynter) > Introductory Electronic Devices and Circuits: Conventional Flow > Version (7th Ed., Robert T. Paynter) > Electronic Devices - Electron Flow Version (5th, Thomas L. Floyd) > Science of Electronics, The: Digital (Thomas L. Floyd & David M. > Buchla) > Science of Electronics, The: Analog Devices (Thomas L. Floyd, David M. > Buchla) > Digital Electronics: A Practical Approach (7th Ed., William Kleitz) > Digital Electronics: A Practical Approach (8th Ed., William Kleitz) > Digital Systems: Principles and Applications (10th Ed., Ronald Tocci, > Neal Widmer, Greg Moss) > Digital Electronics with VHDL - Quartus II Version (William Kleitz) > Digital Fundamentals (9th Ed., Thomas L. Floyd) > Digital Fundamentals with PLD Programming (Thomas L. Floyd) > The 8051 Microcontroller (4th Ed., I. Scott MacKenzie, Raphael Chung- > Wei Phan) > The 8051 Microcontroller and Embedded Systems (2nd Ed., Muhammad Ali > Mazidi, Janice Mazidi & Rolin McKinlay) > INTEL Microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486, > Pentium, Prentium ProProcessor, Pentium II, III, 4, (7th Ed., Barry B. > Brey) > Microcontroller Technology: The 68HC11, 5/E (Peter Spasov) > PIC Microcontroller (Muhammad Ali Mazidi, Rolin McKinlay & Danny > Causey) > Industrial Electronics (James A. Rehg, Glenn J. Sartori) > Programmable Controllers Using the Allen-Bradley SlC-500 Family (2nd > Ed., Dave Geller) > Programmable Logic Controllers (James A. Rehg, Glenn J. Sartori) > Fundamentals of Programmable Logic Controllers, Sensors, and > Communications (3rd Ed., Jon Stenerson) > An Introduction to Programming with Visual Basic 6.0, Update Edition > (4th Ed., Schneider) > C++ Programming Today (Barbara Johnston) > Introduction to Data Communications and Networking (Wayne Tomasi) > Introduction to Telecommunications (2nd Ed., Martha Rosengrant) > Network Security Essentials: Applications and Standards (3rd Ed., > William Stallings) > Information Security: Principles and Practices (Mark Merkow, James > Breithaupt) > Principles and Practice of Information Security (Linda Volonino, > Stephen R. Robinson) > Modern Electronic Communication (8th Ed., Jeff Beasley, Gary M. > Miller) > Modern Electronic Communication (9th Ed., Jeff Beasley, Gary M. > Miller) > Electronic Communications for Technicians (2nd ed., Tom Wheeler) > Concepts In Systems and Signals (2nd Ed., John D. Sherrick) > Understanding Fiber Optics (5th Ed., Jeff Hecht) > Understanding UNIX/LINUX Programming: A Guide to Theory and Practice > (Bruce Molay) > Applying PIC18 Microcontrollers: Architecture, Programming, and > Interfacing using C and Assembly (Barry B. Brey) > Electrical Power and Controls (2nd Ed., Timothy L. Skvarenina, William > E. DeWitt) > Process Control Instrumentation Technology (8th Ed., Curtis Johnson) > Electrical Machines, Drives and Power Systems (6th Ed., Theodore > Wildi) > Introduction to Vacuum Technology (David M. Hata) > Electronic Project Design and Fabrication (6th Ed., Ronald A. Reis) > Technology and Society (3rd Ed., Linda Hjorth, Barbara A. Eichler, > Ahmed S. Khan, John Morello) > Solid State Electronic Devices (6th Ed., Ben Streetman, Sanjay > Banerjee) > Approaching Quantum Computing (Dan C. Marinescu & Gabriela M. > Marinescu) > Foundations of MEMS (Chang Liu) > Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby) > Elements of Engineering Electromagnetics (6th Ed., Nannapaneni > Narayana Rao) > Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti) > Digital Design: Principles and Practices Package (4th Ed., John F. > Wakerly) > VHDL: A Starter's Guide (2nd Ed., Sudhakar Yalamanchili) > Computer Organization and Architecture: Designing for Performance (7th > Ed., William Stallings) > Parallel Programming: Techniques and Applications Using Networked > Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & > Michael Allen) > Fundamentals of Parallel Processing (Harry F. Jordan & Gita Alaghband) > Feedback Control of Dynamic Systems (5th Ed., Gene Franklin, J.D. > Powell, Abbas Emami-Naeini) > Digital & Analog Communication Systems (7th Ed., Leon W. Couch) > Fundamentals of Communication Systems (John G. Proakis, Masoud Salehi) > Modern Wireless Communications (Simon Haykin, Michael Moher) > Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud > Salehi) > Data and Computer Communications (8th Ed., William Stallings) > Cryptography and Network Security (4th Ed., William Stallings) > Computer Networking with Internet Protocols (William Stallings) > Probabilistic Systems and Random Signals (Abraham H Haddad) > Error Control Coding (2nd Ed., Shu Lin & Daniel J. Costello) > Wireless Communications & Networks (2nd ed., William Stallings) > Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) > Detection and Estimation:Theory; and Its Applications (Thomas > Schonhoff & Arthur Giordano) > Signals, Systems, and Transforms (3rd Ed., Charles L. Phillips, John > M. Parr & Eve A. Riskin) > Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., > Edward W. Kamen & Bonnie S Heck) > Digital Signal Processing (4th Ed., John G. Proakis, Dimitris K > Manolakis) > Adaptive Filter Theory (4th Ed., Simon Haykin) > Spectral Analysis of Signals (Petre Stoica & Randolph L. Moses) > Fluency with Information Technology: Skills, Concepts, and > Capabilities (2nd Ed., Lawrence Snyder) > Fluency with Information Technology, Brief Edition (Lawrence Snyder) > Jolly) > Comprehensive Excel 2002 for Office XP (4th Ed., Karen J. Jolly) > Ethics for the Information Age (2nd Ed., Michael J. Quinn) > Computer Science: An Overview (8th Ed., J. Glenn Brookshear) > Computer Science: An Overview (9th Ed., J. Glenn Brookshear) > Concise Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Concise Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Extended Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Extended Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Logic and Design of Computer Programs (Jim Messinger) > Absolute C++ (2nd Ed., Walter Savitch) > Absolute C++ (3rd Ed., Walter Savitch) > Starting Out with C++: Early Objects (6th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > Problem Solving with C++: The Object of Programming (5th Ed., Walter > Savitch) > Problem Solving with C++ (6th Ed., Walter Savitch) > Problem Solving, Abstraction, and Design using C++ (4th Ed., Frank L. > Friedman & Elliot B. Koffman) > Problem Solving, Abstraction & Design Using C++ (5th Ed., Frank L. > Friedman & Elliot B. Koffman) > Ed., Tony Gaddis) > Starting out with C++ Brief Version Updated (4th Ed., Tony Gaddis & > Barret Krupnow) > Starting out with C++ Brief Version (5th Ed., Tony Gaddis & Barret > Krupnow) > Starting Out with C++: Brief Version Update, Visual C++ .NET (4th Ed., > Tony Gaddis & Barret Krupnow) > Starting Out with C++: Early Objects (5th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > C++ By Dissection (Ira Pohl) > Essential C++ for Engineers and Scientists (2nd Ed., Jeri R. Hanly) > C++ Coach: Essentials for Introductory Programming (Jeff Salvage) > C++ Primer (4th Ed., Stanley B. Lippman, Jos.8ee Lajoie & Barbara E. > Moo) > Engineering Computation with MATLAB (David Smith) > Absolute Java with Student Resource Disk (2nd Ed., Walter Savitch) > Absolute Java (3rd Ed., Walter Savitch) > The Art and Science of Java (Eric Roberts) > Building Java Programs: A Back to Basics Approach (Stuart Reges & > Martin Stepp) > Introduction to Programming in Java: An Interdisciplinary Approach > (Robert Sedgewick & Kevin Wayne) > Java Foundations: Introduction to Program Design and Data Structures > (John Lewis, Peter DePasquale & Joe Chase) > Starting Out with Java: Early Objects (3rd Ed., Tony Gaddis) > Ed., Tony Gaddis) > Java Software Solutions (Java 5.0 version): Foundations of Program > Design (4th Ed., John Lewis & William Loftus) > Java Software Solutions: Foundations of Program Design (5th Ed., John > Lewis & William Loftus) > Structures (Tony Gaddis & Godfrey Muganda) > Object of Java, The: Introduction to Programming Using Software > Engineering Principles (2nd Ed, David D. Riley) > Object-Oriented Programming in Java: A Graphical Approach, Preliminary > Edition (Kathryn E. Sanders & Andy van Dam) > Starting Out with Java 5: Control Structures to Objects (Tony Gaddis) > Starting Out with Java 5: Early Objects (Tony Gaddis) > Introduction to Programming Using Java: An Object-Oriented Approach > (2nd Ed., David Arnow, Scott Dexter & Gerald Weiss) > Computing with Java (2nd Ed., Art Gittleman) > Problem Solving with Java, Update (2nd Ed., Elliot B. Koffman & Ursula > Wolz) > Starting Out with Alice: A Visual Introduction to Programming (Tony > Gaddis) > Problem Solving and Program Design in C (4th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Problem Solving and Program Design in C (5th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Starting Out with Visual Basic 2005 (3rd Ed., Tony Gaddis & Kip > Irvine) > Starting Out with Visual Basic 6 (Tony Gaddis, Kip Irvine & Bruce > Denton) > Starting Out with Visual Basic.Net (2nd Ed., Tony Gaddis, Kip Irvine & > Bruce Denton) > Computer Programming Fundamentals with Applications in Visual Basic¬ > 6.0 (Mitchell C. Kerman & Ronald L. Brown) > Advanced VB.NET Alternate with VB.Net CD's (3rd Ed., Kip Irvine & Tony > Gaddis) > Advanced Visual Basic 2005 (4th Ed., Kip Irvine & Tony Gaddis) > C# Software Solutions: Foundations of Program Design (John Lewis) > Problem Solving, Abstraction and Design Using C++, Visual C++.NET > Edition (Frank L. Friedman & Elliot B. Koffman) > Ada 95: Problem Solving and Program Design (3rd Ed., Michael B. > Feldman & Elliot B. Koffman) > Programming and Problem Solving with Delphi (Mitchell C. Kerman) > C Program Design for Engineers (2nd Ed., Jeri R. Hanly & Elliot B. > Koffman) > Data Abstraction & Problem Solving with C++ (5th ed., Frank M. > Carrano) > Data Structures and Algorithm Analysis in C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in C++ (3rd Ed., Mark Allen > Weiss) > Data Abstraction and Problem Solving with C++: Walls and Mirrors (4th > Ed., Frank M. Carrano) > Data Structures and Other Objects Using C++ (3rd Ed., Michael Main & > Walter Savitch) > Data Structures and Problem Solving Using C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in Java (2nd Ed., Mark Allen > Weiss) > Collections Framework (Simon Gray) > Data Abstraction and Problem Solving with Java (2nd Ed., Frank M. > Carrano & Janet J. Prichard) > Data Structures and Other Objects Using Java (3rd Ed., Michael Main) > Data Structures and Problem Solving Using Java (3rd Ed., Mark Allen > Weiss) > Java Software Structures: Designing and Using Data Structures (2nd > Ed., John Lewis, Joseph Chase) > The Object of Data Abstraction and Structures (using Java) (David > Riley) > Classic Data Structures in Java (Timothy Budd) > Data Structures in Java (Thomas A. Standish) > Introduction to the Design and Analysis of Algorithms (1st Ed., Anany > V. Levitin) > Introduction to the Design and Analysis of Algorithms (2nd Ed., Anany > V. Levitin) > Algorithm Design (Jon Kleinberg & .83va Tardos) > Data Structures and Algorithm Analysis in C (2nd Ed., Mark Allen > Weiss) > Computer Algorithms: Introduction to Design and Analysis (3rd Ed., > Sara Baase & Allen Van Gelder) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (4th Ed., George F. Luger) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (5th Ed., George F. Luger) > The Complete A+ Guide to PC Repair (3rd Ed., Cheryl A. Schmidt) > The Complete A+ Guide to PC Repair (4th Ed., Cheryl A. Schmidt) > Complete Computer Repair Textbook (4th Ed., Cheryl A. Schmidt) > Computer Systems Organization and Architecture (John D. Carpinelli) > CMOS VLSI Design: A Circuits and Systems Perspective (3rd Ed., Neil > H.E. Weste & David Harris) > Interactive Computer Graphics: A Top-Down Approach Using OpenGL (4th > Ed., Edward Angel) > File Structures: An Object-Oriented Approach with C++ (3rd Ed., > Michael J. Folk, Bill Zoellick & Greg Riccardi) > Oracle 10g Programming: A Primer (Rajshekhar Sunderraman) > Darwen) > Fundamentals of Database Systems (5th Ed., Ramez Elmasri & Shamkant B. > Navathe) > Database Systems: An Application Oriented Approach, Compete Version > (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > DataBase Systems: A Practical Approach to Design, Implementation and > Management (4th Ed., Thomas M. Connolly & Carolyn E. Begg) > Database Systems: An Application-Oriented Approach, Introductory > Version (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > Fundamentals of Database Systems/Oracle 9i Programming (4th Ed., Ramez > Elmasri, Shamkant B. Navathe & Rajshekhar Sunderraman) > Oracle 9i Programming: A Primer (Rajshekhar Sunderraman) > Principles of Database Systems with Internet and Java Applications > (Greg Riccardi) > Introduction to Data Mining (Pang-Ning Tan, Michael Steinbach & Vipin > Kumar) > Data Mining: A Tutorial Based Primer (Richard Roiger & Michael Geatz) > Learning SQL: A Step-by-Step Guide Using Access (Sikha Bagui & Richard > Earp) > Access 2007 Guidebook (6th Ed., Maggie Trigg & Phyllis Dobson) > Dobson) > Implementing Databases in Oracle 9i (John Day & Craig Van Slyke) > Web 101: Making the Net Work for You (2nd Ed., Wendy G. Lehnert) > Web 101 (3rd Ed., Wendy G. Lehnert & Richard L. Kopec) > Web Developer Foundations: Using XHTML (2nd Ed., Terry Felke-Morris) > Web Development & Design Foundations With XHTML (3rd Ed., Terry Felke- > Morris) > Internet Effectively: A Beginner's Guide to the World Wide Web (Tyrone > Adams & Sharon Scollard) > Light on the Web: Essentials to Making the 'Net Work for You (Wendy G. > Lehnert) > Programming the World Wide Web (3rd Ed., Robert W. Sebesta) > Programming the World Wide Web (4th Ed., Robert W. Sebesta) > XML: Language Mechanics and Applications (Dwight Peltzer) > Practical Perl with CGI Applications (Elizabeth Chang) > Developing Web Applications with Active Server Pages (Thom Luce) > Structure and Interpretation of Signals and Systems (Edward A. Lee & > Pravin Varaiya) > Languages and Machines: An Introduction to the Theory of Computer > Science (3r Ed., Thomas A. Sudkamp) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) > Galin) > Object Oriented Software Development Using Java (2nd Ed., Xiaoping > Jia) > Introduction to the Team Software Process (Watts S. Humphrey) > Software Project Management: A Real-World Guide to Success (Joel > Henry) > Software Engineering (8th Ed., Ian Sommerville) > Object-Oriented Programming featuring Graphical Applications in Java > (Michael J. Laszlo) > Project-Based Software Engineering: An Object-Oriented Approach > (Evelyn Stiller & Cathie LeBlanc) > Engineering of Software, The: A Technical Guide for the Individual > (Dick Hamlet & Joe Maybee) > Concepts of Programming Languages (7th Ed., Robert W. Sebesta) > Concepts of Programming Languages (8th Ed., Robert W. Sebesta) > Advanced Java: Internet Applications (2nd Ed., Art Gittleman) > Objects to Components with Java 2 Platform (Art Gittleman) > C for Java Programmers (Tomasz Muldner) > Pointers on C (Kenneth Reek) > C++ Programming with Design Patterns Revealed (Tomasz Muldner) > The C++ Programming Language (3rd Ed., Bjarne Stroustrup) > Operating Systems: A Systematic View (6th Ed., William S. Davis & T.M. > Rajkumar) > Unix: The Textbook (2nd Ed., Syed Mansoor Sarwar, Robert Koretsky & > Syed Aqeel Sarwar) > Operating Systems (3rd Ed., Gary Nutt) > LINUX & UNIX Programming Tools: A Primer for Software Developers (Syed > Mansoor Sarwar & Khaled H. Al-Saqabi) > Addison-Wesley's Interactive Linux Tutorial and Reference (Edutrends, > Inc.) > Linux: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel > Sarwar) > Kernel Projects for Linux (Gary Nutt) > OSP: An Environment for Operating System Projects (Michael Kifer & > Scott A. Smolka) > Distributed Computing: Principles and Applications (M.L. Liu) > Distributed Operating Systems and Algorithm Analysis (Randy Chow & > Theodore Johnson) > Mastering Networks: An Internet Lab Manual (Jorg Liebeherr & Magda El > Zarki) > Computer Networking: A Top-Down Approach Featuring the Internet (3rd > Ed., James F. Kurose & Keith W. Ross) > Computer Networking: A Top-Down Approach (4th Ed., James F. Kurose & > Keith W. Ross) > Computer Networking Complete Package (3rd Ed., James F. Kurose & Keith > W. Ross) > Network Management: Principles and Practice (Mani Subramanian) > Computer Security: Art and Science (Matt Bishop) > Introduction to Computer Security (Matt Bishop) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) - Math, Statistics & Probability > > Advanced Engineering Mathematics (8th Ed., Erwin Kreyszig) > Advanced Engineering Mathematics (9th Ed., Erwin Kreyszig) > Elementary Differential Equations (7th Ed., Boyce) > Elementary Differential Equations (8th Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (7th > Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (8th > Ed., Boyce & Diprima) > Differential Equations: An Introduction to Modern Methods and > Applications (James Brannan & William Boyce) > Introduction to the Finite Element Method: Theory, Programming and > Applications (Erik G. Thompson) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Elementary Linear Algebra (9th Ed., Anton) > Elementary Linear Algebra with Applications (9th Ed., Howard Anton & > Chris Rorres) > Applied Statistics and Probability for Engineers (3rd Ed., Douglas > Montgomery & George Runger) > Applied Statistics and Probability for Engineers (4th Ed., Douglas > Montgomery & George Runger) > Engineering Statistics (3rd Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Engineering Statistics (4th Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Probability and Statistics in Engineering (4th Ed., William W. Hines, > Douglas Montgomery, David Goldsman & Connie Borror) > Design and Analysis of Experiments (6th Ed., Douglas Montgomery) > Spreadsheet Tools for Engineers using Excel (2nd Ed. Byron S > Gottfried) > Spreadsheet Tools for Engineers using Excel (3rd Ed. Byron S > Gottfried) > Numerical Methods for Engineers (4th Ed. Steven C. Chapra) > Numerical Methods for Engineers (5th Ed. Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (1st Ed., Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (2nd Ed., Steven C. Chapra) > Statistics for Engineers and Scientists (1st Ed, William C. Navidi) > Statistics for Engineers and Scientists (2nd Ed, William C. Navidi) > Probability (Jim Pitman) > Numerical Methods with Matlab (Amos Gilat & Vish Subramaniam) > MATLAB: An Introduction with Applications (2nd Ed., Amos Gilat) > Discrete and Combinatorial Mathematics (5th ed., Ralph P. Grimaldi) > Discrete Mathematics (Sherwood Washburn, Thomas Marlowe & Charles T. > Ryan) > Discrete Mathematics (5th ed., John Dossey, Albert Otto, Lawrence > Spence & Charles Vanden Eynden) > Mathematics for New Technologies (Don Hutchison & Mark Yannotta) > An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy) > Fundamentals of Finite Element Analysis (1st Ed., David V. Hutton) > The Finite Element Method: Its Basis and Fundamentals (6th Ed., > Zienkiewicz, R. L. Taylor & J.Z. Zhu) > Differential Equations (A. King, J. Billingham, S. Otto) > Regression Methods in Biostatistics: Linear, Logistic, Survival, and > Repeated Measures Models (Eric Vittinghoff, David Glidden, Stephen > Shiboski, Charles McCulloch) > A Modern Introduction to Probability and Statistics: Understanding Why > and How (F.M. Dekking, C. Kraaikamp, H.P. Lopuha.8a, L.E. Meester) > Statistical Methods for the Analysis of Repeated Measurements (Charles > S. Davis) > Bayesian Core: A Practical Approach to Computational Bayesian > Statistics (Jean-Michel Marin, Christian Robert) > Essentials of Stochastic Processes (Rick Durrett) > Regression Analysis: Theory, Methods, and Applications (Ashish Sen & > Muni Srivastava) > Applied Probability and Statistics (Mario Lefebvre) > Foundations of Hyperbolic Manifolds (2nd Ed., John Ratcliffe) > Fourier and Laplace Transforms (R. J. Beerends , H. G. ter Morsche) > Infinite-Dimensional Dynamical Systems (James C. Robinson) > Mathematical Methods for Physics and Engineering, (3rd Ed., Riley, > Hobson & Bence) + original Ebook > Numerical Methods in Engineering with MATLAB (Jaan Kiusalaas) + > original Ebook > Numerical Methods in Engineering with Python (Jaan Kiusalaas) + > original Ebook > An Introduction to Numerical Analysis (Endre Suli and David Mayers) + > original Ebook > Fundamentals of Engineering Numerical Analysis (Parviz Moin) > Monte Carlo Statistical Methods (2nd Ed., Christian P. Robert, George > Casella) > Introduction to Mathematical Structures and Proofs (Larry J. Gerstein) > Analyzing Categorical Data (Jeffrey S. Simonoff) > Fundamentals of Complex Analysis with Applications to Engineering, > Science, and Mathematics (3rd Ed., E. Saff & Arthur Snider) > Probability & Statistics for Engineers & Scientists (8th Ed., Walpole, > Myers, Ye) > Statistics for Engineering and the Sciences (5th Ed., Mendenhall & > Sincich) > Miller & Freund's Probability and Statistics for Engineers (7th Ed., > Johnson, Miller, Freund) > Applied Numerical Analysis Using MATLAB (2nd Ed., Fausett) > Numerical Methods Using Matlab (4th Ed., Mathews & Fink) > Applied Numerical Methods for Engineers and Scientists (Rao) > Applied Numerical Analysis Using MATLAB (2nd Ed., Laurene v. Fausett) > Friendly Introduction to Numerical Analysis (Bradie) > Elementary Linear Algebra (2nd Ed., Spence, Insel & Friedberg) > Elementary Linear Algebra with Applications (9th Ed., Kolman & Hill) > Introductory Linear Algebra: An Applied First Course (8th Ed., Kolman > & Hill) > Linear Algebra with Applications (7th Ed., S. Leon) > Linear Algebra for Engineers and Scientists Using Matlab (Hardy) > Linear Algebra with Applications (3rd Ed., Bretscher) > Modern Matrix Algebra (Hill & Kolman) > Partial Differential Equations and Boundary Value Problems with > Fourier Series (2nd ed., Asmar) > Applied Partial Differential Equations (4th Ed., Haberman) > Technical Calculus (5th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics (2th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics with Calculus (2th Ed., Dale Ewen, Joan S. Gary > & James E. Trefzger) > Introductory Mathematics (4th Ed., Cook) > Mathematics for the Technical Trades (Cook) > College Mathematics (7th Ed., Cleaves & Hobbs) > Fundamentals of Statistics (2nd Ed., Michael III Sullivan) > Statistics: Informed Decisions Using Data (2nd Ed., Michael III > Sullivan) > Modern Elementary Statistics (12th Ed., John E. Freund, Benjamin M. > Perles) > Franklin) > Elementary Statistics: Picturing the World (3rd Ed., Larson & Farber) > First Course in Statistics (9th Ed., James T. McClave & Terry Sincich) > Statistics (10th Ed., McClave & Terry Sincich) > Interactive Statistics (3rd Ed., Martha Aliaga & Brenda Gunderson) > Statistics for the Life Sciences (3rd Ed., Samuels & Witmer) > Applied Statistics and the SAS Programming Language (5th Ed., Cody & > Smith) > Biostatistics for the Health Sciences (R. Clifford Blair & Richard > Taylor) > Biostatistics: How It Works (Steve Selvin) > Business Statistics: First Course and Student CD (4th Ed., David M. > Levine, Timothy C. Krehbiel & Mark L. Berenson) > Course in Business Statistics with CD-ROM (4th Ed., Groebner, Shannon, > Fry & Smith) > Business Statistics: Decision Making and Student CD Package (7th Ed., > Groebner) > Business Statistics: A Decision-Making Approach and Student CD Update > Package (6th Ed., Groebner, Shannon, Fry & Smith) > Statistics for Business & Economics (10th Ed., McClave, Benson & > Sincich) > Statistics for Managers Using Excel and Student CD Package (5th Ed., > Levine) > Statistics for Managers Using Microsoft Excel and Student CD Package > (4th Ed., Levine, Stephan, Krehbiel & Berenson) > Statistics for Business and Economics and Student CD (6th Ed., > Newbold, Carlson & Thorne) > Statistics for Business and Economics and Student CD-ROM (5th Ed., > Newbold, Carlson & Thorne) > Basic Business Statistics: Concepts and Applications and CD package > (10th Ed., Berenson, Krehbiel & Levine) > John E. Freund's Mathematical Statistics with Applications (7th Ed., > Miller) > Probability and Statistical Inference (7th Ed., Hogg & Tanis) > Introduction to Mathematical Statistics (6th Ed., Hogg, Craig & > McKean) > Introduction to Mathematical Statistics and Its Applications (4th Ed., > Larsen & Marx) > Brief Course in Mathematical Statistics (Hogg & Tanis) > Fundamentals of Probability, with Stochastic Processes (3rd Ed., Saeed > Ghahramani) > First Course in Probability (7th Ed., Sheldon Ross) > Applied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern) > Multivariate Data Analysis (6th Ed., Hair, Black, Babin, Anderson & > Tatham) > Essential MATLAB for Engineers and Scientists (3rd Ed., Brian D Hahn & > Dan Valentine) > Introduction to Applied Statistical Signal Analysis: Guide to > Biomedical and Electrical Engineering Applications (3rd Ed. Richard > Shiavi) > Construction Mathematics (Surinder Virdi & Roy Baker) > Numerical Methods in Biomedical Engineering (Stanley Dunn, Alkis > Constantinides & Prabhas Moghe) > Probability and Statistics with Integrated Software Routines (Ronald > Deep) > Boundary Value Problems and Partial Differential Equations (5th Ed., > David Powers) > Finite Element Analysis with Error Estimators : An Introduction to the > FEM and Adaptive Error Analysis for Engineering Students (J. Akin) > Basic Engineering Mathematics (4th Ed., John Bird) > Engineering Mathematics (4th Ed., John Bird) > Higher Engineering Mathematics (5th Ed., John Bird) > Mathematics for Electrical Engineering and Computing (Mary > Attenborough) > Introductory Statistics for Engineering Experimentation (Peter Nelson, > Karen Copeland & Marie Coffin) > Understanding Engineering Mathematics (Bill Cox) > Statistics And Probability For Engineering : Applications With > Microsoft Excel (Decoursey) > Business Math Using Calculators: With 10-Key Computer Assisted > Instruction (Burton) > Mathematics for Economics and Business (5th Ed., Ian Jacques) > Business Math, Brief w/CD & Study Guide & Tutor Center Access Card Pkg > (7th Ed., Cleaves & Hobbs) > Math for Merchandising: A Step-by-Step Approach (3rd Ed., Moore) > Mathematics for Business (7th Ed., Salzman , Miller & Clendenen) > Mathematics for Business (8th Ed., Salzman , Miller & Clendenen) > Advanced Engineering Mathematics (2nd Ed, Michael Greenberg) > Basic College Mathematics with Early Integers (K. Elayn Martin-Gay) > Developmental Mathematics (K. Elayn Martin-Gay) > Essentials of Basic College Mathematics (John Jr Tobey, Jr., Jeffrey > Slater) > Basic College Mathematics (5th Ed., John Tobey & Jeffrey Slater) > Prealgebra (5th Ed., K. Elayn Martin-Gay) > Prealgebra & Introductory Algebra (2nd Ed., K. Elayn Martin-Gay) > Prealgebra (3rd Ed., Jamie Blair, John Tobey & Jeffrey Slater) > Elementary Algebra Early Graphing for College Students (3rd Ed., Allen > R. Angel) > Elementary Algebra (Michael Sullivan III, Katherine R. Struve & Janet > Mazzarella) > Elementary Algebra for College Students (7th Ed., Allen R. Angel) > Experiencing Introductory and Intermediate Algebra Through Functions > and Graphs (3rd Ed., JoAnne Thomasson & Robert Pesut) > Introductory Algebra (3rd Ed., K. Elayn Martin-Gay) > Beginning Algebra (6th Ed., John Jr Tobey & Jeffrey Slater) > Beginning Algebra: Early Graphing (Jamie Blair, John Tobey & Jeffrey > Slater) > Beginning and Intermediate Algebra (2nd Ed., Jamie Blair, John Tobey & > Jeffrey Slater) > Introductory Algebra (4th Ed., Robert F Blitzer) > Introductory and Intermediate Algebra (2nd Ed., Robert F Blitzer) > Intermediate Algebra for College Students (7th Ed., Allen R. Angel) > Intermediate Algebra (Michael Sullivan III & Katherine R. Struve) > Intermediate Algebra (3rd Ed., K. Elayn Martin-Gay) > Essentials of Intermediate Algebra for College Students (Robert F. > Blitzer) > Intermediate Algebra (4th Ed., Robert F Blitzer) > Algebra A Combined Approach (3rd Ed., K. Elayn Martin-Gay) > Elementary & Intermediate Algebra (Michael Sullivan III, Katherine R. > Struve & Janet Mazzarella) > Essentials of Introductory and Intermediate Algebra for College > Students (Robert F. Blitzer) > Algebra for College Students (3rd Ed., Allen R. Angel) > Algebra for College Students (5th Ed., Robert F Blitzer) > College Geometry: A Problem Solving Approach with Applications (2nd > Ed., Gary L. Musser, Lynn Trimpe & Vikki R. Maurer) > College Algebra (8th Ed., Michael Sullivan) > College Algebra Essentials (8th Ed., Michael Sullivan) > College Algebra (4th Ed., Robert F. Blitzer) > College Algebra Essentials (2nd Ed., Robert F. Blitzer) > College Algebra: An Early Functions Approach (Robert F. Blitzer) > College Algebra: Concepts Through Functions (Michael Sullivan III & > Michael Sullivan) > College Algebra Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Essentials of College Algebra: Enhanced with Graphing Utilities (4th > Ed., Michael Sullivan III & Michael Sullivan) > Algebra and Trigonometry (8th Ed., Michael Sullivan) > Algebra and Trigonometry (3rd Ed., Robert F. Blitzer) > Algebra and Trigonometry: An Early Functions Approach (Robert F. > Blitzer) > Precalculus: Concepts Through Functions, A Right Triangle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Algebra & Trigonometry (7th Ed., Michael Sullivan) > Algebra and Trigonometry Enhanced With Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Trigonometry (7th Ed., Michael Sullivan) > Trigonometry (8th Ed., Michael Sullivan) > Trigonometry Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus (8th Ed., Michael Sullivan) > Precalculus (3rd Ed., Robert F. Blitzer) > Precalculus Essentials (2nd Ed., Robert F. Blitzer) > Precalculus: Concepts Through Functions, A Unit Circle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Precalculus Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus Essentials: Enhanced with Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Thinking Mathematically (4th Ed., Robert F. Blitzer) > Excursions in Modern Mathematics (5th Ed., Peter Tannenbaum) > Excursions In Modern Mathematics with Mini-Excursions (6th Ed., Peter > Tannenbaum) > Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) > Fundamentals of Mathematics (10th Ed., William M Setek & Michael A > Gallo) > Learning Math in Elementary and Middle School & IMAP Package (4th Ed., > George Cathcart, Yvonne M. Pothier, James H. Vance & Nadine S. Bezuk) > Understanding the Math You Teach: Content and Methods for > Prekindergarten Through Grade 4 (Anita C. Burris) > Algebra Connections (Ira J. Papick & UMO University of Missouri) > Calculus Connections (Asma Harcharras, Dorina Mitrea) > Data Analysis and Probability Connections: Mathematics for Middle > School Teachers (Debra A. Perkowski & Michael Perkowski) > Geometry Connections (John K. Beem) > Elementary Math Modeling Updated (2nd Ed., Mary Ellen Davis & C. Henry > Edwards) > Additional Calculus Topics (11th Ed., Raymond Barnett, Michael Ziegler > & Karl Byleen) > Finite Math and Its Application (9th Ed., Larry J Goldstein, David I > Schneider & Martha J. Siegel) > Introductory Mathematical Analysis for Business, Economics and the > Life and social Sciences (11th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Introductory Mathematical Analysis for Business, Economics and the > Life and Social Sciences (12th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Additional Calculus Topics (9th Ed., Raymond A. Barnett, Michael R. > Ziegler & Karl E. Byleen) > College Mathematics for Business, Economics, Life Sciences and Social > Sciences (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. > Byleen) > Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, > David I Schneider, David I. Lay & Nakhle Asmar) > Calculus and its Applications (11th Ed., Larry J Goldstein, David I > Schneider, David I. Lay & Nakhle Asmar) > Calculus for Business, Economics, Life Sciences and Social Sciences > (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) > Calculus, Early Transcendentals (6th Ed., C. Henry Edwards & David E. > Penney) > Calculus, Early Transcendentals (7th Ed., C. Henry Edwards & David E. > Penney) > Calculus (9th Ed., Dale Varberg, Edwin Purcell & Steve Rigdon) > Calculus Early Transcendentals (Dale Varberg, Edwin Purcell & Steve > Rigdon) > Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley & Karl J. > Smith) > Calculus (6th Ed., Henry Edwards & David E. Penney) > Single Variable Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley > & Karl J. Smith) > Vector Calculus (3rd Ed., Susan J. Colley) > Applied Linear Algebra (Peter J. Olver & Cheri Shakiban) > Introductory Linear Algebra: An Applied First Course (8th Ed., Bernard > Kolman & David R. Hill) > Differential Equations and Linear Algebra (2nd Ed., Jerry Farlow, > James E. Hall, Jean Marie McDill & Beverly H. West) > Differential Equations and Linear Algebra (2nd Ed., C. Henry Edwards & > David E. Penney) > Differential Equations (2nd Ed., John Polking, Al Boggess & David > Arnold) > Differential Equations with Boundary Value Problems (2nd ed., John > Polking, Al Boggess & David Arnold) > Discrete Mathematics with Graph Theory (3rd Ed., Edgar G. Goodaire & > Michael M. Parmenter) > Discrete Mathematics (6th Ed., Richard Johnsonbaugh) > Essential Discrete Mathematics (Todd Feil & Joan Krone) > Business Mathematics, 10th Ed. (Charles D. Miller, Stanley A. Salzman > & Gary Clendenen) > Elementary Statistics (6th Ed., Neil A. Weiss) > Elementary Statistics (7th Ed., Neil A. Weiss) > Elementary Statistics Using the Graphing Calculator: For the TI-83/84 > Plus (Mario F. Triola) > Elementary Statistics Using the TI-83/84 Plus Calculator (2nd Ed., > Mario F. Triola) > Elementary Statistics Update (9th Ed., Mario F. Triola) > Elementary Statistics (10th Ed., Mario F. Triola) > Elementary Statistics With Multimedia Study Guide (10th Ed., Mario F. > Triola) > Essentials of Statistics (2nd Ed., Mario F. Triola) > Essentials of Statistics (3rd Ed., Mario F. Triola) > Introductory Statistics (7th Ed., Neil A. Weiss) > Introductory Statistics (8th Ed., Neil A. Weiss) > Intro Stats (2nd Ed., Richard D. De Veaux, Paul F. Velleman & David E. > Bock) > Stats: Data and Models, (Richard D. De Veaux, Paul F. Velleman & David > E. Bock) > Stats: Data and Models, (2nd ed., Richard D. De Veaux, Paul F. > Velleman & David E. Bock) > Elementary Statistics Using Excel (2nd Ed., Mario F. Triola) > Elementary Statistics Using Excel (3rd Ed., Mario F. Triola) > Stats: Modeling the World (2nd Ed., David E. Bock, Paul F. Velleman & > Richard D. De Veaux) > Statistical Reasoning for Everyday Life (2nd Ed., Jeffrey O. Bennett, > William L. Briggsr & Mario F. Triola) > Business Statistics (Mario F. Triola & LeRoy A. Franklin) > Biostatistics for the Biological and Health Sciences with Statdisk > (Marc M. Triola & Mario F. Triola) > A Course in Probability (Neil A. Weiss) > Probability and Statistics (3rd Ed., Morris H. DeGroot & Mark J. > Schervish) > Statistics for Science and Engineering (John Kinney) > Developmental Mathematics (7th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Mathematical Proofs: A Transition to Advanced Mathematics (Gary > Chartrand, Albert D. Polimeni & Ping Zhang) > Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Ed., > Carol Schumacher) > Elementary Number Theory (5th Ed., Kenneth H. Rosen) > History of Mathematics: Brief Version (Victor J. Katz) > College Geometry: A Discovery Approach (2nd Ed., David Kay) > Geometry: An Investigative Approach (2nd Ed., Phares G. O'Daffer & > Stanley R. Clemens) > A First Course in Abstract Algebra (7th Ed., John B. Fraleigh) > Complex Variables with Applications (3rd Ed., David A. Wunsch) > Numerical Analysis with CD-ROM (Timothy Sauer) > Numerical Analysis and Scientific Computation (Jeffery J. Leader) > Linear Algebra and Differential Equations (Gary L. Peterson & James S. > Sochacki) > Elementary Differential Equations Bound with IDE CD Package (2nd Ed., > Werner E. Kohler & Lee W. Johnson) > Elementary Differential Equations with Boundary Value Problems with > IDE CD Package (2nd Ed., Werner E. Kohler & Lee W. Johnson) > Fundamentals of Differential Equations (6th Ed., Kent B. Nagle, Late, > Edward B. Saff & Arthur David Snider) > Fundamentals of Differential Equations and Boundary Value Problems > (4th Ed., Kent B. Nagle, Late, Edward B. Saff & Arthur David Snider) > Linear Algebra and Its Applications with CD-ROM, Update (3rd Ed., > David C. Lay) > Introduction to Linear Algebra (5th ed., Lee W. Johnson, R. Dean Riess > & Jimmy T. Arnold) > Calculus for the Life Sciences (Marvin L. Bittinger, Neal Brand & John > Quintanilla) > Calculus with Applications for the Life Sciences (Raymond N. > Greenwell, Nathan P. Ritchey & Margaret L. Lial) > Calculus: An Integrated Approach to Functions and Their Rates of > Change, Preliminary Edition (Robin J. Gottlieb) > Calculus (9th Ed., George B. Thomas, Jr. & Ross L. Finney) > Thomas' Calculus, Alternate Edition (9th Ed., George B. Thomas, Jr. & > Ross L. Finney) > Calculus: A Complete Course (2nd Ed., Ross L. Finney, Franklin D. > Demana, Bert K. Waits & Daniel Kennedy) > Calculus (Elgin H. Johnston & Jerry Mathews) > Thomas' Calculus, Updated (10th Ed., George B. Thomas, Jr., Ross L. > Finney, Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus (11th Ed., George B. Thomas, Jr., Maurice D. Weir, > Joel D. Hass & Frank R. Giordano) > Thomas' Calculus Early Transcendentals (11th Ed., George B. Thomas, > Jr., Maurice D. Weir, Joel D. Hass & Frank R. Giordano) > University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, > Jr.) > University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir > & George B. Thomas, Jr.) > Thomas' Calculus, Media Upgrade (11th Ed., George B. Thomas, Jr., > Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Ed., > George B. Thomas, Jr., Maurice D. Weir, Joel D. Hass & Frank R. > Giordano) > Calculus with Applications (8th Ed., Margaret L. Lial, Raymond N. > Greenwell & Nathan P. Ritchey) > Calculus with Applications, Brief Version (8th Ed., Margaret L. Lial, > Raymond N. Greenwell & Nathan P. Ritchey) > Finite Math with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics (8th Ed., Margaret L. Lial, Raymond N. Greenwell & > Nathan P. Ritchey) > Mathematics with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics and Calculus with Applications (7th Ed., Margaret > L. Lial, Raymond N. Greenwell & Nathan P. Ritchey) > Mathematical Ideas (10th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas (11th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas Expanded Edition (10th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Mathematical Ideas Expanded Edition (11th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (3rd Ed., Jeffrey O. Bennett & William L. Briggs) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (4th Ed., Jeffrey O. Bennett & William L. Briggs) > A Problem Solving Approach to Mathematics (9th Ed., Rick Billstein, > Shlomo Libeskind & Johnny W. Lott) > A Survey of Mathematics with Applications (7th Ed., Allen R. Angel, > Christine D. Abbott & Dennis C. Runde) > A Survey of Mathematics with Applications: Expanded Edition (7th Ed., > Allen R. Angel, Christine D. Abbott & Dennis C. Runde) > Mathematics All Around (3rd Ed., Tom Pirnot) > Mathematics for Elementary School Teachers (3rd Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary School Teachers (4th Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary Teachers with Activities (Sybilla > Beckmann) > Mathematics for Elementary Teachers plus Activities Manual (2nd Ed., > Sybilla Beckmann) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (8th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (9th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > Mathematical Reasoning for Elementary Teachers (4th Ed., Calvin T. > Long & Duane W. DeTemple) > Essentials of Using and Understanding Mathematics: A Quantitative > Reasoning Approach (Jeffrey O. Bennett & William L. Briggs) > Technical Calculus with Analytic Geometry (4th Ed., Allyn J. > Washington) > Basic Technical Mathematics (8th Ed., Allyn J. Washington) > Basic Technical Mathematics with Calculus (8th Ed., Allyn J. > Washington) > Basic Technical Mathematics with Calculus Metric Version (8th Ed., > Allyn J. Washington) > Introduction to Technical Mathematics (5th Ed., Allyn J. Washington, > Mario F. Triola & Ellena E. Reda) > A Graphical Approach to Precalculus (4th Ed., John Hornsby, Margaret > L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits (3rd Ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits: A Unit Circle > Approach (4th Ed., John Hornsby, Margaret L. Lial & Gary K. Rockswold) > Precalculus: Functions and Graphs (5th Ed., Franklin Demana, Bert K. > Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphical, Numerical, Algebraic (7th Ed., Franklin > Demana, Bert K. Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphs and Models Graphing Calculator Manual Package (3rd > Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & > Judith A. Penna) > Functioning in the Real World: A Precalculus Experience (2nd Ed., > Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker & Martha J. > Siegel) > Precalculus with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Precalculus (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Mark Dugopolski) > Precalculus (4th Ed., Mark Dugopolski) > Precalculus (3rd Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Precalculus: Functions and Graphs (2nd Ed., Mark Dugopolski) > Fundamentals of Precalculus (Mark Dugopolski) > Trigonometry (Mark Dugopolski) > Trigonometry (2nd Ed., Mark Dugopolski) > Trigonometry (8th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Trigonometry: A Circular Function Approach (Marie Aratari) > A Graphical Approach to Algebra and Trigonometry (4th ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > Algebra and Trigonometry: Graphs and Models Graphing Calculator Manual > Package (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. > Ellenbogen & Judith A. Penna) > Algebra and Trigonometry (2nd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > Algebra and Trigonometry (3rd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > College Algebra and Trigonometry (J. S. Ratti & Marcus S. McWaters) > College Algebra and Trigonometry (3rd Ed., Mark Dugopolski) > College Algebra and Trigonometry (4th Ed., Mark Dugopolski) > Algebra and Trigonometry with Modeling and Visualization (3rd Ed., > Gary K. Rockswold) > College Algebra and Trigonometry (3rd Ed., Margaret L. Lial, John > Hornsby & David I. Schneider) > A Graphical Approach to College Algebra (4th Ed., John Hornsby, > Margaret L. Lial & Gary K. Rockswold) > College Algebra: Graphs and Models Graphing Calculator Manual Package > (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen > & Judith A. Penna) > College Algebra (J. S. Ratti & Marcus S. McWaters) > College Algebra with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Essentials of College Algebra with Modeling and Visualization (3rd > Ed., Gary K. Rockswold) > Essentials of College Algebra (Margaret L. Lial, John Hornsby & David > I. Schneider) > Essentials of College Algebra, Alternate Edition (Margaret L. Lial, > John Hornsby & David I. Schneider) > College Algebra (3rd Ed., Mark Dugopolski) > College Algebra (4th Ed., Mark Dugopolski) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (2nd Ed., Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin > L. Bittinger) > College Algebra (9th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Essentials of Geometry for College Students (2nd Ed., Margaret L. > Lial, Barbara A. Brown, Arnold R. Steffenson & L. Murphy Johnson) > Algebra for College Students (5th Ed., Margaret L. Lial, John Hornsby > & Terry McGinnis) > Introductory and Intermediate Algebra (3rd Ed., argaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (3rd Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (4th Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Elementary and Intermediate Algebra (1st Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Elementary and Intermediate Algebra (2nd Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Introductory and Intermediate Algebra: A Combined Approach (2nd Ed., > Marvin L. Bittinger & Judith A. Beecher) > Introductory and Intermediate Algebra (3rd Ed., Marvin L. Bittinger & > Judith A. Beecher) > Elementary and Intermediate Algebra (George Woodbury) > Elementary and Intermediate Algebra: Concepts and Applications (4th > Ed., Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Beginning and Intermediate Algebra with Applications and Visualization > (Gary K. Rockswold & Terry A. Krieger) > Elementary and Intermediate Algebra: Graphs & Models (2nd Ed., Marvin > L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Foundations of Mathematics (Marvin L. Bittinger & Judith A. Penna) > Intermediate Algebra (9th Ed., Marvin L. Bittinger) > Intermediate Algebra (10th Ed., Marvin L. Bittinger) > Intermediate Algebra: Graphs & Models (2nd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra: Graphs & Models (3rd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra with Applications and Visualization (2nd Ed., > Gary K. Rockswold & Terry A. Krieger) > Intermediate Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Intermediate Algebra (Tom Carson, Ellyn Gillespie & Bill E. Jordan) > Intermediate Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Intermediate Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Beginning Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Developmental Mathematics: Basic Mathematics and Algebra (Margaret L. > Lial, John Hornsby, Terry McGinnis, Stanley A. Salzman & Diana L. > Hestwood) > Prealgebra and Introductory Algebra (Marvin L. Bittinger & David J. > Ellenbogen) > Prealgebra and Introductory Algebra (2nd Ed., Marvin L. Bittinger & > David J. Ellenbogen) > Elementary Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Introductory Algebra (9th Ed., Marvin L. Bittinger) > Introductory Algebra (10th Ed., Marvin L. Bittinger) > Prealgebra and Introductory Algebra (2nd Ed., Margaret L. Lial, John > Hornsby, Terry McGinnis & Diana L. Hestwood) > Elementary Algebra with Early Systems of Equations (Tom Carson & Ellyn > Gillespie) > Elementary Algebra: Concepts and Applications (6th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Elementary Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Introductory Algebra (Richelle M. Blair) > Introductory Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Beginning Algebra with Applications and Visualization (Gary K. > Rockswold & Terry A. Krieger) > Integrated Arithmetic and Basic Algebra (3rd Ed., Bill E. Jordan & > William P. Palow) > Introductory Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Developmental Mathematics (6th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Prealgebra (3rd Ed., Margaret L. Lial & Diana L. Hestwood) > Prealgebra (4th Ed., Marvin L. Bittinger & David J. Ellenbogen) > Prealgebra (5th Ed., Marvin L. Bittinger, David J. Ellenbogen & > Barbara L. Johnson) > Prealgebra (2nd Ed., Tom Carson) > Basic Mathematics (9 th Ed., Marvin L. Bittinger) > Basic Mathematics (10 th Ed., Marvin L. Bittinger) > Basic Mathematics Preliminary Edition (Robert Prior) > Basic Mathematics with Early Integers (Marvin L. Bittinger & Judith A. > Penna) > Basic College Mathematics (7th Ed., Margaret L. Lial, Stanley A. > Salzman & Diana L. Hestwood) > Basic Mathematics through Applications (3rd Ed., Geoffrey Akst & Sadie > Bragg) > Fundamental Mathematics through Applications (3rd Ed., Geoffrey Akst & > Sadie Bragg) > Wave Motion (J. Billingham & A. C. King) > Solving ODEs with MATLAB (L. F. Shampine, I. Gladwell & S. Thompson) > Numerical Solution of Partial Differential Equations: An Introduction > (2nd Ed., K. W. Morton & D. F. Mayers) > Measure Theory and Filtering: Introduction and Applications (Lakhdar > Aggoun & Robert J. Elliott) > Mathematical Models in Biology: An Introduction (Elizabeth S. Allman & > John A. Rhodes) > Insurance Risk and Ruin (David C. M. Dickson) > Data Analysis and Graphics Using R: An Example-based Approach (2nd > Ed., John Maindonald & John Braun) > Convex Optimization (Stephen Boyd & Lieven Vandenberghe) > Lauritzen) > Calculus: Concepts and Methods (Ken Binmore & Joan Davies) > An Introduction to Partial Differential Equations (Yehuda Pinchover & > Jacob Rubinstein) > An Introduction to Ordinary Differential Equations (James C. Robinson) > An Introduction to Mathematical Physiology and Biology (2nd Ed., J. > Mazumdar) > An Introduction to Financial Option Valuation: Mathematics, > Stochastics and Computation (Desmond Higham) > An Interactive Introduction to Mathematical Analysis (Jonathan Lewin) > An Elementary Introduction to Mathematical Finance: Options and other > Topics (2nd Ed., Sheldon M. Ross) > A Course in Financial Calculus (Alison Etheridge) - Physics & Astronomy : > > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Fundamentals of Physics (8th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (6th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (7th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > An Introduction to Thermodynamics and Statistical Mechanics (2nd Ed, > Keith Stowe) > Equilibrium and Non-Equilibrium Statistical Thermodynamics (Michel Le > Bellac, Fabrice Mortessagne & G. George Batrouni) > Elements of Statistical Mechanics: With an Introduction to Quantum > Field Theory and Numerical Simulation (Ivo Sachs & Siddhartha Sen) > Quantum Transport (2nd Ed., Supriyo Datta) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Applied Quantum Mechanics (1st Ed., A. F. J. Levi) + original Ebook > Applied Quantum Mechanics (2nd Ed., A. F. J. Levi) > Astronomy A Physical Perspective (2nd Ed., Marc L. Kutner) + original > Ebook > Classical Mechanics (Douglas Gregory) + original Ebook > Electromagnetic Field Theory Fundamentals (2nd Ed., Singh Guru & > Hiziroglu) > Fundamentals of Quantum Mechanics (C.L. Tang) + original Ebook > Special Relativity (P.M. Schwarz & J.H. Schwarz) > Statistical Thermodynamics (Normand Laurendeau) > Statistical Thermodynamics and Microscale Thermophysics (Van P. Carey) > Thermal Physics (Ralph Baierlein) > Topics in Atomic Physics (Charles E. Burkhardt, Jacob J. Leventhal) > Applied Physics (8th Ed., Dale Ewen, Ronald Nelson, Neill Schurter & > Erik Gundersen) > Orbital Mechanics for Engineering Students (Howard Curtis) > Diagnostic Ultrasound Imaging: Inside Out (Thomas Szabo) > Astronomy: A Beginner's Guide to the Universe (5th Ed., Eric Chaisson > & Steve McMillan) > The Cosmic Perspective Media Update with MasteringAstronomy» and > Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with MasteringAstronomy» > and Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. > Bennett, Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with Astronomy Place > website, Skygazer Planetarium Software (3rd Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective (3rd Ed., Jeffrey O. Bennett, Megan > Donahue, Nicholas Schneider & Mark Voit) > Astronomy Today (5th Ed., Eric Chaisson & Steve McMillan) > An Introduction to Modern Astrophysics (2nd Ed., Bradley W. Carroll & > Dale A. Ostlie) > Conceptual Physical Science (3rd Ed., Paul G. Hewitt, John A. Suchocki > & Leslie Hewitt) > Conceptual Integrated Science (Paul G. Hewitt, Suzanne Lyons, John A. > Suchocki & Jennifer Yeh) > Physics: Concepts & Connections (4th Ed., Art Hobson) > Conceptual Physics (10th Ed., Paul G. Hewitt) > College Physics (6th Ed., Jerry D Wilson, Anthony J Buffa & Bo Lou) > Physics with Mastering Physics (3rd Ed., James S. Walker) > Active Learning Guide (Alan Van Heuvelen & Eugenia Etkina) > E&M TIPERs: Electricity & Magnetism Tasks (C. J. Hieggelke, D. P. > Maloney, T. L. O'Kuma & Steve Kanim) > Physics: Principles with Applications (6th Ed., Douglas C. Giancoli) > Physlet¬ Physics: Interactive Illustrations, Explorations and Problems > for Introductory Physics (Wolfgang Christian & Mario Belloni) > University Physics with Modern Physics with Mastering Physics (11th > Ed., Hugh D. Young & Roger A. Freedman) > Physics for Scientists and Engineers (3rd Ed., Douglas C. Giancoli) > Physics for Scientists and Engineers with Modern Physics (3rd Ed., > Douglas C. Giancoli) > Physlet¬ Quantum Physics: An Interactive Introduction (Mario Belloni, > Wolfgang Christian & Anne Cox) > Introduction to Electrodynamics (3rd Ed., David J. Griffiths) > Introduction to Optics (3rd Ed., Frank L Pedrotti, Leno M Pedrotti & > Leno S Pedrotti) > Introduction to Quantum Mechanics (2nd Ed., David J. Griffiths) > Quantum Mechanics: An Accessible Introduction (Robert Scherrer) > The Physics of Sound (3rd Ed., Richard E Berg & David G Stork) > Classical Electromagnetism (Jerrold Franklin) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Introduction to Color Imaging Science (Hsien-Che Lee) > An Introduction to Astrobiology (Iain Gilmour & Mark A. Sephton) > An Introduction to Galaxies and Cosmology (Mark H. Jones & Robert J. > Lambourne) > An Introduction to the Solar System (Neil McBride & Iain Gilmour) > Quantum Physics (Michel Le Bellac) > Laser Fundamentals (2nd Ed., William T. Silfvast) > Introductory Quantum Optics (Christopher Gerry & Peter Knight) > Introduction to Plasma Physics: With Space and Laboratory Applications > (D. A. Gurnett & A. Bhattacharjee) > A Short Introduction to Quantum Information and Quantum Computation > (Michel Le Bellac) > A Quantum Approach to Condensed Matter Physics (Philip L. Taylor & > Olle Heinonen) > A First Course in String Theory (Barton Zwiebach) > A First Course in Computational Physics and Object-Oriented > Programming with C++ (David Yevick) > A Course in Modern Mathematical Physics: Groups, Hilbert Space and > Differential Geometry (Peter Szekeres) > Time Series Analysis and Its Applications: With R Examples (2nd Ed., > Robert Shumway & David Stoffer) > Introduction to Time Series and Forecasting (Peter Brockwell & Richard > Davis) > Ultrasonic Nondestructive Evaluation Systems: Models and Measurements > (Lester W. Schmerr & Sung-Jin Song) - Civil Engineering : > > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Fundamentals of Structural Analysis, (1st Ed., Leet & Uang) > Fundamentals of Structural Analysis, (2nd Ed., Leet & Uang) > Fundamentals of Structural Analysis, (3rd Ed., Leet & Uang) > Structural and Stress Analysis (2nd Ed., Megson) + Ebook > Statics and Strength of Materials for Architecture and Building > Construction (3rd Ed., Onouye & Kane) > Open Channel Hydraulics (A. Osman Akan) > Fundamentals of Structural Stability (George Simitses & Dewey Hodges) > Introduction to Naval Architecture : Formerly Muckle's Naval > Architecture for Marine Engineers (4th Ed., E C Tupper) > The Management of Construction: A Project Lifecycle Approach (F. > Lawrence Bennett) > Advanced Topics in Finite Element Analysis of Structures: With > Mathematica and MATLAB Computations (Asghar Bhatti) > Elementary Structures for Architects and Builders (5th Ed., Ronald E. > Shaeffer) > Surveying with Construction Applications (6th Ed., Barry F. Kavanagh) > Structural Analysis (6th Ed., Hibbeler) > Dynamics of Structures (3rd Ed., Chopra) > Structures (6th Ed., Daniel Lewis Schodek & Martin Bechthold) > Concrete Structures (Mehdi Setareh & Robert M. Darvas) > Reinforced Concrete Design (6th Ed., Chu-Kia Wang, Charles G. Salmon) > Reinforced Concrete Design (7th Ed., Chu-Kia Wang, Charles G. Salmon & > Jos.8e A. Pincheira) > Reinforced Concrete Design (6th Ed., George F. Limbrunner & Abi > Aghayere) > Reinforced Concrete: Mechanics and Design (4th Ed., James G. MacGregor > & James K. Wight) > Structural Steel Design (4th Ed., Jack C. McCormac) > Design of Reinforced Concrete (6th Ed., Jack C. McCormac & James K. > Nelson) > Design of Reinforced Concrete (7th Edition, ACI 318-05 Code Edition, > by Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (3rd Ed., > James K. Nelson, Jr., Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (4th Ed., Jack > C. McCormac) > Surveying (5th Ed., Jack C. McCormac) > Introduction to Structural Analysis & Design (S. D. Rajan) > Soil Mechanics and Foundations (2nd Ed., Muniram Budhu) > Soils and Foundations (7th Ed., Liu & Evett) > Essentials of Soil Mechanics and Foundations: Basic Geotechnics (7th > Ed., David F. McCarthy) > Building Construction: Principles, Materials, and Systems (Madan > Mehta, Diane Armpriest & Walter Scarborough) > Construction Methods and Management (7th Ed., Stephens W. Nunnally) > Construction Project Administration (8th Ed., Ed Fisk Wayne Reynolds) > Construction Accounting and Financial Management (Steven J. Peterson) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Construction Estimating Using Excel (Stephen J. Peterson) > Heating and Cooling of Buildings: Design for Efficiency (2nd Ed., Jan > F. Kreider, Peter S. Curtiss & Ari Rabl) > Steel Structures: Behavior and LRFD (1st Ed., Ramulu S Vinnakota) > The Engineering of Foundations (1st Ed., Rodrigo Salgado) > Introduction to Transportation Engineering (2nd Ed., Banks) > Construction Contracts (2nd Ed., Hinze) > Urban Transportation Planning (2nd Ed., Meyer & Miller) > Construction Planning, Equipment, and Methods (6th Ed., Peurifoy & > Schexnayder) > Construction Planning, Equipment, and Methods (7th Ed., Peurifoy, > Schexnayder & Aviad Shapira) > Open Channel Hydraulics (Terry Sturm) > Construction Management Fundamentals (Schexnayder & Mayo) > Fundamentals of Structural Dynamics (2nd Ed., Roy R. Craig & Andrew J. > Kurdila) > Structural Concrete: Theory and Design (3rd Ed., M. Nadim Hassoun & > Akthem Al-Manaseer) > Principles of Highway Engineering and Traffic Analysis (3rd Ed., Fred > Mannering, Walter Kilareski & Scott Washburn) - Environmental Engineering, Earth and Environmental Sciences : > > Principles of Environmental Engineering and Science (Mackenzie L Davis > & Susan J Masten) > Introduction to Environmental Engineering (4th Ed., MacKenzie L. Davis > & David A. Cornwell) > Introduction to Environmental Engineering and Science (2nd Ed., > Gilbert M. Masters) > Introduction to Environmental Engineering and Science (3rd Ed., > Gilbert M. Masters & Wendell P. Ela) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) > Introduction to Engineering and the Environment (1st Ed., Edward S. > Rubin) > Basic Environmental Technology: Water Supply, Waste Management & > Pollution Control (5th Ed., Jerry A. Nathanson) > Small and Decentralized Wastewater Management Systems (1st Ed, Crites > & Tchobanoglous) > Water Resources Engineering (R. Wurbs, W. James) > Water and Wastewater Technology (6th Ed., Mark J. Hammer, Sr. & Mark > J. Hammer, Jr.) > Principles of Sequence Stratigraphy (Octavian Catuneanu) > Atmospheric Science: An Introductory Survey (2nd Ed., John Wallace, > Peter Hobbs) > Plant Pathology (5th Ed., George Agrios) > Environmental Engineering (4th Ed., Ruth F Weiner & Robin Matthews) > Groundwater Hydrology (3rd Ed., David Keith Todd & Larry W. Mays) > Groundwater Science (Charles Fitts) > Agriculture's Ethical Horizon (Robert Zimdahl) > Environmental Contaminants: Assessment and Control (Daniel Vallero) > Water Resources Engineering 2005 Edition (Larry W. Mays) > Water-Resources Engineering (2nd Ed., Chin) > Water Chemistry (Benjamin) > Hazardous Waste Management (2nd Ed., Michael D. LaGrega, Phillip L > Buckingham & Jeffrey C Evans) > Environmental Biotechnology: Principles and Applications (1st Ed., > Bruce E. Rittmann & Perry L. McCarty) > Chemistry for Environmental Engineering and Science (5th Ed., Clair N > Sawyer, Perry L. McCarty & Gene F. Parkin) > Geology for Engineers and Environmental Scientists (3rd Ed., Alan E. > Kehew) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Water Treatment: Principles and Design (2nd Ed., by MWH) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & > Baxter Vieux) - Chemistry and Chemical Engineering : > > Mass Transfer Operations (3rd Ed., Treybal) > Mass Transfer in Multicomponent Mixtures (J.A. Wesseling & R. Krishna) > + original Ebook > Principles and Modern Applications of Mass Transfer Operations (Jaime > Benitez) > Diffusion - Mass Transfer in Fluid Systems (2nd Ed., Cussler) > Separation Process Principles (1st Ed, Seader & Henley) > Separation Process Principles (2nd Ed, Seader & Henley) > Equilibrium Staged Separations (Wankat) > Principles of Chemical Separations with Environmental Applications > (Richard D. Noble) > Product and Process Design Principles: Synthesis, Analysis, and > Evaluation (2nd Ed., Seider & Seader) + Ebook > Principles and Practices of Automatic Process Control (3rd Ed., Smith > & Corripio) + Ebook > Process Dynamics and Control (2nd Ed., Seborg & Edgard) > Process Control - A First Course with MATLAB (P.C. Chau) + Ebook > Process Dynamics: Modeling, Analysis and Simulation (Wayne Bequette) > Plant Design and Economics for Chemical Engineers, (5th Ed., Peters & > Timmerhaus) + Ebook > Basic Principles and Calculations in Chemical Engineering (6th Ed., > Himmelblau) > Basic Principles and Calculations in Chemical Engineering (7th Ed., > Himmelblau) > Unit Operations of Chemical Engineering (6th Ed., McCabe & Smith) > Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) > Advanced Transport Phenomena (John C. Slattery) > Introduction to Transport Phenomena (W. Thomson) > Transport Phenomena: A Unified Aprroach (Robert S. Brodkey & Harry C. > Hershey) + Ebook > Transport Phenomena in Multiphase Systems (Faghri & Zhang) > Modeling in Transport Phenomena: A Conceptual Approach (2nd Ed., > Ismail Tosun) + original Ebook > Transport Phenomena (2nd Ed., Bird & Stewart) + Ebook > Solutions to Class 1&2 - Transport Phenomena (Bird) > Chemical Engineering Design (Coulson & Richardson's Chemical > Engineering - Volume 6) - (4th Ed., Sinnott) + original Ebook > Chemical Engineering Design and Analysis - An Introduction (Duncan & > Reimer) > Chemical Reaction Engineering (3rd Ed., Levenspiel) + Ebook > Chemical Reactor Analysis and Design Fundamentals (Rawlings & Ekerdt) > + Ebook > Fundamentals of Chemical Reaction Engineering (1st Ed., Davis) > Conceptual Design of Distillation Systems (1st Ed., Doherty & Malone) > Distillation Theory and its Application to Optimal Design of > Separation Units (F.B. Petlyuk) + original Ebook > Batch Distillation: Simulation, Optional Design and Control (Diwekar) > + Ebook > Fluid Mechanics for Chemical Engineers, (3rd Ed., Noel de Nevers) > Introduction to Chemical Processes: Principles, Analysis, Synthesis > (1st Ed., Regina M. Murphy) > Optimization of Chemical Processes (2nd Ed., Edgar & Himmelblau) + > Ebook > Chemical and Engineering Thermodynamics (3rd Ed., Stanley I. Sandler) > Chemical, Biochemical, and Engineering Thermodynamics (4th Ed., > Stanley I. Sandler) > Introduction to Chemical Engineering Thermodynamics (6th Ed., Smith & > Van Ness) > Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & > Van Ness) > Introductory Chemical Engineering Thermodynamics (J. Elliott, C. Lira) > Engineering and Chemical Thermodynamics (Koretsky) > Phase Equilibria, Phase Diagrams and Phase Transformations - Their > Thermodynamic Basis (2nd Ed., Mats Hillert) > Introduction to Chemical Kinetics and Chemical Reaction Engineering > (Missen, Mims) + original Ebook > Principles of Chemical Kinetics (James House) > Transport Processes and Unit Operations (3rd Ed., Christie J. > Geankoplis) > Transport Processes and Separation Process Principles (4th Ed., > Christie J. Geankoplis) > Elementary Principles of Chemical Processes (3rd Ed., Felder & > Rousseau) + Ebook > Chemical Process Safety: Fundamentals with Applications (2nd Ed., > Crowl & Louvar) + Ebook > Elements of Chemical Reaction Engineering (3rd Ed., Fogler) > Elements of Chemical Reaction Engineering (4th Ed., Fogler) > Group Theory with Applications in Chemical Physics (Patrick Jacobs) > Food Analysis (3rd Ed., Suzanne Nielsen) > Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, > v2.5, 3rd Ed. (Brian F. Woodfield & Matthew C. Asplund) > Introductory Chemistry and CW+ GradeTracker Access Card Package, 2nd > Ed. (Nivaldo J. Tro) > Introductory Chemistry: Concepts and Connections, 4th Ed. (Charles H > Corwin) > Prentice Hall Lab Manual Introductory Chemistry, 4th Ed. (Charles H > Corwin) > General, Organic and Biological Chemistry: Structures of Life with > Student Access Kit for MasteringGOBChemistry», 2nd ed. (Karen C. > Timberlake) > Chemistry: An Introduction to General, Organic, and Biological > Chemistry with The Chemistry Place CD-ROM, 9th Ed (Karen C. > Timberlake) > Conceptual Chemistry, 3rd Ed (John A. Suchocki) > Explorations in Conceptual Chemistry: A Student Activity Manual > (Jeffrey Paradis) > Criminalistics: An Introduction to Forensic Science (9th Ed., Richard > Saferstein) > Physical Chemistry with Spartan Student Physical Chemistry Software > (Thomas Engel & Philip Reid) > Quantum Chemistry and Spectroscopy with Spartan Student Physical > Chemistry Software (Thomas Engel & Philip Reid) > Themodynamics, Statistical Thermodynamics, and Kinetics (Thomas Engel > & Philip Reid) > Physical Chemistry (7th. Ed., Peter Atkins & Julio de Paula) > Chemistry An Introduction to Organic, Inorganic and Physical Chemistry > (3rd Ed., Catherine E. Housecroft & Edwin Constable) > General Chemistry: The Essential Concepts (4th Ed., Raymond Chang) > Chemistry: The Molecular Nature of Matter and Change (3rd Ed., Martin > Silberberg) > Chemistry: The Molecular Nature of Matter and Change (4th Ed., Martin > Silberberg) > General, Organic and Biochemistry (3rd ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (4th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (5th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > Fundamentals of Chemistry (3rd Ed., David E Goldberg) > Fundamentals of Chemistry (4th Ed., David E Goldberg) > Fundamentals of Chemistry (5th Ed., David E Goldberg) > Modern Analytical Chemistry (Harvey) > General Chemistry Lab Manual (Petra A. M. van Koppen) > Practical Interfacing in the Laboratory: Using a PC for > Instrumentation, Data Analysis and Control (Stephen E. Derenzo) > Bioprocess Engineering Principles (Pauline M. Doran) - Industrial Engineering, Business, Economics and Finance : > > Engineering Economy (5th Ed., Leland T Blank & Anthony Tarquin) > Engineering Economy (6th Ed., Leland T Blank & Anthony Tarquin) + > original Ebook > Contemporary Engineering Economics (4th Ed., Chan Park) > Engineering Economy (13th Ed, Sullivan) > Introduction to Statistical Quality Control (5th Ed., Douglas C. > Montgomery) > Managing Engineering and Technology (4th, Morse & Babcock) > (4th Ed, Gryna) > Juran's Quality Planning and Analysis for Enterprise Quality (5th Ed., > Gryna, Chua & DeFeo) > Quality (4th Ed., Summers) > Quality Management (5th Ed., Goetsch & Davis) > Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) > Value Driven Product Planning and Systems Engineering (H. E. Cook & L. > A. Wissmann) > Work Systems: The Methods, Measurement & Management of Work (Mikell P. > Groover) > Occupational Safety and Health for Technologists, Engineers, and > Managers (5th Ed., Goetsch) > Occupational Safety and Health for Technologists, Engineers, and > Managers (6th Ed., Goetsch) > Introduction to Engineering Technology (6th Ed., Robert J. Pond) > Manufacturing Facilities Design and Material Handling (3rd Ed., Meyers > & Stephens) > Fundamentals of Forensic Science (Max Houck & Jay Siegel) > Introduction to Optimum Design (2nd Ed., Jasbir Arora) > Project Management for Business and Engineering : Principles and > Practice (2nd Ed., John Nicholas) > ISO 9001:2000 Quality Registration Step-by-Step (3rd Ed., Fred Dobb) > Systems for Planning and Control in Manufacturing (D. K. Harrison & D. > J. Petty) > Planning and Control of Manufacturing Operations (John Kenworthy) > Professionalism: Real Skills for Workplace Success (Anderson & Bolt) > Customer Service: Career Success Through Customer Loyalty (4th Ed., > Timm) > Customer Service: A Practical Approach (3rd Ed., Harris) > Customer Service: A Practical Approach (4th Ed., Harris) > Serving Internal and External Customers (Anne Swartzlander) > Customer Relationship Management: The Bottom Line to Optimizing Your > ROI (Anton & Petouhoff) > Engineering Economy and the Decision-Making Process (Joseph C. > Hartman) > Engineering Management: Challenges in the New Millennium (C M Chang) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Supply Chain Management (3rd Ed., Sunil Chopra & Peter Meindl) > Industrial Safety and Health Management (5th Ed., C. Ray Asfahl) > Computer Numerical Control: Operation and Programming (3rd Ed., Jon S. > Stenerson & Kelly Curran) > Introduction to Management Science and Student CD Package (8th Ed., > Bernard W. Taylor) > Introduction to Management Science with Student CD (9th Ed., Bernard > W. Taylor) > Operations Research: An Introduction (8th Ed., Taha) > Decision Support Systems and Intelligent Systems (7th Ed., Turban, > Aronson, Ting-Peng Liang) > Decision Support and Business Intelligence Systems (8th Ed., Turban, > Aronson, Ting-Peng Liang & Sharda) > Operations Management and Student CD Package (7th Ed., Krajewski, > Ritzman) > Operations Management: Process and Value Chains (8th Ed., Krajewski, > Ritzman & Malhotra) > Operations Management (8th Ed., Jay Heizer & Render) > Introduction to Operations and Supply Chain Management with Advanced > Decision Support Tools (Cecil Bozarth) > Managing Business Process Flows: Principles of Operations Management > (2nd Ed., Anupind, Chopra, Deshmukh, et al) > Operations Management & Student CD Package (8th Ed., Heizer & Render) > Principles Of Operations Management and Student CD (6th Ed., Heizer & > Render) > Foundations of Operations Management (Ritzman & Krajewski) > Decision Modeling with Microsoft¬ Excel (6th Ed., Moore & Weatherford) > Managing Quality: Integrating The Supply Chain (3rd Ed., S. Thomas > Foster) > Six Sigma: Basic Tools and Techniques (Donna C.S. Summers) > First Course in Quality Engineering (KS Krishnamoorthi) > Statistical Quality Design and Control (2nd Ed., DeVor, Chang & > Sutherland) > Economics: A Tool for Critically Understanding Society (7th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Economics: A Tool for Critically Understanding Society (8th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Introduction to Economic Reasoning (6th Ed., William D. Rohlf, Jr.) > Introduction to Economic Reasoning (7th Ed., William D. Rohlf, Jr.) > Essential Foundations of Economics (3rd Ed., Robin Bade & Michael > Parkin) > Understanding Modern Economics (Roger LeRoy Miller) > The Economics of Macro Issues (3rd Ed., Roger LeRoy Miller & Daniel K. > Benjamin) > Foundations of Economics (3rd Ed., Robin Bade & Michael Parkin) > Economics Today (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (14th Ed., Roger LeRoy Miller) > Economics (Michael A. Leeds, Peter von Allmen & Richard C. Schiming) > Economics: Private Markets and Public Choice (7th Ed., Robert B. > Ekelund, Jr., Rand W. Ressler & Robert D. Tollison) > Principles of Economics, 7th Ed. (Roy J. Ruffin & Paul R. Gregory) > The Economics of Public Issues (14th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > The Economics of Public Issues (15th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > Macroeconomics (7th Ed., Michael Parkin) > Macroeconomics (8th Ed., Michael Parkin) > Foundations of Microeconomics (3rd Ed., Robin Bade & Michael Parkin) > Foundations of Macroeconomics (3rd Ed., Robin Bade & Michael Parkin) > Microeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Macroeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Economics Today: The Micro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Micro View (14th Ed., Roger LeRoy Miller) > Microeconomics (7th Ed., Michael Parkin) > Microeconomics (8th Ed., Michael Parkin) > Macroeconomics (2nd Ed., Stephen D. Williamson) > Macroeconomics (3rd Ed., Stephen D. Williamson) > Macroeconomics Update Edition (5th Ed., Andrew B. Abel, Ben S. > Bernanke) > Macroeconomics (6th Ed., Andrew B. Abel, Ben S. Bernanke & Dean > Croushore) > Macroeconomics (10th Ed., Robert J. Gordon) > Economic Growth (David N. Weil) > Money, the Financial System, and the Economy (5th Ed., R. Glenn > Hubbard) > Money, the Financial System, and the Economy (6th Ed., R. Glenn > Hubbard) > The Economics of Money, Banking and Financial Markets (8th Ed., > Frederic S. Mishkin) > Principles of Money, Banking, and Financial Markets (11th Ed., > Lawrence S. Ritter, William L. Silber & Gregory F. Udell) > International Economics (3rd Ed., James Gerber) > International Economics (4th Ed., James Gerber) > International Economics (7th Ed., Steven Husted & Michael Melvin) > World Trade and Payments: An Introduction (9th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > World Trade and Payments: An Introduction (10th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > International Economics: Theory and Policy (7th Ed., Paul R. Krugman & > Maurice Obstfeld) > International Money and Finance (7th Ed., Michael Melvin) > Economic Development (9th Ed., Michael P. Todaro & Stephen C. Smith) > Microeconomics (4th Ed., Jeffrey M. Perloff) > Microeconomics (Don E. Waldman) > Microeconomics: Theory and Applications with Calculus (Jeffrey M. > Perloff) > Environmental Economics and Policy (5th Ed., Tom Tietenberg) > Environmental and Natural Resource Economics (7th Ed., Tom Tietenberg) > Health Economics (3rd Ed., Charles E. Phelps) > & Elizabeth J. Jensen) > Modern Industrial Organization (4th Ed., Dennis W. Carlton & Jeffrey > M. Perloff) > Modern Labor Economics: Theory and Public Policy (9th Ed., Ronald G. > Ehrenberg & Robert S. Smith) > Law and Economics (4th Ed., Robert Cooter & Thomas Ulen) > Law and Economics (5th Ed., Robert Cooter & Thomas Ulen) > Market Regulation (Roger Sherman) > Public Finance and the American Economy (2nd Ed., Neil Bruce) > The Economics of Sports (2nd Ed., Michael A. Leeds & Peter von Allmen) > The Economics of Sports (3rd Ed., Michael A. Leeds & Peter von Allmen) > Introduction to Econometrics, Brief Edition (James H. Stock & Mark W. > Watson) > Introduction to Econometrics (2nd ed., James H. Stock & Mark W. > Watson) > Econometrics: A Modern Introduction (Michael P. Murray) > Using Econometrics: A Practical Guide (5th Ed., A.H. Studenmund) > Mathematical Methods for Economics (2nd Ed., Michael Klein) > Personal Finance with Financial Planning Software (3rd Ed., Jeff > Madura) > Finance: Investments, Institutions, and Management - Update (2nd Ed., > Stanley G. Eakins) > Introduction to Finance (Lawrence J. Gitman & Jeff Madura) > Principles of Managerial Finance Brief plus MyFinanceLab Student > Access Kit (4th Ed., Lawrence J. Gitman) > Principles of Managerial Finance plus MyFinanceLab Student Access Kit > (11th Ed., Lawrence J. Gitman) > Corporate Finance plus MyFinanceLab Student Access Kit (Jonathan Berk > & Peter DeMarzo) > Risk Takers: Uses and Abuses of Financial Derivatives (John > Marthinsen) > Theory of Asset Pricing (George Pennacchi) > Multinational Business Finance (11th Ed., David K. Eiteman, Arthur I. > Stonehill & Michael H. Moffett) > Fundamentals of Multinational Finance (2nd Ed., Michael H. Moffett, > Arthur I. Stonehill & David K. Eiteman) > Cases in International Finance (2nd Ed., Gunter Dufey & Ian H. Giddy) > Fundamentals of Investing plus MyFinanceLab Student Access Kit and > OTIS Student Access Kit (10th Ed., Lawrence J. Gitman & Michael D. > Joehnk) > Fundamentals of Investing & Wharton's OTIS Student Access Kit Package > (9th Ed., Lawrence J. Gitman & Michael D. Joehnk) > OTIS: Online Trading and Investment Simulator Student Access Kit > (Wharton Learning Lab) > Derivatives Markets (2nd Ed., Robert L. McDonald) > Principles of Risk Management and Insurance (9th Ed., George E. Rejda) > Principles of Risk Management and Insurance (10th Ed., George E. > Rejda) > Financial Markets and Institutions (5th Ed., Frederic S. Mishkin & > Stanley G. Eakins) > Statistical Analysis of Financial Data in S-PLUS (Rene A. Carmona) > Statistics and Finance: An Introduction (David Ruppert) > Mathematical Statistics for Economics and Business (Ron C. > Mittelhammer) - Materials Engineering : > > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials Science and Engineering: An Introduction (6th Ed., William > D. Callister, Jr.) > Materials Science and Engineering: An Introduction (7th Ed., William > D. Callister, Jr.) > Fundamentals of Materials Science and Engineering : Integrated > Approach (2nd Ed., William D. Callister, Jr.) > Science and Design of Engineering Materials (2nd Ed., Schaffer, > Saxena, et al) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Foundations of Materials Science and Engineering (3rd Ed, Smith) > Foundations of Materials Science and Engineering (4th Ed, Smith) > Plastics: Materials and Processing (3rd Ed., Strong) > Engineering Materials: Properties and Selection (8th Ed., Budinski) > Introduction to Materials Science for Engineers (6th Ed., Shackelford) > Materials: Engineering, Science, Processing and Design (Michael Ashby, > Dr Hugh Shercliff & David Cebon) > Principles of Corrosion Engineering and Corrosion Control (Zaki Ahmad) > Analysis and Performance of Fiber Composites (3rd Ed., Bhagwan > Agarwal, Lawrence Broutman & K. Chandrashekhara) > Basic Engineering Plasticity: An Introduction with Engineering and > Manufacturing Applications (David Rees) > Steels: Microstructure and Properties (3rd Ed. Bhadeshia & Honeycombe) > Theory of Plasticity (3rd Ed. Jagabanduhu Chakrabarty) > Engineering Materials Vol. 1 : An Introduction to Properties, > Applications and Design (3rd Ed., Michael Ashby & David R H Jones) > Engineering Materials Vol. 2 : An Introduction to Microstructures, > Processing and Design (3rd Ed., Michael Ashby & David R H Jones) > Plastics: Microstructure and Engineering Applications (3rd Ed., Nigel > Mills) > Laser Processing of Engineering Materials : Principles, Procedure and > Industrial Application (John Ion) > Sintering : Densification, Grain Growth and Microstructure (Suk-Joong > Kang) > Biomaterials Science : An Introduction to Materials in Medicine (2nd > Ed., Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Laminar Composites (by George Staab) + original Ebook > contact me to : newbergh123@yahoo.com > Water Treatment: Principles and Design, 2nd Edition for me. thank you very much! liew168@sina.com > === Subject: Re: List of solutions manual (thousands) posting-account=U0LgTAoAAACT3plNs1Bj32A1VT9Tz6dl 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; InfoPath.2),gzip(gfe),gzip(gfe) > My List of Solutions Manual > contact me to : newbergh...@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. This list (not links) is available from : http://rapidshare.com/files/59002351/List of solutions manual.txt - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files ... read more > I Am in possesion of the following Solution Manuals and will give them for free!!!!!!!!!!!!!!!!!!!!!! just email me at mickeydizzle@gmail.com -Engineering Mechanics Statics 10th & 11th by Hibbeler -Engineering Mechanics Dynamics 11th by Hibbeler -Engineering Mechanics Dynamics 4th Bedford === Subject: mike lalonde posting-account=3isBZgoAAADJM-2G3Oc0CRLy9Sk4yeg_ 5.0),gzip(gfe),gzip(gfe) 42434 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle bacini sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde 4 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde michael lalonde mike lalonde temagami henry merchant tammy dubriel gerry dubriel victor dubriel yvan tonge yvan steve tonge 3 === Subject: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=nsrQxAoAAACDkV1_uYvq7QQjzxtFXYoo Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Do you have this one available? How can I get it? Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton please email me if you have it. I only need solution for ch 9 to 13 I have the rest if you're interested let me know student482@gmail.com alt.history.british, alt.guitar.amps === Subject: See the accepted papers, keynote lecture, plenary lectures, the contents of the Book of the Proceedings (i.e. accepted papers). WSEAS Post-Conference Report for the Conferences MACMESE '07 and DNCOCO '07 (124 images) posting-account=KWYMKQoAAAArfstGv6VUH6u1SaWpz4Xi 5.1),gzip(gfe),gzip(gfe) Click on the link below and see the accepted papers, the keynote and Plenary Speeches, the contents of the Book of the Proceedings as well as nice photos from an MACMESE '07 and DNCOCO '07 excellent conferences in Trinidad and Tobago Islands , co-organized by the University of West Indies and WSEAS ------------------------------------- http://www.wseas.com/wseas/reports/trinidadandtobago/index.html Post-Conference Report for the WSEAS Conferences: MACMESE '07 and DNCOCO '07 Trinidad and Tobago Islands (Caribbean Sea), November 5-7, 2007 http://www.wseas.com/wseas/reports/trinidadandtobago/index.html * This report contains 124 images copyrighted by the WSEAS. All rights reserved. * If you need some image with high resolution please click on the images below * If you need some image with extremely high resolution, contact us by email The University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences, Department of Mathematics and Computer Science, St. Augustine, Trinidad (W. I.) http://www.wseas.com/wseas/reports/trinidadandtobago/index.html and the WSEAS Society (http://www.wseas.org) , coorganized the following two parallel conferences: * 9th WSEAS Int. Conf. on MATHEMATICAL and COMPUTATIONAL METHODS in SCIENCE and ENGINEERING (MACMESE'07) (This conference was part of the MMACTEE international conference until 2006) * 6th WSEAS Int. Conf. on DATA NETWORKS, COMMUNICATIONS, COMPUTERS (DNCOCO '07), (The name of this conference was ISCOCO until 2005) OPENING, KEYNOTE, PLENARY SPEECHES: The two parallel Conferences were opened by Professor Bal Bhatt, who is director of the Department of Mathematics and Computer Science of the University of West Indies and he was the chairman of the conference and Professor Winston Mellowes, who is the Chairman, Professor Dyer Narinesingth, who is the Dean of the University of West Indies, the Campus Principal Professor Bridget Brereton, Mr. John Roopchan of the Ministry of Education and Dr. Bhoendradatt Tewarie, Director of the Institute of Critical Thinking, where the conference was held. After the opening ceremony the first keynote speaker was Professor Biswa N. Datta (Distinguished Research Professor at the Northern Illinois University, USA), who has presented the recent advances on computational methods for active vibration control and model updating in vibrating structures. Professor Eyad H. Abed (Institute for Systems Research, Electrical and Computer Engineering, University of Maryland, USA) who was PLENARY SPEAKER also presented new results on selective modal analysis of dynamic systems On Tuesday, 6th November 2007 (2nd day of the conference), Professor Imre J. Rudas (Institute of Intelligent Engineering Systems John von Neumann Faculty of Informatics Budapest Tech, Budapest, Hungary) who was PLENARY SPEAKER also described interesting aggregation procedures in intelligent systems. http://www.wseas.com/wseas/reports/trinidadandtobago/index.html On Tuesday evening was the cocktail party for all participants of the WSEAS Conference, who were invited at the office of the Campus Principal Professor Bridget Brereton (See pictures below) Both of the WSEAS Conferences in Trinidad were characterized by their friendly atmosphere (see photos below) as well as the high quality of the presentations and discussions. A variety of topics constituted the focus of paper submissions. In regular sessions papers addressed several interesting topics. Prominent lectures provided key-note and plenary speeches for the conference. Moreover, special sessions were organized, and invited lectures were given by well-known researchers. With pride, the WSEAS received the following Important Contributions and upgraded them as Keynote and Plenary Lectures.: KEYNOTE LECTURE: Recent Advances on Computational Methods for Active Vibration Control and Model Updating in Vibrating Structures : Linking Control to Industry by Prof. Biswa N. Datta, Northern Illinois University, USA. PLENARY LECTURE 1: New Results on Selective Modal Analysis of Dynamic Systems by Prof. Eyad H. Abed, University of Maryland, Maryland, USA. PLENARY LECTURE 2: Polynomial Optimization via Sums of Squares Relaxations by Prof. Mihai Putinar, University of California at Santa Barbara, CA, USA. PLENARY LECTURE 3: Aggregation procedures in intelligent systems by Prof. Imre J. Rudas, Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Hungary. PLENARY LECTURE 4: Selection Problems and Multi-criteria Decision Making by Dr. Alexey L Sadovski, Texas A&M University-Corpus Christi, USA. BENEFITS FOR THE PARTCIPANTS: WSEAS, http://www.wseas.org gave a very strong and important tool to all the participants: A new username and password without expiry date for on-line access in the WSEAS Conference proceedings FOR EVER. Conference Statistics Submitted papers: 335 Accepted papers: 147 acceptance ratio = (Number of accepted papers / Number of Submitted)*100 = 43.88% Remark: Two withdrawn accepted papers are considered as accepted papers in our Statistics. .: REVIEW PROCESS: Each paper was reviewed at least by 3 independent reviewers. The WSEAS Secretariat sent each paper to 5 reviewers. Some papers received reviews from 5 different referees. The WSEAS Secretariat forwarded these comments by personalized emails to the responsible for the correspondence author. The full list of the reviewers will be available in the web page: http://www.worldses.org/reviewers.htm The additional features of these 2 conferences 1) Publication of the Proceedings in 3 media: hard-copy, CD, E-Library (A) One Book in the Electrical and Computer Engineering Series and Energy and Environmental Engineering Series of WSEAS (see details, contents, author indices and editors below) with ISBN and ISSN indexed by the major Citation Indices (ISI ranked): www.worldses.org/indexes (B) CD-ROM Proceedings with pages' numbers with ISBN and ISSN indexed by the major Citation Indexes: www.worldses.org/indexes (C) E-Library: http://www.wseas.org/online and possible, for a very small number of papers: (D) JOURNAL PUBLICATION: Expanded and enhanced versions of papers published in the conference proceedings also going to be considered for possible publication in one of the WSEAS journals that participate in the major International Scientific Indices (Elsevier, Scopus, EI, Compendex, INSPEC, CSA .... see: www.worldses.org/indexes ). 2) WSEAS gave a very strong and important tool to all the participants: A new username and password without expiry date for on- line access in the WSEAS Conference proceedings FOR EVER. 3) The Participants received 6 very rich coffee-breaks (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences), 1 Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences) and 1 Gala Dinner with the high quality of the WSEAS 4) Cultural and social part as usual in WSEAS events. 5) The conference Books (Hard-Copy Proceedings), CD-ROM proceedings and Journals (with selected papers) published by WSEAS Press continue to sell for a long time after the meeting has taken place. This is another demonstration of the prestige the scientific community attribute to the meetings organized by the WSEAS. .: BOOK (hard-copy of the Proceedings): Editors: Balswaroop Bhatt (Trinidad and Tobago), Bhoendradatt Tewarie (Trinidad and Tobago), Athina Lazakidou (Greece), Konstantinos Siasiakos (Greece). Pages : 506, price: 80 EUR [Contents], [Order], [Full PDF of the Papers], [Help] .: JOURNALS: .: What is the Permanent Procedure for additional Journal publication for a very small number of High-Quality Papers presented in the WSEAS Conferences in China (after the recommendation of Chairmen). So, the authors with accepted & presented papers received the following e- mail: We have started now the procedure for the evaluation of the extended versions of your papers for possible inclusion in the WSEAS journals after new rounds of review. INTRODUCTION: You know that our goal is to maintain very strong international journals, to increase the impact of our beloved WSEAS Transactions, really top journals as they really are. To this end, we need only high quality papers, breakthrough works of archival value, i.e. papers that are well written from any point of view, completed studies (with their numerical examples or experiments that must be compared with the previous results in the literature), excellent english language and of course correct WSEAS format. The papers also must be substantially extended version of the paper that was presented in the conference (with more than 40% new material). We need papers that will attract the attention of other scholars citing them increasing our impact. In the next few years, the WSEAS transactions must be in every academic library, in every corner of the earth. To this end, we need your high quality contribution. HOW TO PROCEED: a) Check very carefully if your idea is really important, breakthrough in your field and can appear in a Journal of the quality and the level of the WSEAS Transactions. If you doubt, do not send it so easily. Your paper must not be only a good idea. It must be a complete study with theoretical background, complete bibliographical references; without grammatical and syntactical errors. For theoretical works: full comparison with previous published papers is necessary. We need numerical examples, applicability of the method, originality, novelty and directions for future research. For experimental or computational works: full comparison with previous published papers is necessary. We need real experiments with the necessary documentation, while for computational work, we need full benchmarks. Of course along discussions for the applicability of the method, originality, novelty and directions for future research. b) Complete the extended version of your paper until December 31, 2007 and upload it via http://............... (the full web address was given only to authors that presented a paper) until December 31, 2007 c) If your extended version fulfills the paragraph a), then our Editors will send it to 3 independent Reviewers outside your country. If not, our Editors are entitled to reject it from this early stage informing you properly. The positive answer of the 3 reviewers is necessary (attention: 2 yes and 1 no implies NO, i.e. rejection). d) Our Editors will collect the reviewers' remarks and will send them again to you for acceptance/ acceptance after minor revision / acceptance after major revision / rejection e) Possibly new rounds of review will be needed. f) No additional fee is needed in case of acceptance. After all this procedure, the accepted papers that come from WSEAS Conferences in Canada will be published in the various WSEAS Transactions. IF you miss the deadline of December 31, 2007 , or if your paper was not presented in the WSEAS Conferences, THEN: you can upload it quite independently as regular paper from the WSEAS Site for the Journals: http://www.worldses.org/journals/index.html The final list of the papers must have the approval of our Editors and 3 Reviewers, and of course the Editor-in-Chief of the particular Journal. We want only authors that presented their papers to complete this web form: http://............... (the full web address was given only to authors that presented a paper) So, in this form you will need a password (the password was given only to the authors that presented a paper). .: BEST STUDENT PAPERS: The Organizing Committee received the forms that the Session Chairmen filled in after the end of their Sessions and after additional evaluation and discussion decided the following. The Criteria were: a) Originality and scientific impact b) Good presentation c) Paper presented by a student The results of this evaluation will be announced soon in the web page: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html .: INDICES: PROCEEDINGS: The Proceedings related to the Conference are covered by: 1. ISI (ISINET) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 6. ULRICH 9. Directory of Published Proceedings 10. Computer Science Bibliography Administrator 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Engineering Information 15. SCOPUS 16. EBSCO 17. EMBASE 18. Compendex (CPX) 19. GEOBASE 20. BIOBASE 21. BIOTECHNOBASE 22. FLUIDEX 23. OceanBase 24. BEILSTEIN Abstracts 25. World Textiles 26. MEDLINE 27. British Library 28. National Library of Greece 29. German National Library of Science and Technology 30. IARAS Index JOURNALS: The WSEAS journals are covered by: 1. ISI through the INSPEC (IEE) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 7. ULRICH 9. Computer Science Bibliography Administrator 10. British Library 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Swets Information Services 15. Engineering Information 16. SCOPUS 17. EBSCO 18. EMBASE 19. Compendex (CPX) 20. Geobase 21. BIOBASE 22. BIOTECHNOBASE 23. FLUIDEX 24. OceanBase 25. BEILSTEIN Abstracts 26. World Textiles 27. MEDLINE 28. Mayersche 29. Index of Information Systems Journals 30. National Library of Greece 31. IARAS Index .: SOCIAL PART (Coffee-Breaks, Banquet, Excursions) 6 very rich coffee-breaks with Coffee, Tea, Milk, Sweets, Cakes, Pastries, Juices and Sandwiches (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Excellent Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Gala Dinner. Participants enjoyed a wonderful night. .: Some Excursions took place after the conference. See the pictures: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html === Subject: Re: Regarding solution manual for Introduction to Algorithm. Thomas H. Cormen. posting-account=T7fhkAoAAADh6aLufWf8lNSXnUk_5MhJ CLR 1.1.4322),gzip(gfe),gzip(gfe) Did you find the soultions manual? If you do, could you please send it to me. I would appreciate it a lot! === Subject: I need Solution manual posting-account=2Ao9ggkAAAB1JcOMWiDDOjkHclbisJtt Gecko/20061010 Firefox/2.0,gzip(gfe),gzip(gfe) (squid/2.5.STABLE9) I am studying Engineering Electromagnetics. In the Course Some problem I am encountering. I need a Solution Manual of ENGINEERING ELECTROMAGNETICS (7/E) BY HAYT AND BUCK mail this solution of masaddique_159@yahoo.com THIANK YOU === Subject: Re: I need Solution manual Bye! === Subject: Much Help Needed on Difficult Calculus Problems Can anyone offer me any advice on how to work and answer any of the following questions? 1) Find the limit of the sequence x = n square root of n! as n tends to ¡. 2) Determine whether the series ¡ á (n!)^(-1/n) is convergent or divergent. n=1 3) Find the sum of the series ¡ á (1/2^n) tan (x/2^n) for every value of x. n=1 -Drew === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. That's as n tends to infinity. Or you could say informally that n becomes infinite. The problem as stated is pretty trivial since n sqrt(n!) > n for n > 1. --Lynn === Subject: Re: Much Help Needed on Difficult Calculus Problems in alt.math.undergrad: > Can anyone offer me any advice on how to work and answer > any of the following questions? > 1) Find the limit of the sequence x = n square root of n! > as n tends to ¡. Is there a typo in this one? > 2) Determine whether the series > ¡ > á (n!)^(-1/n) is convergent or divergent. > n=1 The denominator of the n-th term is the geometric mean of 1, 2, ..., n. Use the arithmetic mean - geometric mean inequality to compare with a familiar series. [...] Brian === Subject: helpppp pleasee!! whats is the antiderivative of 4x^-1 ?? === Subject: Re: helpppp pleasee!! in alt.math.undergrad: > whats is the antiderivative of 4x^-1 ?? The derivative of ln(x) with respect to x is 1/x, so the derivative of 4 ln(x) is 4/x. Brian === Subject: helpppp mee pleasee i need help using the substitution process to find... the antiderivative of r(radical r^2+2) dr help pleaseee === Subject: Re: helpppp mee pleasee >i need help using the substitution process to find... >the antiderivative of r(radical r^2+2) dr >help pleaseee If that's r sqrt(r^2 + 2) dr u = r^2 + 2 du = 2 r dr, so 1/2 du = r dr Antiderivative of 1/2 sqrt(u) du = 1/2 u^(1/2) du = ? === Subject: sub.. substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this === Subject: Re: sub.. >substitution process to find antiderivative of r(e^-r^2) dr >pleaseee help me with this Your turn. What do you think? === Subject: Re: sub.. > substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this Your turn. What do you think? > think. That appears to be the entire difficulty. === Subject: help with substitution i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee === Subject: Re: help with substitution ok, but my answer has to have a +c in it i think === Subject: Re: help with substitution >i need help using the substitution process to find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. === Subject: Re: help with substitution i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to > learn how to use complicated rules like mathematics has and consequently > consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar lessons? Dave === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar > lessons? Especially *wrong* ones. in rebellion to?? Wonton to flout?? His math is wrong (or wong), too. sqrt -1 doesn't mean anything: sqrt is a function, and one can't subtract a numberfrom it. Maybe he means sqrt(-1). -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com> i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. Yet alas you're not the OP to call me on that. do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar > lessons? > I offer full service help. Why can't they learn English? Do they have a learning disability? Math has even more rules and they're harder rules. What help can be given to those who detest rules? ---- === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. > Yet alas you're not the OP to call me on that. > > do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar lessons? > I offer full service help. > Why can't they learn English? > Do they have a learning disability? > Math has even more rules and they're harder rules. > What help can be given to those who detest rules? ---- Not all OP's are speaking english by nature, have pity with them. -- Vooruit mensen, achteruit! (Elimineer x voor een e-mail) Hou-du. === Subject: Re: help with substitution > >i need help using the substitution process to > find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you > haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always > s capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > consider you unable to > learn how to use complicated rules like mathematics > has and consequently > consider it meaningless to help you. === Subject: [] help with substitution <25173561.1197114231915.JavaMail.jakarta@nitrogen.mathforum.org> help pleaseee I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always s capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > Help. I'm needing help substituting 'eggroll' with a word that coheres your sentence. consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. > === Subject: substitution????? substtution to find antiderivative of (5e^(-3g)) dg === Subject: Re: substitution????? >substtution to find antiderivative of (5e^(-3g)) dg u = -3 g du = -3 dg, so dg = ? === Subject: hellppp me out use the substitution to find the indefinite integral antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please === Subject: Re: hellppp me out <1432039.1197079325702.JavaMail.jakarta@nitrogen.mathforum.org>, The best help we can offer is to advise you to pay more attention in class, and read the assigned sections of the text. === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please cant be done, your hosed! (try dividing first) === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt > > helppp me please >cant be done, your hosed! (try dividing first) > A joke of some sort? === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please If you are going to post all your homework questions, why not group them together in one post so we can keep straight which homework we are doing for you? --Lynn === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please Hint: the derivative of t^3 + 6 t + 3 is 3 t^2 + 6 = 3 (t^2 + 2) === Subject: sorry i just dont get the substitution and... i dont get the substitution process.. can somebody xplain it to me, for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for === Subject: Re: sorry i just dont get the substitution and... >i dont get the substitution process.. can somebody xplain it to me, >for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for The basic idea is that you want to put the given expession in one of the forms that you know an antiderivative for, such as Int u^a du = u^(a+1) / (a + 1) + C for all a except a = -1 Int e^u du = e^u + C So let's look at 6x^2 dx / (2 x^3 + 7)^(3/2) You see that there's an x^3 in the denominator, and an x^2 in the numerator. That's promising, because if we substitute for the x^3 in the denominator, the derivative of x^3 is 2x^2 and so we may have something easy to substitute in the numerator as well (including the dx of course). Looking more closely, we see that we have 2 x^3, whose derivative is 6 x^2. Now that's VERY good, because that's exactly what's in the numerator. So, say we try u = 2 x^3 du = 6 x^2 dx Our expression becomes du / (u + 7)^(3/2) But wait! Now we realize that if we had made the substitution u = 2 x^3 + 7, then du still equals 6 x^2 dx and the resulting expression is even simpler, namely du / u^(3/2) Now *that* is an expression we know an antiderivative for! So, let's do the problem from the beginning. Find an antiderivative for 6x^2 dx / (2 x^3 + 7)^(3/2) Let u = 2 x^3 + 7 Then du = 6 x^2 dx Substituting into the original expression gives du / u^(3/2) = u^(-3/2) du for which an antiderivative is u^(-3/2 + 1) / (-3/2 + 1) = u^(-1/2) / (-1/2) = -2 u^(-1/2) = -2 / u^(1/2) = -2 / sqrt(u) Now, we want to get the answer back in terms of x, so we substitute for u [remember, u = 2 x^3 + 7] and get -2 / (2 x^3 + 7)^(1/2) or -2 / sqrt(2 x^3 + 7) Putting the problem in the form of an indefinite integral, we can now write Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / (2 x^3 + 7)^(1/2) + C or Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / sqrt(2 x^3 + 7) + C The C is the so-called 'constant of integration', which I assume has been discussed in conjunction with antiderivatives and indefinite integrals. === Subject: Complicated Differential Equation Sorry all I made a mistake in the first differential equation post. The equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, and V are all known constants. Is there any way to approximate this expression for i(t)? In my original post the expression didn't have the last term so some suggested using the Lambert W-Function, and another suggested using Newton's method. Would I still be able to use these methods, and if so how would I use them? === Subject: Re: Complicated Differential Equation <30569604.1197093354146.JavaMail.jakarta@nitrogen.mathforum.org>, > Sorry all I made a mistake in the first differential equation post. The > equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, > and V are all known constants. Is there any way to approximate this > expression for i(t)? In my original post the expression didn't have the last > term so some suggested using the Lambert W-Function, and another suggested > using Newton's method. Would I still be able to use these methods, and if so > how would I use them? V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2 gives i(t)/[V-b*i(t)-c*i(t)^2]*i'(t) = 1/a Now use partial fractions to split up i(t)/[V-b*i(t)-c*i(t)^2] At which point integration is possible, and one can solve for i(t). === Subject: =?windows-1256?B?Ljo6IFsgwt7c5uwgyNHk3MfjzCDt3tzm4yDIytPR?= =?windows-1256?B?7dogzOXH0t/cIMjU39zhIOPHysrV3ObRIObH4ePdx8w=?= =?windows-1256?B?3Mfl3CDH5OUg38fj3OEgXSA6Oi4=?= posting-account=OEMLPAoAAAD96Le1WgD9Upxh2I266gSV SIMBAR={94AA8A13-642B-404A-B4A4-C4EFD1151A5B}; Alexa Toolbar),gzip(gfe),gzip(gfe) === Subject: read plz posting-account=Yt8G1goAAACz_ktFECg3NbvAf5VVNJ0C Gecko/2007080210 GranParadiso/3.0a7,gzip(gfe),gzip(gfe) donot mail at hotkid_1@hotmail.com for solution manuals i donot have any === Subject: read plz posting-account=Yt8G1goAAACz_ktFECg3NbvAf5VVNJ0C Gecko/2007080210 GranParadiso/3.0a7,gzip(gfe),gzip(gfe) donot mail at hotkid_1@hotmail.com for solution manuals i donot have any === Subject: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, or just write a bit about the topic, it would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics (Well, you would probably still need logic...). === Subject: Re: Foundations of Mathematics, help? > mathematics, what I mean by that is the things that > define mathematics, and which it is based on. Much in > the same was that mathematics defines much of physics > (I think...) I disagree very sharply with that, by the way. Physics is 'defined' by what we observe in experiments, not by mathematics! > Anyway, I am posting here because I don't have much > of an idea of where to start. If anyone could advise > there, or just write a bit about the topic, it would > be greatly appreciated. > Oh, and if there is anyone out there who wouldn't > mind me asking them some questions that will > undoubtedly come up as I study, please let me know. P.S. I have been told before to study set theory and > formal logic, and I will. But it also occurred to me > that these cannot be the only ways to define the > basis of mathematics (Well, you would probably still > need logic...). === Subject: Re: Foundations of Mathematics, help? mathematics, what I mean by that is the things > that define mathematics, and which it is based on. Much > in the same was that mathematics defines much of > physics (I think...) > I disagree very sharply with that, by the way. > way. Physics is 'defined' by what we observe in > experiments, not by mathematics! > I figured someone would say something like that... And I agree mostly, but it helped express the idea I was trying to, so I used it :) Anyway, I am posting here because I don't have > much of an idea of where to start. If anyone could > advise there, or just write a bit about the topic, it > would be greatly appreciated. Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me > know. P.S. I have been told before to study set theory > and formal logic, and I will. But it also occurred to > me that these cannot be the only ways to define the basis of mathematics (Well, you would probably > still need logic...). > ics and got a lot of intersting hits. Have you tried > that? Yup... === Subject: Re: Foundations of Mathematics, help? Anyway, I am posting here because I don't have much of an idea of where to start. If anyone could advise there, You could read Fraenkel, Bar-Hillel and Levy, _Foundations of Set Theory_ which covers more than its title suggests; and Feferman _The Number Systems_ the subtitle of which is _Foundations of Algebra and Analysis_. > or just write a bit about the topic, it would be greatly appreciated. > Oh, and if there is anyone out there who wouldn't mind me asking them some questions that will undoubtedly come up as I study, please let me know. sci.logic might be good for that. P.S. I have been told before to study set theory and formal logic, and I will. But it also occurred to me that these cannot be the only ways to define the basis of mathematics You could try Mac Lane _Categories for Working Mathematicians_ > (Well, you would probably still need logic...). -- How unlike the home life of our own dear Queen. === Subject: Re: Foundations of Mathematics, help? === Subject: hey guys posting-account=vz_6QQoAAABOxomOXgeWKt9p9p4FZ-ez SV1),gzip(gfe),gzip(gfe) people join this new group and make it an interactive place !! === Subject: solutions manuals posting-account=m06QOgkAAACFEdunwVichFUaRyeknXjQ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Can I get the manuals for: 1) Linear Algebra with Applications, Otto Bretscher,( Pearson Custom Publishing) 2) Fundamentals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Edward B. Saff, Arthur David Snider, (Pearson Custom Publishing) Are they the complete set? You can e-mail me at === Subject: implementation of simplex method in C language hi, I am looking for an implementation of simplex method in C language. === Subject: Re: implementation of simplex method in C language : > I am looking for an implementation of simplex method in C language. Just by any wild chance, could this be a homework assignment? -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: implementation of simplex method in C language >hi, >I am looking for an implementation of simplex method in >C language. http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html === Subject: Re: implementation of simplex method in C language posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > hi, > I am looking for an implementation of simplex method in C language. Why C? What difference does the language make? Or have you been asked to implement it yourself in C as part of an assignment???? I can suggest a number of commercially available LP packages. What are you willing to pay? === Subject: Water Treatment: Principles and Design, 2nd Edition posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) Can you send me Water Treatment: Principles and Design, 2nd Edition thank you very much liew168@sina.com === Subject: Re: Water Treatment: Principles and Design, 2nd Edition Can you send me Water Treatment: Principles and Design, 2nd Edition > thank you very much The answer is of course no. (If someone reading your post has the book and wishes to give it away, they would not know how to get it to you.) May I ask you a question? Why don't you go to a book shop and buy it like any normal person? (If you do so, do remember to mention the author and publisher.) -- How unlike the home life of our own dear Queen. === Subject: Re: List of solutions manual (thousands) posting-account=l38b7goAAABE2yhWy4bLppTaHZRMtIsc SV1),gzip(gfe),gzip(gfe) BERGH .8eæ.93.b9.81F > My List of Solutions Manual > contact me to : newbergh123@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. > This list (not links) is available from : > http://rapidshare.com/files/59002351/List of solutions manual.txt > > - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files > converted to pdf, real instructor sol. manual > Principles of Statics (10th Ed., Hibbeler) > Engineering Mechanics : Dynamics (11th Ed., Hibbeler)-Not mathcad > files converted to pdf, real instructor sol. manual > Principles of Dynamics (10th Ed., Hibbeler) > Mechanics of Materials (4th Ed, Hibbeler) > Mechanics of Materials (6th Ed, Hibbeler) > Mechanics of Materials (7th Ed, Hibbeler) > Statics and Mechanics of Materials (2nd Ed., Hibbeler) > Energy Principles and Variational Methods in Applied Mechanics (2nd > Ed., Reddy) > Theory of Vibrations with Applications (5th Ed., Thomson & Dahleh) > Engineering Vibrations (2nd Ed., Inman) > Engineering Vibrations (3rd Ed., Inman) > Theory of Vibration: An Introduction (2nd Ed., A.A. Shabana) > Vibration of Discrete and Continuous Systems (2nd Ed., Ahmed Shabana) > Introduction to Finite Element Vibration Analysis (Maurice Petyt) > Vibrations and Stability: Advanced Theory, Analysis, and Tools (2nd > Ed., Jon J. Thomsen) > Mechanical Vibrations (4th Ed., Rao) > Mechanical Vibration (William J. Palm, III) > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Finite Element Analysis Theory and Application with ANSYS (2nd Ed., > Moaveni) > Finite Element Analysis Theory and Application with ANSYS (3rd Ed., > Moaveni) > The Finite Element Method and Applications in Engineering Using ANSYS > (Madenci & Guven) + original Ebook > Modeling and Analysis of Dynamic Systems (3rd Ed, Close, Frederick & > Newell) > System Dynamics (1st Ed., William J Palm III) > System Dynamics: Modeling and Simulation of Mechatronic Systems (4th > Ed., Karnopp, Margolis & Rosenberg) > Concepts and Applications of Finite Element Analysis (4th Ed., Cook, > Malkus, Plesha & Witt) > Finite Element Modeling for Stress Analysis (Robert Cook) > Advanced Strength and Applied Elasticity (4th Ed., Ugural) > Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) + > original Ebook > Fracture Mechanics (2nd Ed., Anderson) > Mechanical Behavior of Materials (2nd Ed. Dowling) > Mechanical Behavior of Materials (3rd Ed. Dowling) > Mechanical Behavior of Materials (W.F. Hosford) + original Ebook > Mechanical Behavior of Materials (Keith Bowman) > Theory and Design for Mechanical Measurements (4th Ed, Figliola & > Beasley) > Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Principles of Metal Manufacturing Processes (Beddoes & Bibby) > Materials Selection in Mechanical Design (3rd Ed., Michael Ashby) > Introduction to Manufacturing Processes (3rd Ed., Schey) > Manufacturing Processes for Engineering Materials (5th Ed. Kalpakjian > & Smith) > Manufacturing, Engineering & Technology (4th Ed. Kalpakjian & Smith) > Manufacturing, Engineering & Technology (5th Ed. Kalpakjian & Smith) > Automation, Production Systems, and Computer-Integrated Manufacturing > (2nd Ed., Groover) > Introduction to Robotics: Mechanics and Control (3rd Ed, Craig) > Applied Manufacturing Process Planning: With Emphasis on Metal Forming > and Machining (Nelson, Schneider) > Linear State-Space Control Systems (Robert L. Williams, II & Douglas > A. Lawrence) > Rocket Propulsion Elements (7th Ed., George P. Sutton & Oscar Biblarz) > Mechanics of Flight (Warren F. Phillips) > Fundamentals of Airplane Flight Mechanics (David G. Hull) > Flight Performance of Fixed and Rotary Wing Aircraft (Antonio > Filippone) > Aircraft Structures for Engineering Students (3rd Ed., T.H.G. Megson) > + original ebook > Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson) > + original ebook > Mechanics of Aircraft Structures (2nd Ed, C. T. Sun) > Principles of Helicopter Aerodynamics (2nd Ed., Leishman) > Interactive Aerospace Engineering and Design (Dava Newman) > Fundamentals of Aerodynamics (3th Ed., Anderson) > Fundamentals of Aerodynamics (4th Ed., Anderson) > Introduction to Flight (5th Ed., Anderson) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Mechatronics (Sabri Cetinkunt) > Introduction to Mechatronics and Measurement Systems (3rd Ed., David > G. Alciatore & Michael B. Histand) > Introduction to Engineering Experimentation (2nd Ed., Wheeler & Ganji) > Gas Dynamics (3rd Ed., John & Keith) > Fundamentals of Gas Dynamics (2nd Ed, Robert D. Zucker) + original > Ebook > Internal Combustion Engines: Applied Thermosciences (2nd Ed., Ferguson > & Kirkpatrick) > Automotive Engines (8th Ed., Crouse) > Automotive Brake Systems Package (4th Ed., Rehkopf) > Automotive Engine Performance (2nd Ed., Halderman) > Automotive Mathematics (Jason C. Rouvel) > Blueprint Reading for the Machine Trades (6th Ed., Schultz & Smith) > Modern Welding Technology (6th Ed., Cary & Helzer) > Theory of Ground Vehicles (3rd Ed., J. Y. Wong) > Hydraulic Control Systems (Noah Manring) > Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. > Dixon) + original Ebook > Principles of Turbomachinery in Air-Breathing Engines (Baskharone) > Fundamentals of Jet Propulsion with Applications (Ronald D. Flack) > Fundamentals of Robotic Mechanical Systems: Theory, Methods, and > Algorithms (3rd Ed., Jorge Angeles) > Tissue Mechanics (Cowin, Doty) > BTEC First Engineering Curriculum Support Pack (Mike Tooley) > BTEC First Engineering (Mike Tooley) > Exploring Engineering: An Introduction for Freshmen to Engineering and > to the Design Process (Philip Kosky, George Wise, Robert Balmer & > William Keat) > Engineering Science (5th Ed., W. Bolton) > Fundamentals of Renewable Energy Processes (Aldo da Rosa) + original > Ebook > Renewable Energy (3rd Ed., SÀrensen or Sorensen) + original Ebook > Power Generation Technologies (Paul Breeze) + original Ebook > Concepts in Engineering (Holtzapple & Reece) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Autodesk Inventor (James M. Leake) > Foundations of Engineering (2nd Ed, Holtzapple & Dan Reece) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) - Electrical, Electronics & Computer Engineering > > Electrical Engineering: Principles and Applications (4th Ed., Allan R. > Hambley) > Electric Circuits (8th Ed., James W Nilsson & Susan Riedel) > Electric Circuits (7th Ed., James W Nilsson & Susan Riedel) > Introductory Circuits for Electrical and Computer Engineering (James > W. Nilsson, Susan A. Riedel) > Applied Electromagnetics: Early Transmission Lines Approach (Stuart M. > Wentworth) > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Introduction to Electric Circuits (6th Ed., Richard Dorf & James > Svoboda) > Introduction to Electric Circuits (7th Ed., Richard Dorf & James > Svoboda) > Modern Control Systems (11th Ed., Dorf) > System Dynamics (1st Ed., William J Palm III) > Electric Machines Analysis and Design Applying MatLab (Cathey) > Principles and Applications of Electrical Engineering (4th Ed, > Rizzoni) > Principles and Applications of Electrical Engineering (5th Ed, > Rizzoni) > Fundamentals of Electric Circuits (2nd Ed., Charles Alexander & > Matthew Sadiku) > Fundamentals of Electric Circuits (3rd Ed., Charles Alexander & > Matthew Sadiku) > Microelectronic Circuit Design (2nd Ed., Richard Jaeger & Travis > Blalock) > Microelectronic Circuit Design (3rd Ed., Richard Jaeger & Travis > Blalock) > Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with VHDL Design (2nd Ed., Stephen Brown > & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (1st Ed., Stephen > Brown & Zvonko Vranesic) > Fundamentals of Digital Logic with Verilog Design (2nd Ed., Stephen > Brown & Zvonko Vranesic) > Continuous and Discrete Control Systems (Dorsey) > Design with Operational Amplifiers and Analog Integrated Circuits (3rd > Ed., Sergio Franco) > Engineering Circuit Analysis (6th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Circuit Analysis (7th Ed., William H. Hayt, Jack Kemmerly > & Steven M. Durbin) > Engineering Electromagnetics (7th Ed., William H. Hayt & John A. Buck) > Principles of Electronic Materials and Devices (2nd Ed, Safa O. Kasap) > Principles of Electronic Materials and Devices (3rd Ed, Safa O. Kasap) > A First Lab in Circuits and Electronics (Yannis Tsividis) > Power Electronic Circuits (Issa Batarseh) > Power Electronics: Converters, Applications, and Design (3rd Ed., Ned > Mohan, Tore Undeland & William Robbins) > An Introduction to Digital and Analog Communications (2nd Ed., Simon > Haykin & Michael Moher) > Communication Systems (4th Ed., Simon Haykin) > Signals and Systems (2nd Ed., Simon Haykin & Barry Van Veen) > Programming in Haskell (Graham Hutton) > Logic in Computer Science: Modelling and Reasoning about Systems > (Michael Huth & Mark Ryan) > Introduction to Distributed Algorithms (2nd., Gerard Tel) > Information Theory, Inference and Learning Algorithms (David J. C. > MacKay) > Digital Systems Engineering (William J. Dally & John W. Poulton) > Concepts in Programming Languages (by John C. Mitchell) > Simulation Modeling and Analysis with Expertfit Software (4th Ed., > Averill Law) > Measurement Systems (5th Ed, Ernest Doebelin) > Wireless Communications (Andrea Goldsmith) > Testing of Digital Systems (N. K. Jha & S. Gupta) > Space-Time Coding (Hamid Jafarkhani) > Space-Time Block Coding for Wireless Communications (Erik G. Larsson & > Petre Stoica) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Radio-Frequency Electronics: Circuits and Applications (Jon B. Hagen) > Photonic Devices (Jia-ming Liu) > Networking Wireless Sensors (Bhaskar Krishnamachari) > Mobile Wireless Communications (Mischa Schwartz) > Introduction to Color Imaging Science (Hsien-Che Lee) > Fundamentals of Wireless Communication (David Tse & Pramod Viswanath) > Fundamentals of Modern VLSI Devices (Yuan Taur & Tak H. Ning) > Electronic and Optoelectronic Properties of Semiconductor Structures > (Jasprit Singh) > Digital Signal Processing System Analysis and Design (Paulo S. R. > Diniz) > An Introduction to Statistical Signal Processing (Robert M. Gray) > An Introduction to Radio Frequency Engineering (Christopher Coleman) > Algebraic Codes for Data Transmission (Richard E. Blahut) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Fundamentals of Semiconductor Fabrication (Gary S. May, Simon M. Sze) > Semiconductor Devices: Physics and Technology (2nd Ed, Simon M. Sze) > Electric Machinery (6th Ed., Fitzgerald) + Ebook > Electric Machinery Fundamentals (4th Ed., Chapman) > Electric Machinery and Power System Fundamentals (Chapman) > Local Area Networks (2nd Ed., Keiser) > Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka) > Introduction to Signals and Systems (Lindner) > Digital Signal Processing (3rd Ed., Mitra) > Semiconductor Physics and Devices (3rd Ed., Donald A. Neamen) > Design for Electrical and Computer Engineers (1st Ed., Ralph Ford & > Chris Coulston) > Fundamentals of Modeling and Analyzing Engineering Systems (Cha, > Rosenberg, Dym) > Principles of Linear Systems (Philip E. Sarachik) > Power Systems Harmonics: Fundamentals, Analysis and Filter Design > (George J. Wakileh) > Principles of Adaptive Filters and Self-learning Systems (Anthony > Zaknich) > Control of Robot Manipulators in Joint Space (R. Kelly, V. Santib.87.96ez, > A. Lor.92a) > Modelling and Control of Robot Manipulators (2nd Ed., Lorenzo > Sciavicco, Bruno Siciliano) > Algebraic Methods for Nonlinear Control Systems (2nd Ed., Giuseppe > Conte, Claude H. Moog, Anna Maria Perdon) > Modern Control Engineering - Problems B (3rd Ed. K.OGATA) + Ebook > Modern Control Engineering (4th Ed. K.OGATA) > LabVIEW 8 Student Edition (Bishop) > Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami- > Naeini) > Modeling and Simulation of Dynamic Systems (Woods, Lawrence) > Computer Numerical Control: Operation and Programming (3rd Ed., > Stenerson & Curran) > Engineering Problem Solving with C (3rd Ed., Etter) > Process Control Instrumentation Technology (8th Ed., Johnson) > Electrical Power and Controls (2nd Ed., Skvarenina & DeWitt) > Electronics and Computer Math (8th Ed., Deem & Zannini) > Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based > Introduction (John Semmlow) > Aircraft Digital Electronic and Computer Systems: Principles, > Operation and Maintenance (Mike Tooley) > VLSI Test Principles and Architectures: Design for Testability (Chen, > Cheng, Eklow et al.) > Mechatronics: Principles and Applications (Godfrey Onwubolu) > Machine Vision: Theory, Algorithms, Practicalities (3rd Ed., E. R. > Davies) > Instrumentation and Control Systems (W. Bolton) > Essential Java for Scientists and Engineers (Brian D Hahn & Katherine > M Malan) > Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Ed., > Bernard V. Liengme) > Electric Motors and Drives : Fundamentals, Types and Applications (3rd > Ed., Austin Hughes) > 10-Key Touch Key: Developing Speed and Accuracy (Burton) > Introduction to C++ Programming, Brief (Y. Daniel Liang) > C++ for Business Programmers (2nd Ed., John C. Molluzzo) > Introduction to Java Programming-Comprehensive Version (6th Ed., Y. > Daniel Liang) > Introduction to Java Programming: Fundamentals First (6th Ed., Y. > Daniel Liang) > Objects First With Java: A Practical Introduction Using BlueJ (3rd > Ed., David J. Barnes & Michael Kolling) > Java: An Introduction to Problem Solving and Programming (4th Ed., > Walter Savitch) > Simply Java Programming: An Application-Driven» Tutorial Approach > (Deitel) > Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & > Jeffrey Nyhoff) > Advanced Java» 2 Platform How to Program (Deitel & Santry) > SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) > Introduction to Programming Using Visual Basic 2005 (6th Ed., David I. > Schneider) > Simply Visual Basic 2005 (2nd Ed., Harvey & Paul Deitel & Associates) > Visual Basic 2005 How to Program (3rd Ed., Deitel & Associates) > Introduction to Programming with Visual Basic 6.0 (4th Ed., David I. > Schneider) > Visual Basic.Net Programming (2nd Ed., Jeffrey Tsay) > Simply Visual Basic .NET (Deitel & Nieto) > Mechatronics (Sabri Cetinkunt) > Introduction to Linear Programming (Leonid N. Vaserstein) > Science of Electronics, The: DC/AC (David M. Buchla, Thomas L. Floyd) > Introductory Circuit Analysis (11th Ed., Robert L. Boylestad) > Principles of Electric Circuits: Conventional Current Version (8th > Ed., Thomas Floyd) > Contemporary Electric Circuits: Insights and Analysis (2nd ed., > Strangeway, Petersen, Gassert & Lokken) > Electronics Technology Fundamentals - Conventional Flow (2nd Ed., > Robert T. Paynter & Toby Boydell) > Electronics Fundamentals: Circuits, Devices and Applications (7th Ed., > Thomas L. Floyd) > Principles of Electric Circuits: Electron Flow Version (8th Ed., > Thomas L. Floyd) > Electronics Technology Fundamentals - Electron Flow (2nd Ed., Robert > T. Paynter, Toby Boydell) > Introductory DC/AC Circuits (6th Ed., Nigel P. Cook) > Introductory DC/AC Electronics (6th Ed., Nigel P. Cook) > Electronic Devices - Conventional Current Version (7th Ed., Thomas L. > Floyd) > Electronic Devices - Conventional Current Version (8th Ed., Thomas L. > Floyd) > Electronic Devices - Electron Flow Version (8th, Thomas L. Floyd) > Electronic Devices and Circuit Theory (9th Ed., Robert L. Boylestad, > Louis Nashelsky) > Introductory Electronic Devices and Circuits: Electron Flow Version > (7th Ed., Robert T. Paynter) > Introductory Electronic Devices and Circuits: Conventional Flow > Version (7th Ed., Robert T. Paynter) > Electronic Devices - Electron Flow Version (5th, Thomas L. Floyd) > Science of Electronics, The: Digital (Thomas L. Floyd & David M. > Buchla) > Science of Electronics, The: Analog Devices (Thomas L. Floyd, David M. > Buchla) > Digital Electronics: A Practical Approach (7th Ed., William Kleitz) > Digital Electronics: A Practical Approach (8th Ed., William Kleitz) > Digital Systems: Principles and Applications (10th Ed., Ronald Tocci, > Neal Widmer, Greg Moss) > Digital Electronics with VHDL - Quartus II Version (William Kleitz) > Digital Fundamentals (9th Ed., Thomas L. Floyd) > Digital Fundamentals with PLD Programming (Thomas L. Floyd) > The 8051 Microcontroller (4th Ed., I. Scott MacKenzie, Raphael Chung- > Wei Phan) > The 8051 Microcontroller and Embedded Systems (2nd Ed., Muhammad Ali > Mazidi, Janice Mazidi & Rolin McKinlay) > INTEL Microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486, > Pentium, Prentium ProProcessor, Pentium II, III, 4, (7th Ed., Barry B. > Brey) > Microcontroller Technology: The 68HC11, 5/E (Peter Spasov) > PIC Microcontroller (Muhammad Ali Mazidi, Rolin McKinlay & Danny > Causey) > Industrial Electronics (James A. Rehg, Glenn J. Sartori) > Programmable Controllers Using the Allen-Bradley SlC-500 Family (2nd > Ed., Dave Geller) > Programmable Logic Controllers (James A. Rehg, Glenn J. Sartori) > Fundamentals of Programmable Logic Controllers, Sensors, and > Communications (3rd Ed., Jon Stenerson) > An Introduction to Programming with Visual Basic 6.0, Update Edition > (4th Ed., Schneider) > C++ Programming Today (Barbara Johnston) > Introduction to Data Communications and Networking (Wayne Tomasi) > Introduction to Telecommunications (2nd Ed., Martha Rosengrant) > Network Security Essentials: Applications and Standards (3rd Ed., > William Stallings) > Information Security: Principles and Practices (Mark Merkow, James > Breithaupt) > Principles and Practice of Information Security (Linda Volonino, > Stephen R. Robinson) > Modern Electronic Communication (8th Ed., Jeff Beasley, Gary M. > Miller) > Modern Electronic Communication (9th Ed., Jeff Beasley, Gary M. > Miller) > Electronic Communications for Technicians (2nd ed., Tom Wheeler) > Concepts In Systems and Signals (2nd Ed., John D. Sherrick) > Understanding Fiber Optics (5th Ed., Jeff Hecht) > Understanding UNIX/LINUX Programming: A Guide to Theory and Practice > (Bruce Molay) > Applying PIC18 Microcontrollers: Architecture, Programming, and > Interfacing using C and Assembly (Barry B. Brey) > Electrical Power and Controls (2nd Ed., Timothy L. Skvarenina, William > E. DeWitt) > Process Control Instrumentation Technology (8th Ed., Curtis Johnson) > Electrical Machines, Drives and Power Systems (6th Ed., Theodore > Wildi) > Introduction to Vacuum Technology (David M. Hata) > Electronic Project Design and Fabrication (6th Ed., Ronald A. Reis) > Technology and Society (3rd Ed., Linda Hjorth, Barbara A. Eichler, > Ahmed S. Khan, John Morello) > Solid State Electronic Devices (6th Ed., Ben Streetman, Sanjay > Banerjee) > Approaching Quantum Computing (Dan C. Marinescu & Gabriela M. > Marinescu) > Foundations of MEMS (Chang Liu) > Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby) > Elements of Engineering Electromagnetics (6th Ed., Nannapaneni > Narayana Rao) > Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti) > Digital Design: Principles and Practices Package (4th Ed., John F. > Wakerly) > VHDL: A Starter's Guide (2nd Ed., Sudhakar Yalamanchili) > Computer Organization and Architecture: Designing for Performance (7th > Ed., William Stallings) > Parallel Programming: Techniques and Applications Using Networked > Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & > Michael Allen) > Fundamentals of Parallel Processing (Harry F. Jordan & Gita Alaghband) > Feedback Control of Dynamic Systems (5th Ed., Gene Franklin, J.D. > Powell, Abbas Emami-Naeini) > Digital & Analog Communication Systems (7th Ed., Leon W. Couch) > Fundamentals of Communication Systems (John G. Proakis, Masoud Salehi) > Modern Wireless Communications (Simon Haykin, Michael Moher) > Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud > Salehi) > Data and Computer Communications (8th Ed., William Stallings) > Cryptography and Network Security (4th Ed., William Stallings) > Computer Networking with Internet Protocols (William Stallings) > Probabilistic Systems and Random Signals (Abraham H Haddad) > Error Control Coding (2nd Ed., Shu Lin & Daniel J. Costello) > Wireless Communications & Networks (2nd ed., William Stallings) > Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) > Detection and Estimation:Theory; and Its Applications (Thomas > Schonhoff & Arthur Giordano) > Signals, Systems, and Transforms (3rd Ed., Charles L. Phillips, John > M. Parr & Eve A. Riskin) > Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., > Edward W. Kamen & Bonnie S Heck) > Digital Signal Processing (4th Ed., John G. Proakis, Dimitris K > Manolakis) > Adaptive Filter Theory (4th Ed., Simon Haykin) > Spectral Analysis of Signals (Petre Stoica & Randolph L. Moses) > Fluency with Information Technology: Skills, Concepts, and > Capabilities (2nd Ed., Lawrence Snyder) > Fluency with Information Technology, Brief Edition (Lawrence Snyder) > Jolly) > Comprehensive Excel 2002 for Office XP (4th Ed., Karen J. Jolly) > Ethics for the Information Age (2nd Ed., Michael J. Quinn) > Computer Science: An Overview (8th Ed., J. Glenn Brookshear) > Computer Science: An Overview (9th Ed., J. Glenn Brookshear) > Concise Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Concise Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Extended Prelude to Programming: Concepts and Design (2nd Ed., Stewart > Venit) > Extended Prelude to Programming (3rd Ed., Stewart Venit & Elizabeth > Drake) > Logic and Design of Computer Programs (Jim Messinger) > Absolute C++ (2nd Ed., Walter Savitch) > Absolute C++ (3rd Ed., Walter Savitch) > Starting Out with C++: Early Objects (6th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > Problem Solving with C++: The Object of Programming (5th Ed., Walter > Savitch) > Problem Solving with C++ (6th Ed., Walter Savitch) > Problem Solving, Abstraction, and Design using C++ (4th Ed., Frank L. > Friedman & Elliot B. Koffman) > Problem Solving, Abstraction & Design Using C++ (5th Ed., Frank L. > Friedman & Elliot B. Koffman) > Ed., Tony Gaddis) > Starting out with C++ Brief Version Updated (4th Ed., Tony Gaddis & > Barret Krupnow) > Starting out with C++ Brief Version (5th Ed., Tony Gaddis & Barret > Krupnow) > Starting Out with C++: Brief Version Update, Visual C++ .NET (4th Ed., > Tony Gaddis & Barret Krupnow) > Starting Out with C++: Early Objects (5th Ed., Tony Gaddis, Judy > Walters & Godfrey Muganda) > C++ By Dissection (Ira Pohl) > Essential C++ for Engineers and Scientists (2nd Ed., Jeri R. Hanly) > C++ Coach: Essentials for Introductory Programming (Jeff Salvage) > C++ Primer (4th Ed., Stanley B. Lippman, Jos.8ee Lajoie & Barbara E. > Moo) > Engineering Computation with MATLAB (David Smith) > Absolute Java with Student Resource Disk (2nd Ed., Walter Savitch) > Absolute Java (3rd Ed., Walter Savitch) > The Art and Science of Java (Eric Roberts) > Building Java Programs: A Back to Basics Approach (Stuart Reges & > Martin Stepp) > Introduction to Programming in Java: An Interdisciplinary Approach > (Robert Sedgewick & Kevin Wayne) > Java Foundations: Introduction to Program Design and Data Structures > (John Lewis, Peter DePasquale & Joe Chase) > Starting Out with Java: Early Objects (3rd Ed., Tony Gaddis) > Ed., Tony Gaddis) > Java Software Solutions (Java 5.0 version): Foundations of Program > Design (4th Ed., John Lewis & William Loftus) > Java Software Solutions: Foundations of Program Design (5th Ed., John > Lewis & William Loftus) > Structures (Tony Gaddis & Godfrey Muganda) > Object of Java, The: Introduction to Programming Using Software > Engineering Principles (2nd Ed, David D. Riley) > Object-Oriented Programming in Java: A Graphical Approach, Preliminary > Edition (Kathryn E. Sanders & Andy van Dam) > Starting Out with Java 5: Control Structures to Objects (Tony Gaddis) > Starting Out with Java 5: Early Objects (Tony Gaddis) > Introduction to Programming Using Java: An Object-Oriented Approach > (2nd Ed., David Arnow, Scott Dexter & Gerald Weiss) > Computing with Java (2nd Ed., Art Gittleman) > Problem Solving with Java, Update (2nd Ed., Elliot B. Koffman & Ursula > Wolz) > Starting Out with Alice: A Visual Introduction to Programming (Tony > Gaddis) > Problem Solving and Program Design in C (4th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Problem Solving and Program Design in C (5th Ed., Jeri R. Hanly & > Elliot B. Koffman) > Starting Out with Visual Basic 2005 (3rd Ed., Tony Gaddis & Kip > Irvine) > Starting Out with Visual Basic 6 (Tony Gaddis, Kip Irvine & Bruce > Denton) > Starting Out with Visual Basic.Net (2nd Ed., Tony Gaddis, Kip Irvine & > Bruce Denton) > Computer Programming Fundamentals with Applications in Visual Basic¬ > 6.0 (Mitchell C. Kerman & Ronald L. Brown) > Advanced VB.NET Alternate with VB.Net CD's (3rd Ed., Kip Irvine & Tony > Gaddis) > Advanced Visual Basic 2005 (4th Ed., Kip Irvine & Tony Gaddis) > C# Software Solutions: Foundations of Program Design (John Lewis) > Problem Solving, Abstraction and Design Using C++, Visual C++.NET > Edition (Frank L. Friedman & Elliot B. Koffman) > Ada 95: Problem Solving and Program Design (3rd Ed., Michael B. > Feldman & Elliot B. Koffman) > Programming and Problem Solving with Delphi (Mitchell C. Kerman) > C Program Design for Engineers (2nd Ed., Jeri R. Hanly & Elliot B. > Koffman) > Data Abstraction & Problem Solving with C++ (5th ed., Frank M. > Carrano) > Data Structures and Algorithm Analysis in C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in C++ (3rd Ed., Mark Allen > Weiss) > Data Abstraction and Problem Solving with C++: Walls and Mirrors (4th > Ed., Frank M. Carrano) > Data Structures and Other Objects Using C++ (3rd Ed., Michael Main & > Walter Savitch) > Data Structures and Problem Solving Using C++ (2nd Ed., Mark Allen > Weiss) > Data Structures and Algorithm Analysis in Java (2nd Ed., Mark Allen > Weiss) > Collections Framework (Simon Gray) > Data Abstraction and Problem Solving with Java (2nd Ed., Frank M. > Carrano & Janet J. Prichard) > Data Structures and Other Objects Using Java (3rd Ed., Michael Main) > Data Structures and Problem Solving Using Java (3rd Ed., Mark Allen > Weiss) > Java Software Structures: Designing and Using Data Structures (2nd > Ed., John Lewis, Joseph Chase) > The Object of Data Abstraction and Structures (using Java) (David > Riley) > Classic Data Structures in Java (Timothy Budd) > Data Structures in Java (Thomas A. Standish) > Introduction to the Design and Analysis of Algorithms (1st Ed., Anany > V. Levitin) > Introduction to the Design and Analysis of Algorithms (2nd Ed., Anany > V. Levitin) > Algorithm Design (Jon Kleinberg & .83va Tardos) > Data Structures and Algorithm Analysis in C (2nd Ed., Mark Allen > Weiss) > Computer Algorithms: Introduction to Design and Analysis (3rd Ed., > Sara Baase & Allen Van Gelder) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (4th Ed., George F. Luger) > Artificial Intelligence: Structures and Strategies for Complex Problem > Solving (5th Ed., George F. Luger) > The Complete A+ Guide to PC Repair (3rd Ed., Cheryl A. Schmidt) > The Complete A+ Guide to PC Repair (4th Ed., Cheryl A. Schmidt) > Complete Computer Repair Textbook (4th Ed., Cheryl A. Schmidt) > Computer Systems Organization and Architecture (John D. Carpinelli) > CMOS VLSI Design: A Circuits and Systems Perspective (3rd Ed., Neil > H.E. Weste & David Harris) > Interactive Computer Graphics: A Top-Down Approach Using OpenGL (4th > Ed., Edward Angel) > File Structures: An Object-Oriented Approach with C++ (3rd Ed., > Michael J. Folk, Bill Zoellick & Greg Riccardi) > Oracle 10g Programming: A Primer (Rajshekhar Sunderraman) > Darwen) > Fundamentals of Database Systems (5th Ed., Ramez Elmasri & Shamkant B. > Navathe) > Database Systems: An Application Oriented Approach, Compete Version > (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > DataBase Systems: A Practical Approach to Design, Implementation and > Management (4th Ed., Thomas M. Connolly & Carolyn E. Begg) > Database Systems: An Application-Oriented Approach, Introductory > Version (2nd Ed., Michael Kifer, Arthur Bernstein & Philip M. Lewis) > Fundamentals of Database Systems/Oracle 9i Programming (4th Ed., Ramez > Elmasri, Shamkant B. Navathe & Rajshekhar Sunderraman) > Oracle 9i Programming: A Primer (Rajshekhar Sunderraman) > Principles of Database Systems with Internet and Java Applications > (Greg Riccardi) > Introduction to Data Mining (Pang-Ning Tan, Michael Steinbach & Vipin > Kumar) > Data Mining: A Tutorial Based Primer (Richard Roiger & Michael Geatz) > Learning SQL: A Step-by-Step Guide Using Access (Sikha Bagui & Richard > Earp) > Access 2007 Guidebook (6th Ed., Maggie Trigg & Phyllis Dobson) > Dobson) > Implementing Databases in Oracle 9i (John Day & Craig Van Slyke) > Web 101: Making the Net Work for You (2nd Ed., Wendy G. Lehnert) > Web 101 (3rd Ed., Wendy G. Lehnert & Richard L. Kopec) > Web Developer Foundations: Using XHTML (2nd Ed., Terry Felke-Morris) > Web Development & Design Foundations With XHTML (3rd Ed., Terry Felke- > Morris) > Internet Effectively: A Beginner's Guide to the World Wide Web (Tyrone > Adams & Sharon Scollard) > Light on the Web: Essentials to Making the 'Net Work for You (Wendy G. > Lehnert) > Programming the World Wide Web (3rd Ed., Robert W. Sebesta) > Programming the World Wide Web (4th Ed., Robert W. Sebesta) > XML: Language Mechanics and Applications (Dwight Peltzer) > Practical Perl with CGI Applications (Elizabeth Chang) > Developing Web Applications with Active Server Pages (Thom Luce) > Structure and Interpretation of Signals and Systems (Edward A. Lee & > Pravin Varaiya) > Languages and Machines: An Introduction to the Theory of Computer > Science (3r Ed., Thomas A. Sudkamp) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) > Galin) > Object Oriented Software Development Using Java (2nd Ed., Xiaoping > Jia) > Introduction to the Team Software Process (Watts S. Humphrey) > Software Project Management: A Real-World Guide to Success (Joel > Henry) > Software Engineering (8th Ed., Ian Sommerville) > Object-Oriented Programming featuring Graphical Applications in Java > (Michael J. Laszlo) > Project-Based Software Engineering: An Object-Oriented Approach > (Evelyn Stiller & Cathie LeBlanc) > Engineering of Software, The: A Technical Guide for the Individual > (Dick Hamlet & Joe Maybee) > Concepts of Programming Languages (7th Ed., Robert W. Sebesta) > Concepts of Programming Languages (8th Ed., Robert W. Sebesta) > Advanced Java: Internet Applications (2nd Ed., Art Gittleman) > Objects to Components with Java 2 Platform (Art Gittleman) > C for Java Programmers (Tomasz Muldner) > Pointers on C (Kenneth Reek) > C++ Programming with Design Patterns Revealed (Tomasz Muldner) > The C++ Programming Language (3rd Ed., Bjarne Stroustrup) > Operating Systems: A Systematic View (6th Ed., William S. Davis & T.M. > Rajkumar) > Unix: The Textbook (2nd Ed., Syed Mansoor Sarwar, Robert Koretsky & > Syed Aqeel Sarwar) > Operating Systems (3rd Ed., Gary Nutt) > LINUX & UNIX Programming Tools: A Primer for Software Developers (Syed > Mansoor Sarwar & Khaled H. Al-Saqabi) > Addison-Wesley's Interactive Linux Tutorial and Reference (Edutrends, > Inc.) > Linux: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel > Sarwar) > Kernel Projects for Linux (Gary Nutt) > OSP: An Environment for Operating System Projects (Michael Kifer & > Scott A. Smolka) > Distributed Computing: Principles and Applications (M.L. Liu) > Distributed Operating Systems and Algorithm Analysis (Randy Chow & > Theodore Johnson) > Mastering Networks: An Internet Lab Manual (Jorg Liebeherr & Magda El > Zarki) > Computer Networking: A Top-Down Approach Featuring the Internet (3rd > Ed., James F. Kurose & Keith W. Ross) > Computer Networking: A Top-Down Approach (4th Ed., James F. Kurose & > Keith W. Ross) > Computer Networking Complete Package (3rd Ed., James F. Kurose & Keith > W. Ross) > Network Management: Principles and Practice (Mani Subramanian) > Computer Security: Art and Science (Matt Bishop) > Introduction to Computer Security (Matt Bishop) > How to Break Software Security (James A. Whittaker & Herbert H. > Thompson) - Math, Statistics & Probability > > Advanced Engineering Mathematics (8th Ed., Erwin Kreyszig) > Advanced Engineering Mathematics (9th Ed., Erwin Kreyszig) > Elementary Differential Equations (7th Ed., Boyce) > Elementary Differential Equations (8th Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (7th > Ed., Boyce & Diprima) > Elementary Differential Equations and Boundary Value Problems (8th > Ed., Boyce & Diprima) > Differential Equations: An Introduction to Modern Methods and > Applications (James Brannan & William Boyce) > Introduction to the Finite Element Method: Theory, Programming and > Applications (Erik G. Thompson) > Measurement and Data Analysis for Engineering and Science (Patrick F > Dunn) > Elementary Linear Algebra (9th Ed., Anton) > Elementary Linear Algebra with Applications (9th Ed., Howard Anton & > Chris Rorres) > Applied Statistics and Probability for Engineers (3rd Ed., Douglas > Montgomery & George Runger) > Applied Statistics and Probability for Engineers (4th Ed., Douglas > Montgomery & George Runger) > Engineering Statistics (3rd Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Engineering Statistics (4th Ed., Douglas Montgomery, George Runger & > Norma Faris Hubele) > Probability and Statistics in Engineering (4th Ed., William W. Hines, > Douglas Montgomery, David Goldsman & Connie Borror) > Design and Analysis of Experiments (6th Ed., Douglas Montgomery) > Spreadsheet Tools for Engineers using Excel (2nd Ed. Byron S > Gottfried) > Spreadsheet Tools for Engineers using Excel (3rd Ed. Byron S > Gottfried) > Numerical Methods for Engineers (4th Ed. Steven C. Chapra) > Numerical Methods for Engineers (5th Ed. Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (1st Ed., Steven C. Chapra) > Applied Numerical Methods with MATLAB for Engineers and Scientists > (2nd Ed., Steven C. Chapra) > Statistics for Engineers and Scientists (1st Ed, William C. Navidi) > Statistics for Engineers and Scientists (2nd Ed, William C. Navidi) > Probability (Jim Pitman) > Numerical Methods with Matlab (Amos Gilat & Vish Subramaniam) > MATLAB: An Introduction with Applications (2nd Ed., Amos Gilat) > Discrete and Combinatorial Mathematics (5th ed., Ralph P. Grimaldi) > Discrete Mathematics (Sherwood Washburn, Thomas Marlowe & Charles T. > Ryan) > Discrete Mathematics (5th ed., John Dossey, Albert Otto, Lawrence > Spence & Charles Vanden Eynden) > Mathematics for New Technologies (Don Hutchison & Mark Yannotta) > An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy) > Fundamentals of Finite Element Analysis (1st Ed., David V. Hutton) > The Finite Element Method: Its Basis and Fundamentals (6th Ed., > Zienkiewicz, R. L. Taylor & J.Z. Zhu) > Differential Equations (A. King, J. Billingham, S. Otto) > Regression Methods in Biostatistics: Linear, Logistic, Survival, and > Repeated Measures Models (Eric Vittinghoff, David Glidden, Stephen > Shiboski, Charles McCulloch) > A Modern Introduction to Probability and Statistics: Understanding Why > and How (F.M. Dekking, C. Kraaikamp, H.P. Lopuha.8a, L.E. Meester) > Statistical Methods for the Analysis of Repeated Measurements (Charles > S. Davis) > Bayesian Core: A Practical Approach to Computational Bayesian > Statistics (Jean-Michel Marin, Christian Robert) > Essentials of Stochastic Processes (Rick Durrett) > Regression Analysis: Theory, Methods, and Applications (Ashish Sen & > Muni Srivastava) > Applied Probability and Statistics (Mario Lefebvre) > Foundations of Hyperbolic Manifolds (2nd Ed., John Ratcliffe) > Fourier and Laplace Transforms (R. J. Beerends , H. G. ter Morsche) > Infinite-Dimensional Dynamical Systems (James C. Robinson) > Mathematical Methods for Physics and Engineering, (3rd Ed., Riley, > Hobson & Bence) + original Ebook > Numerical Methods in Engineering with MATLAB (Jaan Kiusalaas) + > original Ebook > Numerical Methods in Engineering with Python (Jaan Kiusalaas) + > original Ebook > An Introduction to Numerical Analysis (Endre Suli and David Mayers) + > original Ebook > Fundamentals of Engineering Numerical Analysis (Parviz Moin) > Monte Carlo Statistical Methods (2nd Ed., Christian P. Robert, George > Casella) > Introduction to Mathematical Structures and Proofs (Larry J. Gerstein) > Analyzing Categorical Data (Jeffrey S. Simonoff) > Fundamentals of Complex Analysis with Applications to Engineering, > Science, and Mathematics (3rd Ed., E. Saff & Arthur Snider) > Probability & Statistics for Engineers & Scientists (8th Ed., Walpole, > Myers, Ye) > Statistics for Engineering and the Sciences (5th Ed., Mendenhall & > Sincich) > Miller & Freund's Probability and Statistics for Engineers (7th Ed., > Johnson, Miller, Freund) > Applied Numerical Analysis Using MATLAB (2nd Ed., Fausett) > Numerical Methods Using Matlab (4th Ed., Mathews & Fink) > Applied Numerical Methods for Engineers and Scientists (Rao) > Applied Numerical Analysis Using MATLAB (2nd Ed., Laurene v. Fausett) > Friendly Introduction to Numerical Analysis (Bradie) > Elementary Linear Algebra (2nd Ed., Spence, Insel & Friedberg) > Elementary Linear Algebra with Applications (9th Ed., Kolman & Hill) > Introductory Linear Algebra: An Applied First Course (8th Ed., Kolman > & Hill) > Linear Algebra with Applications (7th Ed., S. Leon) > Linear Algebra for Engineers and Scientists Using Matlab (Hardy) > Linear Algebra with Applications (3rd Ed., Bretscher) > Modern Matrix Algebra (Hill & Kolman) > Partial Differential Equations and Boundary Value Problems with > Fourier Series (2nd ed., Asmar) > Applied Partial Differential Equations (4th Ed., Haberman) > Technical Calculus (5th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics (2th Ed., Dale Ewen, Joan S. Gary & James E. > Trefzger) > Technical Mathematics with Calculus (2th Ed., Dale Ewen, Joan S. Gary > & James E. Trefzger) > Introductory Mathematics (4th Ed., Cook) > Mathematics for the Technical Trades (Cook) > College Mathematics (7th Ed., Cleaves & Hobbs) > Fundamentals of Statistics (2nd Ed., Michael III Sullivan) > Statistics: Informed Decisions Using Data (2nd Ed., Michael III > Sullivan) > Modern Elementary Statistics (12th Ed., John E. Freund, Benjamin M. > Perles) > Franklin) > Elementary Statistics: Picturing the World (3rd Ed., Larson & Farber) > First Course in Statistics (9th Ed., James T. McClave & Terry Sincich) > Statistics (10th Ed., McClave & Terry Sincich) > Interactive Statistics (3rd Ed., Martha Aliaga & Brenda Gunderson) > Statistics for the Life Sciences (3rd Ed., Samuels & Witmer) > Applied Statistics and the SAS Programming Language (5th Ed., Cody & > Smith) > Biostatistics for the Health Sciences (R. Clifford Blair & Richard > Taylor) > Biostatistics: How It Works (Steve Selvin) > Business Statistics: First Course and Student CD (4th Ed., David M. > Levine, Timothy C. Krehbiel & Mark L. Berenson) > Course in Business Statistics with CD-ROM (4th Ed., Groebner, Shannon, > Fry & Smith) > Business Statistics: Decision Making and Student CD Package (7th Ed., > Groebner) > Business Statistics: A Decision-Making Approach and Student CD Update > Package (6th Ed., Groebner, Shannon, Fry & Smith) > Statistics for Business & Economics (10th Ed., McClave, Benson & > Sincich) > Statistics for Managers Using Excel and Student CD Package (5th Ed., > Levine) > Statistics for Managers Using Microsoft Excel and Student CD Package > (4th Ed., Levine, Stephan, Krehbiel & Berenson) > Statistics for Business and Economics and Student CD (6th Ed., > Newbold, Carlson & Thorne) > Statistics for Business and Economics and Student CD-ROM (5th Ed., > Newbold, Carlson & Thorne) > Basic Business Statistics: Concepts and Applications and CD package > (10th Ed., Berenson, Krehbiel & Levine) > John E. Freund's Mathematical Statistics with Applications (7th Ed., > Miller) > Probability and Statistical Inference (7th Ed., Hogg & Tanis) > Introduction to Mathematical Statistics (6th Ed., Hogg, Craig & > McKean) > Introduction to Mathematical Statistics and Its Applications (4th Ed., > Larsen & Marx) > Brief Course in Mathematical Statistics (Hogg & Tanis) > Fundamentals of Probability, with Stochastic Processes (3rd Ed., Saeed > Ghahramani) > First Course in Probability (7th Ed., Sheldon Ross) > Applied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern) > Multivariate Data Analysis (6th Ed., Hair, Black, Babin, Anderson & > Tatham) > Essential MATLAB for Engineers and Scientists (3rd Ed., Brian D Hahn & > Dan Valentine) > Introduction to Applied Statistical Signal Analysis: Guide to > Biomedical and Electrical Engineering Applications (3rd Ed. Richard > Shiavi) > Construction Mathematics (Surinder Virdi & Roy Baker) > Numerical Methods in Biomedical Engineering (Stanley Dunn, Alkis > Constantinides & Prabhas Moghe) > Probability and Statistics with Integrated Software Routines (Ronald > Deep) > Boundary Value Problems and Partial Differential Equations (5th Ed., > David Powers) > Finite Element Analysis with Error Estimators : An Introduction to the > FEM and Adaptive Error Analysis for Engineering Students (J. Akin) > Basic Engineering Mathematics (4th Ed., John Bird) > Engineering Mathematics (4th Ed., John Bird) > Higher Engineering Mathematics (5th Ed., John Bird) > Mathematics for Electrical Engineering and Computing (Mary > Attenborough) > Introductory Statistics for Engineering Experimentation (Peter Nelson, > Karen Copeland & Marie Coffin) > Understanding Engineering Mathematics (Bill Cox) > Statistics And Probability For Engineering : Applications With > Microsoft Excel (Decoursey) > Business Math Using Calculators: With 10-Key Computer Assisted > Instruction (Burton) > Mathematics for Economics and Business (5th Ed., Ian Jacques) > Business Math, Brief w/CD & Study Guide & Tutor Center Access Card Pkg > (7th Ed., Cleaves & Hobbs) > Math for Merchandising: A Step-by-Step Approach (3rd Ed., Moore) > Mathematics for Business (7th Ed., Salzman , Miller & Clendenen) > Mathematics for Business (8th Ed., Salzman , Miller & Clendenen) > Advanced Engineering Mathematics (2nd Ed, Michael Greenberg) > Basic College Mathematics with Early Integers (K. Elayn Martin-Gay) > Developmental Mathematics (K. Elayn Martin-Gay) > Essentials of Basic College Mathematics (John Jr Tobey, Jr., Jeffrey > Slater) > Basic College Mathematics (5th Ed., John Tobey & Jeffrey Slater) > Prealgebra (5th Ed., K. Elayn Martin-Gay) > Prealgebra & Introductory Algebra (2nd Ed., K. Elayn Martin-Gay) > Prealgebra (3rd Ed., Jamie Blair, John Tobey & Jeffrey Slater) > Elementary Algebra Early Graphing for College Students (3rd Ed., Allen > R. Angel) > Elementary Algebra (Michael Sullivan III, Katherine R. Struve & Janet > Mazzarella) > Elementary Algebra for College Students (7th Ed., Allen R. Angel) > Experiencing Introductory and Intermediate Algebra Through Functions > and Graphs (3rd Ed., JoAnne Thomasson & Robert Pesut) > Introductory Algebra (3rd Ed., K. Elayn Martin-Gay) > Beginning Algebra (6th Ed., John Jr Tobey & Jeffrey Slater) > Beginning Algebra: Early Graphing (Jamie Blair, John Tobey & Jeffrey > Slater) > Beginning and Intermediate Algebra (2nd Ed., Jamie Blair, John Tobey & > Jeffrey Slater) > Introductory Algebra (4th Ed., Robert F Blitzer) > Introductory and Intermediate Algebra (2nd Ed., Robert F Blitzer) > Intermediate Algebra for College Students (7th Ed., Allen R. Angel) > Intermediate Algebra (Michael Sullivan III & Katherine R. Struve) > Intermediate Algebra (3rd Ed., K. Elayn Martin-Gay) > Essentials of Intermediate Algebra for College Students (Robert F. > Blitzer) > Intermediate Algebra (4th Ed., Robert F Blitzer) > Algebra A Combined Approach (3rd Ed., K. Elayn Martin-Gay) > Elementary & Intermediate Algebra (Michael Sullivan III, Katherine R. > Struve & Janet Mazzarella) > Essentials of Introductory and Intermediate Algebra for College > Students (Robert F. Blitzer) > Algebra for College Students (3rd Ed., Allen R. Angel) > Algebra for College Students (5th Ed., Robert F Blitzer) > College Geometry: A Problem Solving Approach with Applications (2nd > Ed., Gary L. Musser, Lynn Trimpe & Vikki R. Maurer) > College Algebra (8th Ed., Michael Sullivan) > College Algebra Essentials (8th Ed., Michael Sullivan) > College Algebra (4th Ed., Robert F. Blitzer) > College Algebra Essentials (2nd Ed., Robert F. Blitzer) > College Algebra: An Early Functions Approach (Robert F. Blitzer) > College Algebra: Concepts Through Functions (Michael Sullivan III & > Michael Sullivan) > College Algebra Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Essentials of College Algebra: Enhanced with Graphing Utilities (4th > Ed., Michael Sullivan III & Michael Sullivan) > Algebra and Trigonometry (8th Ed., Michael Sullivan) > Algebra and Trigonometry (3rd Ed., Robert F. Blitzer) > Algebra and Trigonometry: An Early Functions Approach (Robert F. > Blitzer) > Precalculus: Concepts Through Functions, A Right Triangle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Algebra & Trigonometry (7th Ed., Michael Sullivan) > Algebra and Trigonometry Enhanced With Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Trigonometry (7th Ed., Michael Sullivan) > Trigonometry (8th Ed., Michael Sullivan) > Trigonometry Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus (8th Ed., Michael Sullivan) > Precalculus (3rd Ed., Robert F. Blitzer) > Precalculus Essentials (2nd Ed., Robert F. Blitzer) > Precalculus: Concepts Through Functions, A Unit Circle Approach to > Trigonometry (Michael Sullivan III & Michael Sullivan) > Precalculus Enhanced with Graphing Utilities (4th Ed., Michael > Sullivan III & Michael Sullivan) > Precalculus Essentials: Enhanced with Graphing Utilities (4th Ed., > Michael Sullivan III & Michael Sullivan) > Thinking Mathematically (4th Ed., Robert F. Blitzer) > Excursions in Modern Mathematics (5th Ed., Peter Tannenbaum) > Excursions In Modern Mathematics with Mini-Excursions (6th Ed., Peter > Tannenbaum) > Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) > Fundamentals of Mathematics (10th Ed., William M Setek & Michael A > Gallo) > Learning Math in Elementary and Middle School & IMAP Package (4th Ed., > George Cathcart, Yvonne M. Pothier, James H. Vance & Nadine S. Bezuk) > Understanding the Math You Teach: Content and Methods for > Prekindergarten Through Grade 4 (Anita C. Burris) > Algebra Connections (Ira J. Papick & UMO University of Missouri) > Calculus Connections (Asma Harcharras, Dorina Mitrea) > Data Analysis and Probability Connections: Mathematics for Middle > School Teachers (Debra A. Perkowski & Michael Perkowski) > Geometry Connections (John K. Beem) > Elementary Math Modeling Updated (2nd Ed., Mary Ellen Davis & C. Henry > Edwards) > Additional Calculus Topics (11th Ed., Raymond Barnett, Michael Ziegler > & Karl Byleen) > Finite Math and Its Application (9th Ed., Larry J Goldstein, David I > Schneider & Martha J. Siegel) > Introductory Mathematical Analysis for Business, Economics and the > Life and social Sciences (11th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Introductory Mathematical Analysis for Business, Economics and the > Life and Social Sciences (12th Ed., Ernest F Haeussler, Richard S. > Paul & R.J. Wood) > Additional Calculus Topics (9th Ed., Raymond A. Barnett, Michael R. > Ziegler & Karl E. Byleen) > College Mathematics for Business, Economics, Life Sciences and Social > Sciences (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. > Byleen) > Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, > David I Schneider, David I. Lay & Nakhle Asmar) > Calculus and its Applications (11th Ed., Larry J Goldstein, David I > Schneider, David I. Lay & Nakhle Asmar) > Calculus for Business, Economics, Life Sciences and Social Sciences > (10th Ed., Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) > Calculus, Early Transcendentals (6th Ed., C. Henry Edwards & David E. > Penney) > Calculus, Early Transcendentals (7th Ed., C. Henry Edwards & David E. > Penney) > Calculus (9th Ed., Dale Varberg, Edwin Purcell & Steve Rigdon) > Calculus Early Transcendentals (Dale Varberg, Edwin Purcell & Steve > Rigdon) > Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley & Karl J. > Smith) > Calculus (6th Ed., Henry Edwards & David E. Penney) > Single Variable Calculus (3rd Ed., Monty J. Strauss, Gerald L. Bradley > & Karl J. Smith) > Vector Calculus (3rd Ed., Susan J. Colley) > Applied Linear Algebra (Peter J. Olver & Cheri Shakiban) > Introductory Linear Algebra: An Applied First Course (8th Ed., Bernard > Kolman & David R. Hill) > Differential Equations and Linear Algebra (2nd Ed., Jerry Farlow, > James E. Hall, Jean Marie McDill & Beverly H. West) > Differential Equations and Linear Algebra (2nd Ed., C. Henry Edwards & > David E. Penney) > Differential Equations (2nd Ed., John Polking, Al Boggess & David > Arnold) > Differential Equations with Boundary Value Problems (2nd ed., John > Polking, Al Boggess & David Arnold) > Discrete Mathematics with Graph Theory (3rd Ed., Edgar G. Goodaire & > Michael M. Parmenter) > Discrete Mathematics (6th Ed., Richard Johnsonbaugh) > Essential Discrete Mathematics (Todd Feil & Joan Krone) > Business Mathematics, 10th Ed. (Charles D. Miller, Stanley A. Salzman > & Gary Clendenen) > Elementary Statistics (6th Ed., Neil A. Weiss) > Elementary Statistics (7th Ed., Neil A. Weiss) > Elementary Statistics Using the Graphing Calculator: For the TI-83/84 > Plus (Mario F. Triola) > Elementary Statistics Using the TI-83/84 Plus Calculator (2nd Ed., > Mario F. Triola) > Elementary Statistics Update (9th Ed., Mario F. Triola) > Elementary Statistics (10th Ed., Mario F. Triola) > Elementary Statistics With Multimedia Study Guide (10th Ed., Mario F. > Triola) > Essentials of Statistics (2nd Ed., Mario F. Triola) > Essentials of Statistics (3rd Ed., Mario F. Triola) > Introductory Statistics (7th Ed., Neil A. Weiss) > Introductory Statistics (8th Ed., Neil A. Weiss) > Intro Stats (2nd Ed., Richard D. De Veaux, Paul F. Velleman & David E. > Bock) > Stats: Data and Models, (Richard D. De Veaux, Paul F. Velleman & David > E. Bock) > Stats: Data and Models, (2nd ed., Richard D. De Veaux, Paul F. > Velleman & David E. Bock) > Elementary Statistics Using Excel (2nd Ed., Mario F. Triola) > Elementary Statistics Using Excel (3rd Ed., Mario F. Triola) > Stats: Modeling the World (2nd Ed., David E. Bock, Paul F. Velleman & > Richard D. De Veaux) > Statistical Reasoning for Everyday Life (2nd Ed., Jeffrey O. Bennett, > William L. Briggsr & Mario F. Triola) > Business Statistics (Mario F. Triola & LeRoy A. Franklin) > Biostatistics for the Biological and Health Sciences with Statdisk > (Marc M. Triola & Mario F. Triola) > A Course in Probability (Neil A. Weiss) > Probability and Statistics (3rd Ed., Morris H. DeGroot & Mark J. > Schervish) > Statistics for Science and Engineering (John Kinney) > Developmental Mathematics (7th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Mathematical Proofs: A Transition to Advanced Mathematics (Gary > Chartrand, Albert D. Polimeni & Ping Zhang) > Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Ed., > Carol Schumacher) > Elementary Number Theory (5th Ed., Kenneth H. Rosen) > History of Mathematics: Brief Version (Victor J. Katz) > College Geometry: A Discovery Approach (2nd Ed., David Kay) > Geometry: An Investigative Approach (2nd Ed., Phares G. O'Daffer & > Stanley R. Clemens) > A First Course in Abstract Algebra (7th Ed., John B. Fraleigh) > Complex Variables with Applications (3rd Ed., David A. Wunsch) > Numerical Analysis with CD-ROM (Timothy Sauer) > Numerical Analysis and Scientific Computation (Jeffery J. Leader) > Linear Algebra and Differential Equations (Gary L. Peterson & James S. > Sochacki) > Elementary Differential Equations Bound with IDE CD Package (2nd Ed., > Werner E. Kohler & Lee W. Johnson) > Elementary Differential Equations with Boundary Value Problems with > IDE CD Package (2nd Ed., Werner E. Kohler & Lee W. Johnson) > Fundamentals of Differential Equations (6th Ed., Kent B. Nagle, Late, > Edward B. Saff & Arthur David Snider) > Fundamentals of Differential Equations and Boundary Value Problems > (4th Ed., Kent B. Nagle, Late, Edward B. Saff & Arthur David Snider) > Linear Algebra and Its Applications with CD-ROM, Update (3rd Ed., > David C. Lay) > Introduction to Linear Algebra (5th ed., Lee W. Johnson, R. Dean Riess > & Jimmy T. Arnold) > Calculus for the Life Sciences (Marvin L. Bittinger, Neal Brand & John > Quintanilla) > Calculus with Applications for the Life Sciences (Raymond N. > Greenwell, Nathan P. Ritchey & Margaret L. Lial) > Calculus: An Integrated Approach to Functions and Their Rates of > Change, Preliminary Edition (Robin J. Gottlieb) > Calculus (9th Ed., George B. Thomas, Jr. & Ross L. Finney) > Thomas' Calculus, Alternate Edition (9th Ed., George B. Thomas, Jr. & > Ross L. Finney) > Calculus: A Complete Course (2nd Ed., Ross L. Finney, Franklin D. > Demana, Bert K. Waits & Daniel Kennedy) > Calculus (Elgin H. Johnston & Jerry Mathews) > Thomas' Calculus, Updated (10th Ed., George B. Thomas, Jr., Ross L. > Finney, Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus (11th Ed., George B. Thomas, Jr., Maurice D. Weir, > Joel D. Hass & Frank R. Giordano) > Thomas' Calculus Early Transcendentals (11th Ed., George B. Thomas, > Jr., Maurice D. Weir, Joel D. Hass & Frank R. Giordano) > University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, > Jr.) > University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir > & George B. Thomas, Jr.) > Thomas' Calculus, Media Upgrade (11th Ed., George B. Thomas, Jr., > Maurice D. Weir & Frank R. Giordano) > Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Ed., > George B. Thomas, Jr., Maurice D. Weir, Joel D. Hass & Frank R. > Giordano) > Calculus with Applications (8th Ed., Margaret L. Lial, Raymond N. > Greenwell & Nathan P. Ritchey) > Calculus with Applications, Brief Version (8th Ed., Margaret L. Lial, > Raymond N. Greenwell & Nathan P. Ritchey) > Finite Math with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics (8th Ed., Margaret L. Lial, Raymond N. Greenwell & > Nathan P. Ritchey) > Mathematics with Applications (9th Ed., Margaret L. Lial, Thomas W. > Hungerford & John Holcomb) > Finite Mathematics and Calculus with Applications (7th Ed., Margaret > L. Lial, Raymond N. Greenwell & Nathan P. Ritchey) > Mathematical Ideas (10th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas (11th Ed., Charles D. Miller, Vern E. Heeren & John > Hornsby) > Mathematical Ideas Expanded Edition (10th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Mathematical Ideas Expanded Edition (11th Ed., Charles D. Miller, Vern > E. Heeren & John Hornsby) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (3rd Ed., Jeffrey O. Bennett & William L. Briggs) > Using and Understanding Mathematics: A Quantitative Reasoning Approach > (4th Ed., Jeffrey O. Bennett & William L. Briggs) > A Problem Solving Approach to Mathematics (9th Ed., Rick Billstein, > Shlomo Libeskind & Johnny W. Lott) > A Survey of Mathematics with Applications (7th Ed., Allen R. Angel, > Christine D. Abbott & Dennis C. Runde) > A Survey of Mathematics with Applications: Expanded Edition (7th Ed., > Allen R. Angel, Christine D. Abbott & Dennis C. Runde) > Mathematics All Around (3rd Ed., Tom Pirnot) > Mathematics for Elementary School Teachers (3rd Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary School Teachers (4th Ed., Phares O'Daffer, > Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) > Mathematics for Elementary Teachers with Activities (Sybilla > Beckmann) > Mathematics for Elementary Teachers plus Activities Manual (2nd Ed., > Sybilla Beckmann) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (8th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > A Problem Solving Approach to Mathematics for Elementary School > Teachers (9th Ed., Rick Billstein, Shlomo Libeskind & Johnny W. Lott) > Mathematical Reasoning for Elementary Teachers (4th Ed., Calvin T. > Long & Duane W. DeTemple) > Essentials of Using and Understanding Mathematics: A Quantitative > Reasoning Approach (Jeffrey O. Bennett & William L. Briggs) > Technical Calculus with Analytic Geometry (4th Ed., Allyn J. > Washington) > Basic Technical Mathematics (8th Ed., Allyn J. Washington) > Basic Technical Mathematics with Calculus (8th Ed., Allyn J. > Washington) > Basic Technical Mathematics with Calculus Metric Version (8th Ed., > Allyn J. Washington) > Introduction to Technical Mathematics (5th Ed., Allyn J. Washington, > Mario F. Triola & Ellena E. Reda) > A Graphical Approach to Precalculus (4th Ed., John Hornsby, Margaret > L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits (3rd Ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > A Graphical Approach to Precalculus with Limits: A Unit Circle > Approach (4th Ed., John Hornsby, Margaret L. Lial & Gary K. Rockswold) > Precalculus: Functions and Graphs (5th Ed., Franklin Demana, Bert K. > Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphical, Numerical, Algebraic (7th Ed., Franklin > Demana, Bert K. Waits, Gregory D. Foley & Daniel Kennedy) > Precalculus: Graphs and Models Graphing Calculator Manual Package (3rd > Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & > Judith A. Penna) > Functioning in the Real World: A Precalculus Experience (2nd Ed., > Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker & Martha J. > Siegel) > Precalculus with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Precalculus (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Judith A. Beecher, Judith A. Penna & Marvin L. > Bittinger) > Precalculus (3rd Ed., Mark Dugopolski) > Precalculus (4th Ed., Mark Dugopolski) > Precalculus (3rd Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Precalculus: Functions and Graphs (2nd Ed., Mark Dugopolski) > Fundamentals of Precalculus (Mark Dugopolski) > Trigonometry (Mark Dugopolski) > Trigonometry (2nd Ed., Mark Dugopolski) > Trigonometry (8th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Trigonometry: A Circular Function Approach (Marie Aratari) > A Graphical Approach to Algebra and Trigonometry (4th ed., John > Hornsby, Margaret L. Lial & Gary K. Rockswold) > Algebra and Trigonometry: Graphs and Models Graphing Calculator Manual > Package (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. > Ellenbogen & Judith A. Penna) > Algebra and Trigonometry (2nd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > Algebra and Trigonometry (3rd Ed., Judith A. Beecher, Judith A. Penna > & Marvin L. Bittinger) > College Algebra and Trigonometry (J. S. Ratti & Marcus S. McWaters) > College Algebra and Trigonometry (3rd Ed., Mark Dugopolski) > College Algebra and Trigonometry (4th Ed., Mark Dugopolski) > Algebra and Trigonometry with Modeling and Visualization (3rd Ed., > Gary K. Rockswold) > College Algebra and Trigonometry (3rd Ed., Margaret L. Lial, John > Hornsby & David I. Schneider) > A Graphical Approach to College Algebra (4th Ed., John Hornsby, > Margaret L. Lial & Gary K. Rockswold) > College Algebra: Graphs and Models Graphing Calculator Manual Package > (3rd Ed., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen > & Judith A. Penna) > College Algebra (J. S. Ratti & Marcus S. McWaters) > College Algebra with Modeling and Visualization (3rd Ed., Gary K. > Rockswold) > Essentials of College Algebra with Modeling and Visualization (3rd > Ed., Gary K. Rockswold) > Essentials of College Algebra (Margaret L. Lial, John Hornsby & David > I. Schneider) > Essentials of College Algebra, Alternate Edition (Margaret L. Lial, > John Hornsby & David I. Schneider) > College Algebra (3rd Ed., Mark Dugopolski) > College Algebra (4th Ed., Mark Dugopolski) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra in Context with Applications for the Managerial, Life, > and Social Sciences (2nd Ed., Ronald J. Harshbarger & Lisa S. Yocco) > College Algebra (2nd Ed., Judith A. Beecher, Judith A. Penna & Marvin > L. Bittinger) > College Algebra (9th Ed., Margaret L. Lial, John Hornsby & David I. > Schneider) > Essentials of Geometry for College Students (2nd Ed., Margaret L. > Lial, Barbara A. Brown, Arnold R. Steffenson & L. Murphy Johnson) > Algebra for College Students (5th Ed., Margaret L. Lial, John Hornsby > & Terry McGinnis) > Introductory and Intermediate Algebra (3rd Ed., argaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (3rd Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Beginning and Intermediate Algebra (4th Ed., Margaret L. Lial, John > Hornsby & Terry McGinnis) > Elementary and Intermediate Algebra (1st Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Elementary and Intermediate Algebra (2nd Ed., Tom Carson, Ellyn > Gillespie & Bill E. Jordan) > Introductory and Intermediate Algebra: A Combined Approach (2nd Ed., > Marvin L. Bittinger & Judith A. Beecher) > Introductory and Intermediate Algebra (3rd Ed., Marvin L. Bittinger & > Judith A. Beecher) > Elementary and Intermediate Algebra (George Woodbury) > Elementary and Intermediate Algebra: Concepts and Applications (4th > Ed., Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Beginning and Intermediate Algebra with Applications and Visualization > (Gary K. Rockswold & Terry A. Krieger) > Elementary and Intermediate Algebra: Graphs & Models (2nd Ed., Marvin > L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) > Foundations of Mathematics (Marvin L. Bittinger & Judith A. Penna) > Intermediate Algebra (9th Ed., Marvin L. Bittinger) > Intermediate Algebra (10th Ed., Marvin L. Bittinger) > Intermediate Algebra: Graphs & Models (2nd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra: Graphs & Models (3rd Ed., Marvin L. Bittinger, > David J. Ellenbogen & Barbara L. Johnson) > Intermediate Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Intermediate Algebra with Applications and Visualization (2nd Ed., > Gary K. Rockswold & Terry A. Krieger) > Intermediate Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Intermediate Algebra (Tom Carson, Ellyn Gillespie & Bill E. Jordan) > Intermediate Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Intermediate Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Beginning Algebra (10th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Developmental Mathematics: Basic Mathematics and Algebra (Margaret L. > Lial, John Hornsby, Terry McGinnis, Stanley A. Salzman & Diana L. > Hestwood) > Prealgebra and Introductory Algebra (Marvin L. Bittinger & David J. > Ellenbogen) > Prealgebra and Introductory Algebra (2nd Ed., Marvin L. Bittinger & > David J. Ellenbogen) > Elementary Algebra (2nd Ed., Tom Carson, Ellyn Gillespie & Bill E. > Jordan) > Introductory Algebra (9th Ed., Marvin L. Bittinger) > Introductory Algebra (10th Ed., Marvin L. Bittinger) > Prealgebra and Introductory Algebra (2nd Ed., Margaret L. Lial, John > Hornsby, Terry McGinnis & Diana L. Hestwood) > Elementary Algebra with Early Systems of Equations (Tom Carson & Ellyn > Gillespie) > Elementary Algebra: Concepts and Applications (6th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Elementary Algebra: Concepts and Applications (7th Ed., Marvin L. > Bittinger & David J. Ellenbogen) > Introductory Algebra (Richelle M. Blair) > Introductory Algebra (8th Ed., Margaret L. Lial, John Hornsby & Terry > McGinnis) > Beginning Algebra with Applications and Visualization (Gary K. > Rockswold & Terry A. Krieger) > Integrated Arithmetic and Basic Algebra (3rd Ed., Bill E. Jordan & > William P. Palow) > Introductory Algebra through Applications (Geoffrey Akst & Sadie > Bragg) > Developmental Mathematics (6th Ed., Marvin L. Bittinger & Judith A. > Beecher) > Prealgebra (3rd Ed., Margaret L. Lial & Diana L. Hestwood) > Prealgebra (4th Ed., Marvin L. Bittinger & David J. Ellenbogen) > Prealgebra (5th Ed., Marvin L. Bittinger, David J. Ellenbogen & > Barbara L. Johnson) > Prealgebra (2nd Ed., Tom Carson) > Basic Mathematics (9 th Ed., Marvin L. Bittinger) > Basic Mathematics (10 th Ed., Marvin L. Bittinger) > Basic Mathematics Preliminary Edition (Robert Prior) > Basic Mathematics with Early Integers (Marvin L. Bittinger & Judith A. > Penna) > Basic College Mathematics (7th Ed., Margaret L. Lial, Stanley A. > Salzman & Diana L. Hestwood) > Basic Mathematics through Applications (3rd Ed., Geoffrey Akst & Sadie > Bragg) > Fundamental Mathematics through Applications (3rd Ed., Geoffrey Akst & > Sadie Bragg) > Wave Motion (J. Billingham & A. C. King) > Solving ODEs with MATLAB (L. F. Shampine, I. Gladwell & S. Thompson) > Numerical Solution of Partial Differential Equations: An Introduction > (2nd Ed., K. W. Morton & D. F. Mayers) > Measure Theory and Filtering: Introduction and Applications (Lakhdar > Aggoun & Robert J. Elliott) > Mathematical Models in Biology: An Introduction (Elizabeth S. Allman & > John A. Rhodes) > Insurance Risk and Ruin (David C. M. Dickson) > Data Analysis and Graphics Using R: An Example-based Approach (2nd > Ed., John Maindonald & John Braun) > Convex Optimization (Stephen Boyd & Lieven Vandenberghe) > Lauritzen) > Calculus: Concepts and Methods (Ken Binmore & Joan Davies) > An Introduction to Partial Differential Equations (Yehuda Pinchover & > Jacob Rubinstein) > An Introduction to Ordinary Differential Equations (James C. Robinson) > An Introduction to Mathematical Physiology and Biology (2nd Ed., J. > Mazumdar) > An Introduction to Financial Option Valuation: Mathematics, > Stochastics and Computation (Desmond Higham) > An Interactive Introduction to Mathematical Analysis (Jonathan Lewin) > An Elementary Introduction to Mathematical Finance: Options and other > Topics (2nd Ed., Sheldon M. Ross) > A Course in Financial Calculus (Alison Etheridge) - Physics & Astronomy : > > Fundamentals of Electromagnetics with Engineering Applications (Stuart > M. Wentworth) > Fundamentals of Physics (8th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (6th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Fundamentals of Physics (7th Ed., David Halliday, Robert Resnick & > Jearl Walker) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > An Introduction to Thermodynamics and Statistical Mechanics (2nd Ed, > Keith Stowe) > Equilibrium and Non-Equilibrium Statistical Thermodynamics (Michel Le > Bellac, Fabrice Mortessagne & G. George Batrouni) > Elements of Statistical Mechanics: With an Introduction to Quantum > Field Theory and Numerical Simulation (Ivo Sachs & Siddhartha Sen) > Quantum Transport (2nd Ed., Supriyo Datta) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Applied Quantum Mechanics (1st Ed., A. F. J. Levi) + original Ebook > Applied Quantum Mechanics (2nd Ed., A. F. J. Levi) > Astronomy A Physical Perspective (2nd Ed., Marc L. Kutner) + original > Ebook > Classical Mechanics (Douglas Gregory) + original Ebook > Electromagnetic Field Theory Fundamentals (2nd Ed., Singh Guru & > Hiziroglu) > Fundamentals of Quantum Mechanics (C.L. Tang) + original Ebook > Special Relativity (P.M. Schwarz & J.H. Schwarz) > Statistical Thermodynamics (Normand Laurendeau) > Statistical Thermodynamics and Microscale Thermophysics (Van P. Carey) > Thermal Physics (Ralph Baierlein) > Topics in Atomic Physics (Charles E. Burkhardt, Jacob J. Leventhal) > Applied Physics (8th Ed., Dale Ewen, Ronald Nelson, Neill Schurter & > Erik Gundersen) > Orbital Mechanics for Engineering Students (Howard Curtis) > Diagnostic Ultrasound Imaging: Inside Out (Thomas Szabo) > Astronomy: A Beginner's Guide to the Universe (5th Ed., Eric Chaisson > & Steve McMillan) > The Cosmic Perspective Media Update with MasteringAstronomy» and > Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with MasteringAstronomy» > and Voyager SkyGazer Planetarium Software (4th Ed., Jeffrey O. > Bennett, Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective Media Update with Astronomy Place > website, Skygazer Planetarium Software (3rd Ed., Jeffrey O. Bennett, > Megan Donahue, Nicholas Schneider & Mark Voit) > The Essential Cosmic Perspective (3rd Ed., Jeffrey O. Bennett, Megan > Donahue, Nicholas Schneider & Mark Voit) > Astronomy Today (5th Ed., Eric Chaisson & Steve McMillan) > An Introduction to Modern Astrophysics (2nd Ed., Bradley W. Carroll & > Dale A. Ostlie) > Conceptual Physical Science (3rd Ed., Paul G. Hewitt, John A. Suchocki > & Leslie Hewitt) > Conceptual Integrated Science (Paul G. Hewitt, Suzanne Lyons, John A. > Suchocki & Jennifer Yeh) > Physics: Concepts & Connections (4th Ed., Art Hobson) > Conceptual Physics (10th Ed., Paul G. Hewitt) > College Physics (6th Ed., Jerry D Wilson, Anthony J Buffa & Bo Lou) > Physics with Mastering Physics (3rd Ed., James S. Walker) > Active Learning Guide (Alan Van Heuvelen & Eugenia Etkina) > E&M TIPERs: Electricity & Magnetism Tasks (C. J. Hieggelke, D. P. > Maloney, T. L. O'Kuma & Steve Kanim) > Physics: Principles with Applications (6th Ed., Douglas C. Giancoli) > Physlet¬ Physics: Interactive Illustrations, Explorations and Problems > for Introductory Physics (Wolfgang Christian & Mario Belloni) > University Physics with Modern Physics with Mastering Physics (11th > Ed., Hugh D. Young & Roger A. Freedman) > Physics for Scientists and Engineers (3rd Ed., Douglas C. Giancoli) > Physics for Scientists and Engineers with Modern Physics (3rd Ed., > Douglas C. Giancoli) > Physlet¬ Quantum Physics: An Interactive Introduction (Mario Belloni, > Wolfgang Christian & Anne Cox) > Introduction to Electrodynamics (3rd Ed., David J. Griffiths) > Introduction to Optics (3rd Ed., Frank L Pedrotti, Leno M Pedrotti & > Leno S Pedrotti) > Introduction to Quantum Mechanics (2nd Ed., David J. Griffiths) > Quantum Mechanics: An Accessible Introduction (Robert Scherrer) > The Physics of Sound (3rd Ed., Richard E Berg & David G Stork) > Classical Electromagnetism (Jerrold Franklin) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Introduction to Color Imaging Science (Hsien-Che Lee) > An Introduction to Astrobiology (Iain Gilmour & Mark A. Sephton) > An Introduction to Galaxies and Cosmology (Mark H. Jones & Robert J. > Lambourne) > An Introduction to the Solar System (Neil McBride & Iain Gilmour) > Quantum Physics (Michel Le Bellac) > Laser Fundamentals (2nd Ed., William T. Silfvast) > Introductory Quantum Optics (Christopher Gerry & Peter Knight) > Introduction to Plasma Physics: With Space and Laboratory Applications > (D. A. Gurnett & A. Bhattacharjee) > A Short Introduction to Quantum Information and Quantum Computation > (Michel Le Bellac) > A Quantum Approach to Condensed Matter Physics (Philip L. Taylor & > Olle Heinonen) > A First Course in String Theory (Barton Zwiebach) > A First Course in Computational Physics and Object-Oriented > Programming with C++ (David Yevick) > A Course in Modern Mathematical Physics: Groups, Hilbert Space and > Differential Geometry (Peter Szekeres) > Time Series Analysis and Its Applications: With R Examples (2nd Ed., > Robert Shumway & David Stoffer) > Introduction to Time Series and Forecasting (Peter Brockwell & Richard > Davis) > Ultrasonic Nondestructive Evaluation Systems: Models and Measurements > (Lester W. Schmerr & Sung-Jin Song) - Civil Engineering : > > Mechanical and Structural Vibrations: Theory and Applications (by > Jerry H. Ginsberg) > Fundamentals of Structural Analysis, (1st Ed., Leet & Uang) > Fundamentals of Structural Analysis, (2nd Ed., Leet & Uang) > Fundamentals of Structural Analysis, (3rd Ed., Leet & Uang) > Structural and Stress Analysis (2nd Ed., Megson) + Ebook > Statics and Strength of Materials for Architecture and Building > Construction (3rd Ed., Onouye & Kane) > Open Channel Hydraulics (A. Osman Akan) > Fundamentals of Structural Stability (George Simitses & Dewey Hodges) > Introduction to Naval Architecture : Formerly Muckle's Naval > Architecture for Marine Engineers (4th Ed., E C Tupper) > The Management of Construction: A Project Lifecycle Approach (F. > Lawrence Bennett) > Advanced Topics in Finite Element Analysis of Structures: With > Mathematica and MATLAB Computations (Asghar Bhatti) > Elementary Structures for Architects and Builders (5th Ed., Ronald E. > Shaeffer) > Surveying with Construction Applications (6th Ed., Barry F. Kavanagh) > Structural Analysis (6th Ed., Hibbeler) > Dynamics of Structures (3rd Ed., Chopra) > Structures (6th Ed., Daniel Lewis Schodek & Martin Bechthold) > Concrete Structures (Mehdi Setareh & Robert M. Darvas) > Reinforced Concrete Design (6th Ed., Chu-Kia Wang, Charles G. Salmon) > Reinforced Concrete Design (7th Ed., Chu-Kia Wang, Charles G. Salmon & > Jos.8e A. Pincheira) > Reinforced Concrete Design (6th Ed., George F. Limbrunner & Abi > Aghayere) > Reinforced Concrete: Mechanics and Design (4th Ed., James G. MacGregor > & James K. Wight) > Structural Steel Design (4th Ed., Jack C. McCormac) > Design of Reinforced Concrete (6th Ed., Jack C. McCormac & James K. > Nelson) > Design of Reinforced Concrete (7th Edition, ACI 318-05 Code Edition, > by Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (3rd Ed., > James K. Nelson, Jr., Jack C. McCormac) > Structural Analysis: Using Classical and Matrix Methods (4th Ed., Jack > C. McCormac) > Surveying (5th Ed., Jack C. McCormac) > Introduction to Structural Analysis & Design (S. D. Rajan) > Soil Mechanics and Foundations (2nd Ed., Muniram Budhu) > Soils and Foundations (7th Ed., Liu & Evett) > Essentials of Soil Mechanics and Foundations: Basic Geotechnics (7th > Ed., David F. McCarthy) > Building Construction: Principles, Materials, and Systems (Madan > Mehta, Diane Armpriest & Walter Scarborough) > Construction Methods and Management (7th Ed., Stephens W. Nunnally) > Construction Project Administration (8th Ed., Ed Fisk Wayne Reynolds) > Construction Accounting and Financial Management (Steven J. Peterson) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Construction Estimating Using Excel (Stephen J. Peterson) > Heating and Cooling of Buildings: Design for Efficiency (2nd Ed., Jan > F. Kreider, Peter S. Curtiss & Ari Rabl) > Steel Structures: Behavior and LRFD (1st Ed., Ramulu S Vinnakota) > The Engineering of Foundations (1st Ed., Rodrigo Salgado) > Introduction to Transportation Engineering (2nd Ed., Banks) > Construction Contracts (2nd Ed., Hinze) > Urban Transportation Planning (2nd Ed., Meyer & Miller) > Construction Planning, Equipment, and Methods (6th Ed., Peurifoy & > Schexnayder) > Construction Planning, Equipment, and Methods (7th Ed., Peurifoy, > Schexnayder & Aviad Shapira) > Open Channel Hydraulics (Terry Sturm) > Construction Management Fundamentals (Schexnayder & Mayo) > Fundamentals of Structural Dynamics (2nd Ed., Roy R. Craig & Andrew J. > Kurdila) > Structural Concrete: Theory and Design (3rd Ed., M. Nadim Hassoun & > Akthem Al-Manaseer) > Principles of Highway Engineering and Traffic Analysis (3rd Ed., Fred > Mannering, Walter Kilareski & Scott Washburn) - Environmental Engineering, Earth and Environmental Sciences : > > Principles of Environmental Engineering and Science (Mackenzie L Davis > & Susan J Masten) > Introduction to Environmental Engineering (4th Ed., MacKenzie L. Davis > & David A. Cornwell) > Introduction to Environmental Engineering and Science (2nd Ed., > Gilbert M. Masters) > Introduction to Environmental Engineering and Science (3rd Ed., > Gilbert M. Masters & Wendell P. Ela) > Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. > Kraushaar) > Introduction to Engineering and the Environment (1st Ed., Edward S. > Rubin) > Basic Environmental Technology: Water Supply, Waste Management & > Pollution Control (5th Ed., Jerry A. Nathanson) > Small and Decentralized Wastewater Management Systems (1st Ed, Crites > & Tchobanoglous) > Water Resources Engineering (R. Wurbs, W. James) > Water and Wastewater Technology (6th Ed., Mark J. Hammer, Sr. & Mark > J. Hammer, Jr.) > Principles of Sequence Stratigraphy (Octavian Catuneanu) > Atmospheric Science: An Introductory Survey (2nd Ed., John Wallace, > Peter Hobbs) > Plant Pathology (5th Ed., George Agrios) > Environmental Engineering (4th Ed., Ruth F Weiner & Robin Matthews) > Groundwater Hydrology (3rd Ed., David Keith Todd & Larry W. Mays) > Groundwater Science (Charles Fitts) > Agriculture's Ethical Horizon (Robert Zimdahl) > Environmental Contaminants: Assessment and Control (Daniel Vallero) > Water Resources Engineering 2005 Edition (Larry W. Mays) > Water-Resources Engineering (2nd Ed., Chin) > Water Chemistry (Benjamin) > Hazardous Waste Management (2nd Ed., Michael D. LaGrega, Phillip L > Buckingham & Jeffrey C Evans) > Environmental Biotechnology: Principles and Applications (1st Ed., > Bruce E. Rittmann & Perry L. McCarty) > Chemistry for Environmental Engineering and Science (5th Ed., Clair N > Sawyer, Perry L. McCarty & Gene F. Parkin) > Geology for Engineers and Environmental Scientists (3rd Ed., Alan E. > Kehew) > Ocean Waves and Oscillating Systems (Johannes Falnes) > Water Treatment: Principles and Design (2nd Ed., by MWH) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & > Baxter Vieux) - Chemistry and Chemical Engineering : > > Mass Transfer Operations (3rd Ed., Treybal) > Mass Transfer in Multicomponent Mixtures (J.A. Wesseling & R. Krishna) > + original Ebook > Principles and Modern Applications of Mass Transfer Operations (Jaime > Benitez) > Diffusion - Mass Transfer in Fluid Systems (2nd Ed., Cussler) > Separation Process Principles (1st Ed, Seader & Henley) > Separation Process Principles (2nd Ed, Seader & Henley) > Equilibrium Staged Separations (Wankat) > Principles of Chemical Separations with Environmental Applications > (Richard D. Noble) > Product and Process Design Principles: Synthesis, Analysis, and > Evaluation (2nd Ed., Seider & Seader) + Ebook > Principles and Practices of Automatic Process Control (3rd Ed., Smith > & Corripio) + Ebook > Process Dynamics and Control (2nd Ed., Seborg & Edgard) > Process Control - A First Course with MATLAB (P.C. Chau) + Ebook > Process Dynamics: Modeling, Analysis and Simulation (Wayne Bequette) > Plant Design and Economics for Chemical Engineers, (5th Ed., Peters & > Timmerhaus) + Ebook > Basic Principles and Calculations in Chemical Engineering (6th Ed., > Himmelblau) > Basic Principles and Calculations in Chemical Engineering (7th Ed., > Himmelblau) > Unit Operations of Chemical Engineering (6th Ed., McCabe & Smith) > Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) > Advanced Transport Phenomena (John C. Slattery) > Introduction to Transport Phenomena (W. Thomson) > Transport Phenomena: A Unified Aprroach (Robert S. Brodkey & Harry C. > Hershey) + Ebook > Transport Phenomena in Multiphase Systems (Faghri & Zhang) > Modeling in Transport Phenomena: A Conceptual Approach (2nd Ed., > Ismail Tosun) + original Ebook > Transport Phenomena (2nd Ed., Bird & Stewart) + Ebook > Solutions to Class 1&2 - Transport Phenomena (Bird) > Chemical Engineering Design (Coulson & Richardson's Chemical > Engineering - Volume 6) - (4th Ed., Sinnott) + original Ebook > Chemical Engineering Design and Analysis - An Introduction (Duncan & > Reimer) > Chemical Reaction Engineering (3rd Ed., Levenspiel) + Ebook > Chemical Reactor Analysis and Design Fundamentals (Rawlings & Ekerdt) > + Ebook > Fundamentals of Chemical Reaction Engineering (1st Ed., Davis) > Conceptual Design of Distillation Systems (1st Ed., Doherty & Malone) > Distillation Theory and its Application to Optimal Design of > Separation Units (F.B. Petlyuk) + original Ebook > Batch Distillation: Simulation, Optional Design and Control (Diwekar) > + Ebook > Fluid Mechanics for Chemical Engineers, (3rd Ed., Noel de Nevers) > Introduction to Chemical Processes: Principles, Analysis, Synthesis > (1st Ed., Regina M. Murphy) > Optimization of Chemical Processes (2nd Ed., Edgar & Himmelblau) + > Ebook > Chemical and Engineering Thermodynamics (3rd Ed., Stanley I. Sandler) > Chemical, Biochemical, and Engineering Thermodynamics (4th Ed., > Stanley I. Sandler) > Introduction to Chemical Engineering Thermodynamics (6th Ed., Smith & > Van Ness) > Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & > Van Ness) > Introductory Chemical Engineering Thermodynamics (J. Elliott, C. Lira) > Engineering and Chemical Thermodynamics (Koretsky) > Phase Equilibria, Phase Diagrams and Phase Transformations - Their > Thermodynamic Basis (2nd Ed., Mats Hillert) > Introduction to Chemical Kinetics and Chemical Reaction Engineering > (Missen, Mims) + original Ebook > Principles of Chemical Kinetics (James House) > Transport Processes and Unit Operations (3rd Ed., Christie J. > Geankoplis) > Transport Processes and Separation Process Principles (4th Ed., > Christie J. Geankoplis) > Elementary Principles of Chemical Processes (3rd Ed., Felder & > Rousseau) + Ebook > Chemical Process Safety: Fundamentals with Applications (2nd Ed., > Crowl & Louvar) + Ebook > Elements of Chemical Reaction Engineering (3rd Ed., Fogler) > Elements of Chemical Reaction Engineering (4th Ed., Fogler) > Group Theory with Applications in Chemical Physics (Patrick Jacobs) > Food Analysis (3rd Ed., Suzanne Nielsen) > Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, > v2.5, 3rd Ed. (Brian F. Woodfield & Matthew C. Asplund) > Introductory Chemistry and CW+ GradeTracker Access Card Package, 2nd > Ed. (Nivaldo J. Tro) > Introductory Chemistry: Concepts and Connections, 4th Ed. (Charles H > Corwin) > Prentice Hall Lab Manual Introductory Chemistry, 4th Ed. (Charles H > Corwin) > General, Organic and Biological Chemistry: Structures of Life with > Student Access Kit for MasteringGOBChemistry», 2nd ed. (Karen C. > Timberlake) > Chemistry: An Introduction to General, Organic, and Biological > Chemistry with The Chemistry Place CD-ROM, 9th Ed (Karen C. > Timberlake) > Conceptual Chemistry, 3rd Ed (John A. Suchocki) > Explorations in Conceptual Chemistry: A Student Activity Manual > (Jeffrey Paradis) > Criminalistics: An Introduction to Forensic Science (9th Ed., Richard > Saferstein) > Physical Chemistry with Spartan Student Physical Chemistry Software > (Thomas Engel & Philip Reid) > Quantum Chemistry and Spectroscopy with Spartan Student Physical > Chemistry Software (Thomas Engel & Philip Reid) > Themodynamics, Statistical Thermodynamics, and Kinetics (Thomas Engel > & Philip Reid) > Physical Chemistry (7th. Ed., Peter Atkins & Julio de Paula) > Chemistry An Introduction to Organic, Inorganic and Physical Chemistry > (3rd Ed., Catherine E. Housecroft & Edwin Constable) > General Chemistry: The Essential Concepts (4th Ed., Raymond Chang) > Chemistry: The Molecular Nature of Matter and Change (3rd Ed., Martin > Silberberg) > Chemistry: The Molecular Nature of Matter and Change (4th Ed., Martin > Silberberg) > General, Organic and Biochemistry (3rd ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (4th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > General, Organic and Biochemistry (5th ed., Katherine J. Denniston, > Joseph J. Topping & Robert L. Caret) > Fundamentals of Chemistry (3rd Ed., David E Goldberg) > Fundamentals of Chemistry (4th Ed., David E Goldberg) > Fundamentals of Chemistry (5th Ed., David E Goldberg) > Modern Analytical Chemistry (Harvey) > General Chemistry Lab Manual (Petra A. M. van Koppen) > Practical Interfacing in the Laboratory: Using a PC for > Instrumentation, Data Analysis and Control (Stephen E. Derenzo) > Bioprocess Engineering Principles (Pauline M. Doran) - Industrial Engineering, Business, Economics and Finance : > > Engineering Economy (5th Ed., Leland T Blank & Anthony Tarquin) > Engineering Economy (6th Ed., Leland T Blank & Anthony Tarquin) + > original Ebook > Contemporary Engineering Economics (4th Ed., Chan Park) > Engineering Economy (13th Ed, Sullivan) > Introduction to Statistical Quality Control (5th Ed., Douglas C. > Montgomery) > Managing Engineering and Technology (4th, Morse & Babcock) > (4th Ed, Gryna) > Juran's Quality Planning and Analysis for Enterprise Quality (5th Ed., > Gryna, Chua & DeFeo) > Quality (4th Ed., Summers) > Quality Management (5th Ed., Goetsch & Davis) > Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) > Value Driven Product Planning and Systems Engineering (H. E. Cook & L. > A. Wissmann) > Work Systems: The Methods, Measurement & Management of Work (Mikell P. > Groover) > Occupational Safety and Health for Technologists, Engineers, and > Managers (5th Ed., Goetsch) > Occupational Safety and Health for Technologists, Engineers, and > Managers (6th Ed., Goetsch) > Introduction to Engineering Technology (6th Ed., Robert J. Pond) > Manufacturing Facilities Design and Material Handling (3rd Ed., Meyers > & Stephens) > Fundamentals of Forensic Science (Max Houck & Jay Siegel) > Introduction to Optimum Design (2nd Ed., Jasbir Arora) > Project Management for Business and Engineering : Principles and > Practice (2nd Ed., John Nicholas) > ISO 9001:2000 Quality Registration Step-by-Step (3rd Ed., Fred Dobb) > Systems for Planning and Control in Manufacturing (D. K. Harrison & D. > J. Petty) > Planning and Control of Manufacturing Operations (John Kenworthy) > Professionalism: Real Skills for Workplace Success (Anderson & Bolt) > Customer Service: Career Success Through Customer Loyalty (4th Ed., > Timm) > Customer Service: A Practical Approach (3rd Ed., Harris) > Customer Service: A Practical Approach (4th Ed., Harris) > Serving Internal and External Customers (Anne Swartzlander) > Customer Relationship Management: The Bottom Line to Optimizing Your > ROI (Anton & Petouhoff) > Engineering Economy and the Decision-Making Process (Joseph C. > Hartman) > Engineering Management: Challenges in the New Millennium (C M Chang) > Cost Analysis and Estimating for Engineering and Management (Phillip > F. Ostwald & Timothy S. McLaren) > Supply Chain Management (3rd Ed., Sunil Chopra & Peter Meindl) > Industrial Safety and Health Management (5th Ed., C. Ray Asfahl) > Computer Numerical Control: Operation and Programming (3rd Ed., Jon S. > Stenerson & Kelly Curran) > Introduction to Management Science and Student CD Package (8th Ed., > Bernard W. Taylor) > Introduction to Management Science with Student CD (9th Ed., Bernard > W. Taylor) > Operations Research: An Introduction (8th Ed., Taha) > Decision Support Systems and Intelligent Systems (7th Ed., Turban, > Aronson, Ting-Peng Liang) > Decision Support and Business Intelligence Systems (8th Ed., Turban, > Aronson, Ting-Peng Liang & Sharda) > Operations Management and Student CD Package (7th Ed., Krajewski, > Ritzman) > Operations Management: Process and Value Chains (8th Ed., Krajewski, > Ritzman & Malhotra) > Operations Management (8th Ed., Jay Heizer & Render) > Introduction to Operations and Supply Chain Management with Advanced > Decision Support Tools (Cecil Bozarth) > Managing Business Process Flows: Principles of Operations Management > (2nd Ed., Anupind, Chopra, Deshmukh, et al) > Operations Management & Student CD Package (8th Ed., Heizer & Render) > Principles Of Operations Management and Student CD (6th Ed., Heizer & > Render) > Foundations of Operations Management (Ritzman & Krajewski) > Decision Modeling with Microsoft¬ Excel (6th Ed., Moore & Weatherford) > Managing Quality: Integrating The Supply Chain (3rd Ed., S. Thomas > Foster) > Six Sigma: Basic Tools and Techniques (Donna C.S. Summers) > First Course in Quality Engineering (KS Krishnamoorthi) > Statistical Quality Design and Control (2nd Ed., DeVor, Chang & > Sutherland) > Economics: A Tool for Critically Understanding Society (7th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Economics: A Tool for Critically Understanding Society (8th Ed., Tom > Riddell, Jean Shackelford, Steve C. Stamos & Geoffrey Schneider) > Introduction to Economic Reasoning (6th Ed., William D. Rohlf, Jr.) > Introduction to Economic Reasoning (7th Ed., William D. Rohlf, Jr.) > Essential Foundations of Economics (3rd Ed., Robin Bade & Michael > Parkin) > Understanding Modern Economics (Roger LeRoy Miller) > The Economics of Macro Issues (3rd Ed., Roger LeRoy Miller & Daniel K. > Benjamin) > Foundations of Economics (3rd Ed., Robin Bade & Michael Parkin) > Economics Today (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Macro View (14th Ed., Roger LeRoy Miller) > Economics (Michael A. Leeds, Peter von Allmen & Richard C. Schiming) > Economics: Private Markets and Public Choice (7th Ed., Robert B. > Ekelund, Jr., Rand W. Ressler & Robert D. Tollison) > Principles of Economics, 7th Ed. (Roy J. Ruffin & Paul R. Gregory) > The Economics of Public Issues (14th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > The Economics of Public Issues (15th Ed., Roger LeRoy Miller, Daniel > K. Benjamin & Douglass C. North) > Macroeconomics (7th Ed., Michael Parkin) > Macroeconomics (8th Ed., Michael Parkin) > Foundations of Microeconomics (3rd Ed., Robin Bade & Michael Parkin) > Foundations of Macroeconomics (3rd Ed., Robin Bade & Michael Parkin) > Microeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Macroeconomics MyEconLab Homework Edition (Michael A. Leeds, Peter von > Allmen & Richard C. Schiming) > Economics Today: The Micro View (13th Ed., Roger LeRoy Miller) > Economics Today: The Micro View (14th Ed., Roger LeRoy Miller) > Microeconomics (7th Ed., Michael Parkin) > Microeconomics (8th Ed., Michael Parkin) > Macroeconomics (2nd Ed., Stephen D. Williamson) > Macroeconomics (3rd Ed., Stephen D. Williamson) > Macroeconomics Update Edition (5th Ed., Andrew B. Abel, Ben S. > Bernanke) > Macroeconomics (6th Ed., Andrew B. Abel, Ben S. Bernanke & Dean > Croushore) > Macroeconomics (10th Ed., Robert J. Gordon) > Economic Growth (David N. Weil) > Money, the Financial System, and the Economy (5th Ed., R. Glenn > Hubbard) > Money, the Financial System, and the Economy (6th Ed., R. Glenn > Hubbard) > The Economics of Money, Banking and Financial Markets (8th Ed., > Frederic S. Mishkin) > Principles of Money, Banking, and Financial Markets (11th Ed., > Lawrence S. Ritter, William L. Silber & Gregory F. Udell) > International Economics (3rd Ed., James Gerber) > International Economics (4th Ed., James Gerber) > International Economics (7th Ed., Steven Husted & Michael Melvin) > World Trade and Payments: An Introduction (9th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > World Trade and Payments: An Introduction (10th Ed., Richard E. Caves, > Jeffrey A. Frankel & Ronald W. Jones) > International Economics: Theory and Policy (7th Ed., Paul R. Krugman & > Maurice Obstfeld) > International Money and Finance (7th Ed., Michael Melvin) > Economic Development (9th Ed., Michael P. Todaro & Stephen C. Smith) > Microeconomics (4th Ed., Jeffrey M. Perloff) > Microeconomics (Don E. Waldman) > Microeconomics: Theory and Applications with Calculus (Jeffrey M. > Perloff) > Environmental Economics and Policy (5th Ed., Tom Tietenberg) > Environmental and Natural Resource Economics (7th Ed., Tom Tietenberg) > Health Economics (3rd Ed., Charles E. Phelps) > & Elizabeth J. Jensen) > Modern Industrial Organization (4th Ed., Dennis W. Carlton & Jeffrey > M. Perloff) > Modern Labor Economics: Theory and Public Policy (9th Ed., Ronald G. > Ehrenberg & Robert S. Smith) > Law and Economics (4th Ed., Robert Cooter & Thomas Ulen) > Law and Economics (5th Ed., Robert Cooter & Thomas Ulen) > Market Regulation (Roger Sherman) > Public Finance and the American Economy (2nd Ed., Neil Bruce) > The Economics of Sports (2nd Ed., Michael A. Leeds & Peter von Allmen) > The Economics of Sports (3rd Ed., Michael A. Leeds & Peter von Allmen) > Introduction to Econometrics, Brief Edition (James H. Stock & Mark W. > Watson) > Introduction to Econometrics (2nd ed., James H. Stock & Mark W. > Watson) > Econometrics: A Modern Introduction (Michael P. Murray) > Using Econometrics: A Practical Guide (5th Ed., A.H. Studenmund) > Mathematical Methods for Economics (2nd Ed., Michael Klein) > Personal Finance with Financial Planning Software (3rd Ed., Jeff > Madura) > Finance: Investments, Institutions, and Management - Update (2nd Ed., > Stanley G. Eakins) > Introduction to Finance (Lawrence J. Gitman & Jeff Madura) > Principles of Managerial Finance Brief plus MyFinanceLab Student > Access Kit (4th Ed., Lawrence J. Gitman) > Principles of Managerial Finance plus MyFinanceLab Student Access Kit > (11th Ed., Lawrence J. Gitman) > Corporate Finance plus MyFinanceLab Student Access Kit (Jonathan Berk > & Peter DeMarzo) > Risk Takers: Uses and Abuses of Financial Derivatives (John > Marthinsen) > Theory of Asset Pricing (George Pennacchi) > Multinational Business Finance (11th Ed., David K. Eiteman, Arthur I. > Stonehill & Michael H. Moffett) > Fundamentals of Multinational Finance (2nd Ed., Michael H. Moffett, > Arthur I. Stonehill & David K. Eiteman) > Cases in International Finance (2nd Ed., Gunter Dufey & Ian H. Giddy) > Fundamentals of Investing plus MyFinanceLab Student Access Kit and > OTIS Student Access Kit (10th Ed., Lawrence J. Gitman & Michael D. > Joehnk) > Fundamentals of Investing & Wharton's OTIS Student Access Kit Package > (9th Ed., Lawrence J. Gitman & Michael D. Joehnk) > OTIS: Online Trading and Investment Simulator Student Access Kit > (Wharton Learning Lab) > Derivatives Markets (2nd Ed., Robert L. McDonald) > Principles of Risk Management and Insurance (9th Ed., George E. Rejda) > Principles of Risk Management and Insurance (10th Ed., George E. > Rejda) > Financial Markets and Institutions (5th Ed., Frederic S. Mishkin & > Stanley G. Eakins) > Statistical Analysis of Financial Data in S-PLUS (Rene A. Carmona) > Statistics and Finance: An Introduction (David Ruppert) > Mathematical Statistics for Economics and Business (Ron C. > Mittelhammer) - Materials Engineering : > > Fundamentals of Modern Manufacturing: Materials, Processes, and > Systems (3rd Ed., Mikell P. Groover) > Materials Science and Engineering: An Introduction (6th Ed., William > D. Callister, Jr.) > Materials Science and Engineering: An Introduction (7th Ed., William > D. Callister, Jr.) > Fundamentals of Materials Science and Engineering : Integrated > Approach (2nd Ed., William D. Callister, Jr.) > Science and Design of Engineering Materials (2nd Ed., Schaffer, > Saxena, et al) > Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. > T. Black, Ronald A. Kohser) > DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul > DeGarmo, J. T. Black, Ronald A. Kohser) > Foundations of Materials Science and Engineering (3rd Ed, Smith) > Foundations of Materials Science and Engineering (4th Ed, Smith) > Plastics: Materials and Processing (3rd Ed., Strong) > Engineering Materials: Properties and Selection (8th Ed., Budinski) > Introduction to Materials Science for Engineers (6th Ed., Shackelford) > Materials: Engineering, Science, Processing and Design (Michael Ashby, > Dr Hugh Shercliff & David Cebon) > Principles of Corrosion Engineering and Corrosion Control (Zaki Ahmad) > Analysis and Performance of Fiber Composites (3rd Ed., Bhagwan > Agarwal, Lawrence Broutman & K. Chandrashekhara) > Basic Engineering Plasticity: An Introduction with Engineering and > Manufacturing Applications (David Rees) > Steels: Microstructure and Properties (3rd Ed. Bhadeshia & Honeycombe) > Theory of Plasticity (3rd Ed. Jagabanduhu Chakrabarty) > Engineering Materials Vol. 1 : An Introduction to Properties, > Applications and Design (3rd Ed., Michael Ashby & David R H Jones) > Engineering Materials Vol. 2 : An Introduction to Microstructures, > Processing and Design (3rd Ed., Michael Ashby & David R H Jones) > Plastics: Microstructure and Engineering Applications (3rd Ed., Nigel > Mills) > Laser Processing of Engineering Materials : Principles, Procedure and > Industrial Application (John Ion) > Sintering : Densification, Grain Growth and Microstructure (Suk-Joong > Kang) > Biomaterials Science : An Introduction to Materials in Medicine (2nd > Ed., Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) > Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) > Smart Electronic Materials: Fundamentals and Applications (Jasprit > Singh) > Laminar Composites (by George Staab) + original Ebook > contact me to : newbergh123@yahoo.com > Water Treatment: Principles and Design, 2nd Edition for me. thank you very much! liew168@sina.com > === Subject: Re: List of solutions manual (thousands) posting-account=U0LgTAoAAACT3plNs1Bj32A1VT9Tz6dl 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; InfoPath.2),gzip(gfe),gzip(gfe) > My List of Solutions Manual > contact me to : newbergh...@yahoo.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. This list (not links) is available from : http://rapidshare.com/files/59002351/List of solutions manual.txt - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos.8e) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original Ebook > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering Mechanics: Dynamics (4th Ed., Shames) > Introduction to Solid Mechanics (3rd Ed.., Shames) > Elastic And Inelastic Stress Analysis (Shames) > Statics and Strengths of Materials (6th Ed., Morrow & Kokernak) > Engineering Mechanics : Statics (11th Ed., Hibbeler)-Not mathcad files ... read more > I Am in possesion of the following Solution Manuals and will give them for free!!!!!!!!!!!!!!!!!!!!!! just email me at mickeydizzle@gmail.com -Engineering Mechanics Statics 10th & 11th by Hibbeler -Engineering Mechanics Dynamics 11th by Hibbeler -Engineering Mechanics Dynamics 4th Bedford === Subject: mike lalonde posting-account=3isBZgoAAADJM-2G3Oc0CRLy9Sk4yeg_ 5.0),gzip(gfe),gzip(gfe) 42434 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle bacini sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde 4 345 mike lalonde sudbury temagami lalonde jason tesker angela legrow darryl lalonde donna manchester roger mustelle sudbury darryl temagami vicky terreault nancy daigle unitz proxy ontera proxy steve harrison angela legrow micheline dumont catherine urhere paul lalonde michael lalonde mike lalonde temagami henry merchant tammy dubriel gerry dubriel victor dubriel yvan tonge yvan steve tonge 3 === Subject: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=nsrQxAoAAACDkV1_uYvq7QQjzxtFXYoo Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Do you have this one available? How can I get it? Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton please email me if you have it. I only need solution for ch 9 to 13 I have the rest if you're interested let me know student482@gmail.com alt.history.british, alt.guitar.amps === Subject: See the accepted papers, keynote lecture, plenary lectures, the contents of the Book of the Proceedings (i.e. accepted papers). WSEAS Post-Conference Report for the Conferences MACMESE '07 and DNCOCO '07 (124 images) posting-account=KWYMKQoAAAArfstGv6VUH6u1SaWpz4Xi 5.1),gzip(gfe),gzip(gfe) Click on the link below and see the accepted papers, the keynote and Plenary Speeches, the contents of the Book of the Proceedings as well as nice photos from an MACMESE '07 and DNCOCO '07 excellent conferences in Trinidad and Tobago Islands , co-organized by the University of West Indies and WSEAS ------------------------------------- http://www.wseas.com/wseas/reports/trinidadandtobago/index.html Post-Conference Report for the WSEAS Conferences: MACMESE '07 and DNCOCO '07 Trinidad and Tobago Islands (Caribbean Sea), November 5-7, 2007 http://www.wseas.com/wseas/reports/trinidadandtobago/index.html * This report contains 124 images copyrighted by the WSEAS. All rights reserved. * If you need some image with high resolution please click on the images below * If you need some image with extremely high resolution, contact us by email The University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences, Department of Mathematics and Computer Science, St. Augustine, Trinidad (W. I.) http://www.wseas.com/wseas/reports/trinidadandtobago/index.html and the WSEAS Society (http://www.wseas.org) , coorganized the following two parallel conferences: * 9th WSEAS Int. Conf. on MATHEMATICAL and COMPUTATIONAL METHODS in SCIENCE and ENGINEERING (MACMESE'07) (This conference was part of the MMACTEE international conference until 2006) * 6th WSEAS Int. Conf. on DATA NETWORKS, COMMUNICATIONS, COMPUTERS (DNCOCO '07), (The name of this conference was ISCOCO until 2005) OPENING, KEYNOTE, PLENARY SPEECHES: The two parallel Conferences were opened by Professor Bal Bhatt, who is director of the Department of Mathematics and Computer Science of the University of West Indies and he was the chairman of the conference and Professor Winston Mellowes, who is the Chairman, Professor Dyer Narinesingth, who is the Dean of the University of West Indies, the Campus Principal Professor Bridget Brereton, Mr. John Roopchan of the Ministry of Education and Dr. Bhoendradatt Tewarie, Director of the Institute of Critical Thinking, where the conference was held. After the opening ceremony the first keynote speaker was Professor Biswa N. Datta (Distinguished Research Professor at the Northern Illinois University, USA), who has presented the recent advances on computational methods for active vibration control and model updating in vibrating structures. Professor Eyad H. Abed (Institute for Systems Research, Electrical and Computer Engineering, University of Maryland, USA) who was PLENARY SPEAKER also presented new results on selective modal analysis of dynamic systems On Tuesday, 6th November 2007 (2nd day of the conference), Professor Imre J. Rudas (Institute of Intelligent Engineering Systems John von Neumann Faculty of Informatics Budapest Tech, Budapest, Hungary) who was PLENARY SPEAKER also described interesting aggregation procedures in intelligent systems. http://www.wseas.com/wseas/reports/trinidadandtobago/index.html On Tuesday evening was the cocktail party for all participants of the WSEAS Conference, who were invited at the office of the Campus Principal Professor Bridget Brereton (See pictures below) Both of the WSEAS Conferences in Trinidad were characterized by their friendly atmosphere (see photos below) as well as the high quality of the presentations and discussions. A variety of topics constituted the focus of paper submissions. In regular sessions papers addressed several interesting topics. Prominent lectures provided key-note and plenary speeches for the conference. Moreover, special sessions were organized, and invited lectures were given by well-known researchers. With pride, the WSEAS received the following Important Contributions and upgraded them as Keynote and Plenary Lectures.: KEYNOTE LECTURE: Recent Advances on Computational Methods for Active Vibration Control and Model Updating in Vibrating Structures : Linking Control to Industry by Prof. Biswa N. Datta, Northern Illinois University, USA. PLENARY LECTURE 1: New Results on Selective Modal Analysis of Dynamic Systems by Prof. Eyad H. Abed, University of Maryland, Maryland, USA. PLENARY LECTURE 2: Polynomial Optimization via Sums of Squares Relaxations by Prof. Mihai Putinar, University of California at Santa Barbara, CA, USA. PLENARY LECTURE 3: Aggregation procedures in intelligent systems by Prof. Imre J. Rudas, Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Hungary. PLENARY LECTURE 4: Selection Problems and Multi-criteria Decision Making by Dr. Alexey L Sadovski, Texas A&M University-Corpus Christi, USA. BENEFITS FOR THE PARTCIPANTS: WSEAS, http://www.wseas.org gave a very strong and important tool to all the participants: A new username and password without expiry date for on-line access in the WSEAS Conference proceedings FOR EVER. Conference Statistics Submitted papers: 335 Accepted papers: 147 acceptance ratio = (Number of accepted papers / Number of Submitted)*100 = 43.88% Remark: Two withdrawn accepted papers are considered as accepted papers in our Statistics. .: REVIEW PROCESS: Each paper was reviewed at least by 3 independent reviewers. The WSEAS Secretariat sent each paper to 5 reviewers. Some papers received reviews from 5 different referees. The WSEAS Secretariat forwarded these comments by personalized emails to the responsible for the correspondence author. The full list of the reviewers will be available in the web page: http://www.worldses.org/reviewers.htm The additional features of these 2 conferences 1) Publication of the Proceedings in 3 media: hard-copy, CD, E-Library (A) One Book in the Electrical and Computer Engineering Series and Energy and Environmental Engineering Series of WSEAS (see details, contents, author indices and editors below) with ISBN and ISSN indexed by the major Citation Indices (ISI ranked): www.worldses.org/indexes (B) CD-ROM Proceedings with pages' numbers with ISBN and ISSN indexed by the major Citation Indexes: www.worldses.org/indexes (C) E-Library: http://www.wseas.org/online and possible, for a very small number of papers: (D) JOURNAL PUBLICATION: Expanded and enhanced versions of papers published in the conference proceedings also going to be considered for possible publication in one of the WSEAS journals that participate in the major International Scientific Indices (Elsevier, Scopus, EI, Compendex, INSPEC, CSA .... see: www.worldses.org/indexes ). 2) WSEAS gave a very strong and important tool to all the participants: A new username and password without expiry date for on- line access in the WSEAS Conference proceedings FOR EVER. 3) The Participants received 6 very rich coffee-breaks (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences), 1 Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences) and 1 Gala Dinner with the high quality of the WSEAS 4) Cultural and social part as usual in WSEAS events. 5) The conference Books (Hard-Copy Proceedings), CD-ROM proceedings and Journals (with selected papers) published by WSEAS Press continue to sell for a long time after the meeting has taken place. This is another demonstration of the prestige the scientific community attribute to the meetings organized by the WSEAS. .: BOOK (hard-copy of the Proceedings): Editors: Balswaroop Bhatt (Trinidad and Tobago), Bhoendradatt Tewarie (Trinidad and Tobago), Athina Lazakidou (Greece), Konstantinos Siasiakos (Greece). Pages : 506, price: 80 EUR [Contents], [Order], [Full PDF of the Papers], [Help] .: JOURNALS: .: What is the Permanent Procedure for additional Journal publication for a very small number of High-Quality Papers presented in the WSEAS Conferences in China (after the recommendation of Chairmen). So, the authors with accepted & presented papers received the following e- mail: We have started now the procedure for the evaluation of the extended versions of your papers for possible inclusion in the WSEAS journals after new rounds of review. INTRODUCTION: You know that our goal is to maintain very strong international journals, to increase the impact of our beloved WSEAS Transactions, really top journals as they really are. To this end, we need only high quality papers, breakthrough works of archival value, i.e. papers that are well written from any point of view, completed studies (with their numerical examples or experiments that must be compared with the previous results in the literature), excellent english language and of course correct WSEAS format. The papers also must be substantially extended version of the paper that was presented in the conference (with more than 40% new material). We need papers that will attract the attention of other scholars citing them increasing our impact. In the next few years, the WSEAS transactions must be in every academic library, in every corner of the earth. To this end, we need your high quality contribution. HOW TO PROCEED: a) Check very carefully if your idea is really important, breakthrough in your field and can appear in a Journal of the quality and the level of the WSEAS Transactions. If you doubt, do not send it so easily. Your paper must not be only a good idea. It must be a complete study with theoretical background, complete bibliographical references; without grammatical and syntactical errors. For theoretical works: full comparison with previous published papers is necessary. We need numerical examples, applicability of the method, originality, novelty and directions for future research. For experimental or computational works: full comparison with previous published papers is necessary. We need real experiments with the necessary documentation, while for computational work, we need full benchmarks. Of course along discussions for the applicability of the method, originality, novelty and directions for future research. b) Complete the extended version of your paper until December 31, 2007 and upload it via http://............... (the full web address was given only to authors that presented a paper) until December 31, 2007 c) If your extended version fulfills the paragraph a), then our Editors will send it to 3 independent Reviewers outside your country. If not, our Editors are entitled to reject it from this early stage informing you properly. The positive answer of the 3 reviewers is necessary (attention: 2 yes and 1 no implies NO, i.e. rejection). d) Our Editors will collect the reviewers' remarks and will send them again to you for acceptance/ acceptance after minor revision / acceptance after major revision / rejection e) Possibly new rounds of review will be needed. f) No additional fee is needed in case of acceptance. After all this procedure, the accepted papers that come from WSEAS Conferences in Canada will be published in the various WSEAS Transactions. IF you miss the deadline of December 31, 2007 , or if your paper was not presented in the WSEAS Conferences, THEN: you can upload it quite independently as regular paper from the WSEAS Site for the Journals: http://www.worldses.org/journals/index.html The final list of the papers must have the approval of our Editors and 3 Reviewers, and of course the Editor-in-Chief of the particular Journal. We want only authors that presented their papers to complete this web form: http://............... (the full web address was given only to authors that presented a paper) So, in this form you will need a password (the password was given only to the authors that presented a paper). .: BEST STUDENT PAPERS: The Organizing Committee received the forms that the Session Chairmen filled in after the end of their Sessions and after additional evaluation and discussion decided the following. The Criteria were: a) Originality and scientific impact b) Good presentation c) Paper presented by a student The results of this evaluation will be announced soon in the web page: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html .: INDICES: PROCEEDINGS: The Proceedings related to the Conference are covered by: 1. ISI (ISINET) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 6. ULRICH 9. Directory of Published Proceedings 10. Computer Science Bibliography Administrator 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Engineering Information 15. SCOPUS 16. EBSCO 17. EMBASE 18. Compendex (CPX) 19. GEOBASE 20. BIOBASE 21. BIOTECHNOBASE 22. FLUIDEX 23. OceanBase 24. BEILSTEIN Abstracts 25. World Textiles 26. MEDLINE 27. British Library 28. National Library of Greece 29. German National Library of Science and Technology 30. IARAS Index JOURNALS: The WSEAS journals are covered by: 1. ISI through the INSPEC (IEE) 2. INSPEC (IET, former IEE) 3. CSA (Cambridge Scientific Abstracts) 4. ELSEVIER and Elsevier Bibliographic Database 5. ZENTRALBLATT 7. ULRICH 9. Computer Science Bibliography Administrator 10. British Library 11. American Chemical Society and its Index: Chemical Abstracts Service 12. European Library in Paris (France) 13. DEST Database (Australia) 14. Swets Information Services 15. Engineering Information 16. SCOPUS 17. EBSCO 18. EMBASE 19. Compendex (CPX) 20. Geobase 21. BIOBASE 22. BIOTECHNOBASE 23. FLUIDEX 24. OceanBase 25. BEILSTEIN Abstracts 26. World Textiles 27. MEDLINE 28. Mayersche 29. Index of Information Systems Journals 30. National Library of Greece 31. IARAS Index .: SOCIAL PART (Coffee-Breaks, Banquet, Excursions) 6 very rich coffee-breaks with Coffee, Tea, Milk, Sweets, Cakes, Pastries, Juices and Sandwiches (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Excellent Welcome Drink (offered by the University of the West Indies (http://www.uwi.tt), St.. Augustine Institute of Mathematical Sciences). 1 Gala Dinner. Participants enjoyed a wonderful night. .: Some Excursions took place after the conference. See the pictures: http://www.wseas.com/wseas/reports/trinidadandtobago/index.html === Subject: Re: Regarding solution manual for Introduction to Algorithm. Thomas H. Cormen. posting-account=T7fhkAoAAADh6aLufWf8lNSXnUk_5MhJ CLR 1.1.4322),gzip(gfe),gzip(gfe) Did you find the soultions manual? If you do, could you please send it to me. I would appreciate it a lot! === Subject: I need Solution manual posting-account=2Ao9ggkAAAB1JcOMWiDDOjkHclbisJtt Gecko/20061010 Firefox/2.0,gzip(gfe),gzip(gfe) (squid/2.5.STABLE9) I am studying Engineering Electromagnetics. In the Course Some problem I am encountering. I need a Solution Manual of ENGINEERING ELECTROMAGNETICS (7/E) BY HAYT AND BUCK mail this solution of masaddique_159@yahoo.com THIANK YOU === Subject: Re: I need Solution manual Bye! === Subject: Much Help Needed on Difficult Calculus Problems Can anyone offer me any advice on how to work and answer any of the following questions? 1) Find the limit of the sequence x = n square root of n! as n tends to ¡. 2) Determine whether the series ¡ á (n!)^(-1/n) is convergent or divergent. n=1 3) Find the sum of the series ¡ á (1/2^n) tan (x/2^n) for every value of x. n=1 -Drew === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. === Subject: Re: Much Help Needed on Difficult Calculus Problems 1) Find the limit of the sequence x = n square root of n! as n tends to infinite. That's as n tends to infinity. Or you could say informally that n becomes infinite. The problem as stated is pretty trivial since n sqrt(n!) > n for n > 1. --Lynn === Subject: Re: Much Help Needed on Difficult Calculus Problems in alt.math.undergrad: > Can anyone offer me any advice on how to work and answer > any of the following questions? > 1) Find the limit of the sequence x = n square root of n! > as n tends to ¡. Is there a typo in this one? > 2) Determine whether the series > ¡ > á (n!)^(-1/n) is convergent or divergent. > n=1 The denominator of the n-th term is the geometric mean of 1, 2, ..., n. Use the arithmetic mean - geometric mean inequality to compare with a familiar series. [...] Brian === Subject: helpppp pleasee!! whats is the antiderivative of 4x^-1 ?? === Subject: Re: helpppp pleasee!! in alt.math.undergrad: > whats is the antiderivative of 4x^-1 ?? The derivative of ln(x) with respect to x is 1/x, so the derivative of 4 ln(x) is 4/x. Brian === Subject: helpppp mee pleasee i need help using the substitution process to find... the antiderivative of r(radical r^2+2) dr help pleaseee === Subject: Re: helpppp mee pleasee >i need help using the substitution process to find... >the antiderivative of r(radical r^2+2) dr >help pleaseee If that's r sqrt(r^2 + 2) dr u = r^2 + 2 du = 2 r dr, so 1/2 du = r dr Antiderivative of 1/2 sqrt(u) du = 1/2 u^(1/2) du = ? === Subject: sub.. substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this === Subject: Re: sub.. >substitution process to find antiderivative of r(e^-r^2) dr >pleaseee help me with this Your turn. What do you think? === Subject: Re: sub.. > substitution process to find antiderivative of r(e^-r^2) dr pleaseee help me with this Your turn. What do you think? > think. That appears to be the entire difficulty. === Subject: help with substitution i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee === Subject: Re: help with substitution ok, but my answer has to have a +c in it i think === Subject: Re: help with substitution >i need help using the substitution process to find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com i need help using the substitution process to find... the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. === Subject: Re: help with substitution i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to > learn how to use complicated rules like mathematics has and consequently > consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar lessons? Dave === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. Why not spend your time helping with the math instead of giving grammar > lessons? Especially *wrong* ones. in rebellion to?? Wonton to flout?? His math is wrong (or wong), too. sqrt -1 doesn't mean anything: sqrt is a function, and one can't subtract a numberfrom it. Maybe he means sqrt(-1). -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ If there's one thing I know, it's men. I ought to: it's been my life work. -- Marie Dressler, in /Dinner at Eight/ === Subject: Re: help with substitution <84vjl3hfa9f70ffs9k6nbkemirril8g37t@4ax.com> i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. Yet alas you're not the OP to call me on that. do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar > lessons? > I offer full service help. Why can't they learn English? Do they have a learning disability? Math has even more rules and they're harder rules. What help can be given to those who detest rules? ---- === Subject: Re: help with substitution > i need help using the substitution process to find... > the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > > help pleaseee > u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du Shouldn't this be u^(-3/2) du? You are correct, of course. > Yet alas you're not the OP to call me on that. > > do you not? May I now assume, you can integrate it? Why not spend your time helping with the math instead of giving grammar lessons? > I offer full service help. > Why can't they learn English? > Do they have a learning disability? > Math has even more rules and they're harder rules. > What help can be given to those who detest rules? ---- Not all OP's are speaking english by nature, have pity with them. -- Vooruit mensen, achteruit! (Elimineer x voor een e-mail) Hou-du. === Subject: Re: help with substitution > >i need help using the substitution process to > find... >the antiderivative of (6x^2 dx)/(2x^3+7)^(3/2) > >help pleaseee u = 2 x^3 + 7 du = 6 x^2 dx > Good start. So you get > integral u^(3/2) du do you not? May I now assume, you can integrate it? I'm in rebellion to the grammar Nazis of the web who > abuse English punctuation. Here's some help you > haven't > asked for: > Sentences begin with a capital letter. > The first person singular pronoun 'I' is always > s capitalized. > In contrast, 'i' is the imaginary number sqrt -1. > Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > consider you unable to > learn how to use complicated rules like mathematics > has and consequently > consider it meaningless to help you. === Subject: [] help with substitution <25173561.1197114231915.JavaMail.jakarta@nitrogen.mathforum.org> help pleaseee I'm in rebellion to the grammar Nazis of the web who abuse English punctuation. Here's some help you haven't asked for: Sentences begin with a capital letter. The first person singular pronoun 'I' is always s capitalized. In contrast, 'i' is the imaginary number sqrt -1. Sentences end with a period and a space comes after. If you're wonton to flout these simple rules, I'll wonton? Personally I'm more eggroll about rules! > Help. I'm needing help substituting 'eggroll' with a word that coheres your sentence. consider you unable to learn how to use complicated rules like mathematics has and consequently consider it meaningless to help you. > === Subject: substitution????? substtution to find antiderivative of (5e^(-3g)) dg === Subject: Re: substitution????? >substtution to find antiderivative of (5e^(-3g)) dg u = -3 g du = -3 dg, so dg = ? === Subject: hellppp me out use the substitution to find the indefinite integral antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please === Subject: Re: hellppp me out <1432039.1197079325702.JavaMail.jakarta@nitrogen.mathforum.org>, The best help we can offer is to advise you to pay more attention in class, and read the assigned sections of the text. === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please cant be done, your hosed! (try dividing first) === Subject: Re: hellppp me out > use the substitution to find the indefinite integral > > antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt > > helppp me please >cant be done, your hosed! (try dividing first) > A joke of some sort? === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please If you are going to post all your homework questions, why not group them together in one post so we can keep straight which homework we are doing for you? --Lynn === Subject: Re: hellppp me out >use the substitution to find the indefinite integral >antiderivative of (t^2 + 2)/(t^3 + 6t +3) dt helppp me please Hint: the derivative of t^3 + 6 t + 3 is 3 t^2 + 6 = 3 (t^2 + 2) === Subject: sorry i just dont get the substitution and... i dont get the substitution process.. can somebody xplain it to me, for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for === Subject: Re: sorry i just dont get the substitution and... >i dont get the substitution process.. can somebody xplain it to me, >for example this problem n then i can try to figure out te others... antiderivative (6x^2)dx / ((2x^3+7)^(3/2)) ust run through how to let u=?.... and how to come up with an answer and waht i am looking for The basic idea is that you want to put the given expession in one of the forms that you know an antiderivative for, such as Int u^a du = u^(a+1) / (a + 1) + C for all a except a = -1 Int e^u du = e^u + C So let's look at 6x^2 dx / (2 x^3 + 7)^(3/2) You see that there's an x^3 in the denominator, and an x^2 in the numerator. That's promising, because if we substitute for the x^3 in the denominator, the derivative of x^3 is 2x^2 and so we may have something easy to substitute in the numerator as well (including the dx of course). Looking more closely, we see that we have 2 x^3, whose derivative is 6 x^2. Now that's VERY good, because that's exactly what's in the numerator. So, say we try u = 2 x^3 du = 6 x^2 dx Our expression becomes du / (u + 7)^(3/2) But wait! Now we realize that if we had made the substitution u = 2 x^3 + 7, then du still equals 6 x^2 dx and the resulting expression is even simpler, namely du / u^(3/2) Now *that* is an expression we know an antiderivative for! So, let's do the problem from the beginning. Find an antiderivative for 6x^2 dx / (2 x^3 + 7)^(3/2) Let u = 2 x^3 + 7 Then du = 6 x^2 dx Substituting into the original expression gives du / u^(3/2) = u^(-3/2) du for which an antiderivative is u^(-3/2 + 1) / (-3/2 + 1) = u^(-1/2) / (-1/2) = -2 u^(-1/2) = -2 / u^(1/2) = -2 / sqrt(u) Now, we want to get the answer back in terms of x, so we substitute for u [remember, u = 2 x^3 + 7] and get -2 / (2 x^3 + 7)^(1/2) or -2 / sqrt(2 x^3 + 7) Putting the problem in the form of an indefinite integral, we can now write Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / (2 x^3 + 7)^(1/2) + C or Int 6x^2 dx / (2 x^3 + 7)^(3/2) = -2 / sqrt(2 x^3 + 7) + C The C is the so-called 'constant of integration', which I assume has been discussed in conjunction with antiderivatives and indefinite integrals. === Subject: Complicated Differential Equation Sorry all I made a mistake in the first differential equation post. The equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, and V are all known constants. Is there any way to approximate this expression for i(t)? In my original post the expression didn't have the last term so some suggested using the Lambert W-Function, and another suggested using Newton's method. Would I still be able to use these methods, and if so how would I use them? === Subject: Re: Complicated Differential Equation <30569604.1197093354146.JavaMail.jakarta@nitrogen.mathforum.org>, > Sorry all I made a mistake in the first differential equation post. The > equation should read as follows: V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2. Where a,b,c, > and V are all known constants. Is there any way to approximate this > expression for i(t)? In my original post the expression didn't have the last > term so some suggested using the Lambert W-Function, and another suggested > using Newton's method. Would I still be able to use these methods, and if so > how would I use them? V=b*i(t)+a*i(t)*i'(t)+c*i(t)^2 gives i(t)/[V-b*i(t)-c*i(t)^2]*i'(t) = 1/a Now use partial fractions to split up i(t)/[V-b*i(t)-c*i(t)^2] At which point integration is possible, and one can solve for i(t). === Subject: Re: solutions manual posting-account=B4_SqwoAAACGEFBNbAgH7qBnxybkNR0U AppleWebKit/419.2 (KHTML, like Gecko) Safari/419.3,gzip(gfe),gzip(gfe) > Hello everyone. Who has the solutions manual for the following books Foundations of Electromagntic Theory, 4th Edition by Milford, Reitz, > and Christy > An Introducttion to Thermal Physics by Daniel V. Schroeder Please send me. I really need it. > BHUPALA, I hope you have it. Pjccanoy2...@yahoo.com hello you wouldnt happen to have the solutions for thermal physics would you? === Subject: Funning around with Integral Calculus posting-account=Bdg5ngoAAABEariw6PbB1G_LUE895pfi Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) I was reading a book about infinite series and there was a chapter about convergence tests. There was a series that they suggested using the comparison test because the integral test would be difficult. the integral is to be evaluated zero to infinity. the integrand is (x^3-1)/(x^4+4). so I write: (x^3-1)/(x^4+4)=x^3/(x^4+4)-1/(x^4+4) To evaluate the first term is an easy u substitution. The second term is for some reason giving me pause. I suspect that it is a partial fraction situation, the problem is that I forgot how to efficiently compute partial fractions. Any have any clues Later === Subject: Re: Funning around with Integral Calculus You were warned that it was difficult! The first step is to factor the denominator. The easy way to do that is think of it as the DIFFERENCE of two squares- specifically, x^4+ 4= (x^2)^2- (-4)= (x^2)^2- (2i)^3= (x^2- 2i)(x^2+ 2i). To factor each of those, take the square root of 2i and -2i. You can think of 2i, in the complex plane as 2 units up on the imaginary axis. It's two square roots are at distance sqrt(2) on the line at angle 90/2= 45 degrees to the x-axis. That is, sqrt(2)/2+ sqrt(2)i/2 and sqrt(2)/2- sqrt(2)i/2. The roots of -2i are just the negatives of those: -sqrt{2)/2- sqrt(2)i/2 and -sqrt(2)/2+ sqrt(2)i/2. That is, x^4+ 4 factors, over the complex numbers, as (x- sqrt(2)/2- sqrt(2)i/2)(x+sqrt(2)/2- sqrt(2)i/2)(x-sqrt(2)/2- sqrt(2)i/2)(x-sqrt(2)/2+ sqrt(2)i/2). But we need the factors over the real numbers. Put those back together again by writing them as (x- (sqrt(2)/2- sqrt(2)i/2))(x+ (sqrt(2)/2+ sqrt(2)i/2))(x- (sqrt(2)/2- sqrt(2)i/2))(x+ (sqrt(2)/2- sqrt(2)i/2)) which can then be written as two sum and difference products: ((x- sqrt(2)/2)- sqrt(2)i/2)((x- sqrt(2)/2)+ sqrt(2)i/2)((x+ sqrt(2)/2)- sqrt(2)i/2)((x+ sqrt(2)/2)+ sqrt(2)i/2)= ((x- sqrt(2)/2)^2+ 1/2)((x+ sqrt(2)/2)^2+ 1/2). 1/(x^4+ 4)= 1/((x- sqrt(2)/2)^2+ 1/2)((x+ sqrt(2)/2)^2+ 1/2) and, by partial fractions that separates as (Ax+ B)/((x- sqrt(2)/2)^2+ 1/2)+ (Cx+ D)/((x+ sqrt(2)/2)^2+ 1/2). To find A, B, and C, multiply on both sides by the denominator on the left: 1= (Ax+ B)((x+ sqrt(2)/2)^2+ 1/2)+ (Cx+ D)((x- sqrt(2)/2)^2+ 1/2). That has to be true for all x so you can let x be 4 simple values (0, 1, -1, 2 for example) giving you 4 equations to solve for A, B, C, and D. The x/(x^+ a^2) term can be integrated by letting u= x^2 and the 1/(x^2+ a^2) term integrates as an arctangent. === Subject: Re: Funning around with Integral Calculus <33539770.1197125592451.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=Bdg5ngoAAABEariw6PbB1G_LUE895pfi Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > You were warned that it was difficult! The first step is to factor the denominator. The easy way to do that is think of it as the DIFFERENCE of two squares- specifically, x^4+ 4= (x^2)^2- (-4)= (x^2)^2- (2i)^3= (x^2- 2i)(x^2+ 2i). when i do this it all falls in line very nicely. it's been a long === Subject: Re: Funning around with Integral Calculus posting-account=ogMREwkAAAC5xUr8sg7heGtsvzzF18LA 1.1.4322),gzip(gfe),gzip(gfe) On Dec 8, 9:06 am, rehamkcir...@gmail.com about convergence tests. There was a series that they suggested using > the comparison test because the integral test would be difficult. the > integral is to be evaluated zero to infinity. the integrand is > (x^3-1)/(x^4+4). so I write: (x^3-1)/(x^4+4)=x^3/(x^4+4)-1/(x^4+4) To evaluate the first term is an easy u substitution. The second term > is for some reason giving me pause. I suspect that it is a partial > fraction situation, the problem is that I forgot how to efficiently > compute partial fractions. Any have any clues Later Well, you COULD do a partial fraction breakdown, but that isn't the best way to go, unless you are very clever, or don't mind using complex roots. (the denominator DOES factor into two quadratics, but it isn't obvious[*].) The reason the integral test would be tough is exactly for this reason. Since the problem mentions comparison tests, you are probably meant to use the Limit Comparison Test (LCT). Direct comparison won't work, since you can only get larger, divergent series to compare with easily. Using the LCT: note that this is a rational expression (numerator and denominator are polynomials), and the numerator is one degree less than the denominator. This suggests using the LCT, comparing to 1/x. Properly done, this quickly shows that either the given series and that for 1/x both converge, or both diverge. 1/x is divergent (you can show this many ways), so the given series diverges (and so does the integral) [*] x^4 + 4 factors into (x^2 -2x +2)(x^2 +2x +2), which leads to the partial fractions: (x^3 -1) / (x^4 +4) = (Ax + B) / (x^2 -2x +2) + (Cx + D)/(x^2 +2x +2), for some real values A, B, C, and D. This may (I haven't worked it out, and won't) then require the use of a trig substitution or completion of the square in the denominators (or the use of a comparison test, but if you are doing that, then you wouldn't be at this point anyway.) With luck, you won't end up with the difference of two divergent integrals/series, as that requires more work to resolve. === Subject: Re: Solution manual of textbooks in ebook format! Get it in hours! I am looking for the solutions manual for Fundamentals of Electromagnetics with Engineering Applications ISBN#: 0471263559 I am also looking for the sol man to Fundamentals of digital Signal Processing ISBN#: 0130160776 Please let me know as soon as possible Jake === Subject: Elements of the theory of computation: Solutions manual posting-account=2cz15QoAAABtzw5wWAZyCqOgXQxqwD1o SIMBAR={4DC2B8B0-53C2-4C4B-AFE2-CBE326FC4E79}; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Can anybody send me the solutions manual for: Elements of the theory of Computation by Lewis and Papadimitriou????? My email is sofisland(at)yahoo.gr === Subject: Re: Elements of the theory of computation: Solutions manual Can anybody send me the solutions manual for: Elements of the theory > of Computation by Lewis and Papadimitriou????? Maybe, but I bet they won't. I wouldn't be a bit surprised if people are getting thoroughly pissed off with all these requests for solution manuals. The place to get them from is the publisher not this nor any other newsgroup. > My email is sofisland(at)yahoo.gr -- How unlike the home life of our own dear Queen. === Subject: Re: does anybody know how to find the area between curves?? i did 1, now all i need is 2 pleasee === Subject: AREA BETWEEN CURVES the 2 curves are... y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5) now i think the point of intersections are x= 0 and 1 so i would do the antiderivative from 0 to 1 of the top curve - bottom curve,,, but wwhat is the top curve and what is the bottom curve? === Subject: Re: AREA BETWEEN CURVES On 2007-12-08 20:33:09 -0500, Ryan said: > the 2 curves are... y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5) > now i think the point of intersections are x= 0 and 1 > so i would do the antiderivative from 0 to 1 of the top curve - bottom > curve,,, but wwhat is the top curve and what is the bottom curve? First of all, note that your problem can be simplified to finding the area bounded by y = x^5 and y = x^3. You can drop the 2ln(x+5) because both of them have it. You just have to make sure the domain of integration is x > -5. Second, it is immediately obvious from the simplified problem that the common points are -1, 0, 1. Note these are all > -5. So, you need to integrate from -1 to 1 of |x^5-x^3|, or in short int_{-1, 1} |x^5 - x^3| dx. Can you integrate this? You will need to break it up into two pieces to get rid of the absolute value sign first. -- -kira === Subject: Re: AREA BETWEEN CURVES <18994772.1197182019271.JavaMail.jakarta@nitrogen.mathforum.org>, Ryan > the 2 curves are... y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5) > now i think the point of intersections are x= 0 and 1 > so i would do the antiderivative from 0 to 1 of the top curve - bottom > curve,,, but wwhat is the top curve and what is the bottom curve? According to my calculations, the curves also intersect and -1. To see who is on top just check at say -1/2 and 1/2. -- Paul Sperry Columbia, SC (USA) === Subject: Re: does anybody know how to find the area between curves?? > Here are two problems I got up to drawing the graph and finding the point > of intersection, but thats it.. can anybody help me > finish them 1) y= x^2 - 18 , y = x - 6 and 2) x = 0, x = 4 , y = 1/(x+1) , y = (x-1)/2 === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) What is ment with optimum compression ? Whatever the case may be, the program is useless to determine what the maximum compressed file size would be. WinZip and WinRar for example compress much better than ent.exe indicates should be theoretically possible. Bye, Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) No. Your dead wrong there. Have you even tried this? Optimum compression means the theoretical maximum you could (losslessy) compress a file. No program could compress file a file filled with random bytes. If it could then by definition the data would not be random. That's how compression works - by finding patterns! > What is ment with optimum compression ? Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. WinZip and WinRar for example compress much better than ent.exe indicates > should be theoretically possible. Bye, > Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) Well something is wrong with the program or the theory. I run ent.exe in a dos box on Windows XP x64 Pro Edition. I tried two files: 1. 212 MB AVI (video only) Entropy: 6.211472 bits per byte. Reduction would be 22 percent. The same file compressed with WinRar: 79.2 MB, that's clearly more than 50% compression. 2. 900 KB BMP (Picture) Reduction would be something like 15 procent. It was way over 50 procent WinRar file only 300 KB or so. Try it yourself I would say ;) Bye, Skybuck. > No. Your dead wrong there. Have you even tried this? Optimum compression means the theoretical maximum you could (losslessy) > compress a file. No program could compress file a file filled with random bytes. If it > could then by definition the data would not be random. That's how compression works - by finding patterns! > What is ment with optimum compression ? > Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. > WinZip and WinRar for example compress much better than ent.exe indicates > should be theoretically possible. > Bye, > Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) > Well something is wrong with the program or the theory. I run ent.exe in a dos box on Windows XP x64 Pro Edition. I tried two files: 1. 212 MB AVI (video only) Entropy: 6.211472 bits per byte. Reduction would be 22 percent. The same file compressed with WinRar: 79.2 MB, that's clearly more than 50% compression. 2. 900 KB BMP (Picture) Reduction would be something like 15 procent. It was way over 50 procent WinRar file only 300 KB or so. Try it yourself I would say ;) Bye, > Skybuck. No. Your dead wrong there. Have you even tried this? > Optimum compression means the theoretical maximum you could (losslessy) > compress a file. > No program could compress file a file filled with random bytes. If it > could then by definition the data would not be random. > That's how compression works - by finding patterns! > What is ment with optimum compression ? Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. WinZip and WinRar for example compress much better than ent.exe indicates > should be theoretically possible. You have this all backwards. It is not an issue if this program or that program produces better compression. The ent program is a test for randomness like properties. If the ent program can perform some significant amount of compression (like 1 or 2 percent for small files or even less for larger files) then that file's data is significantly non-random. That is all the test does. The file IS non-random. The estimates are just that, estimates from a simple compression program. Of course sophisticated programs will do better or no body would bother with them. Don't be deliberately thick. Bye, > Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) Simply put I don't believe you. Can you please upload a sample avi and compressed archive to a service like rapidshare. Here is a 10k file filled with random noise from delphis random number generator: http://rapidshare.de/files/38183629/rand.bin.html Try and compress it ;), can't be done! Files with high entropy can't be compressed for the same reason you when you zip a zip file it won't get smaller. Think about it. > Well something is wrong with the program or the theory. I run ent.exe in a dos box on Windows XP x64 Pro Edition. I tried two files: 1. 212 MB AVI (video only) Entropy: 6.211472 bits per byte. Reduction would be 22 percent. The same file compressed with WinRar: 79.2 MB, that's clearly more than 50% compression. 2. 900 KB BMP (Picture) Reduction would be something like 15 procent. It was way over 50 procent WinRar file only 300 KB or so. Try it yourself I would say ;) Bye, > Skybuck. No. Your dead wrong there. Have you even tried this? > Optimum compression means the theoretical maximum you could (losslessy) > compress a file. > No program could compress file a file filled with random bytes. If it > could then by definition the data would not be random. > That's how compression works - by finding patterns! > What is ment with optimum compression ? Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. WinZip and WinRar for example compress much better than ent.exe indicates > should be theoretically possible. Bye, > Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) I have my own webdrive, I put a BMP on it for you, and the compressed RAR file and the TEXTENT.TXT which contains the output of the ent.exe TEST.BMP http://members.home.nl/hbthouppermans/EntropyTest/ Test.bmp is 900 KB Test.rar is 347 KB Ent.exe Test.bmp output: Entropy = 6.723972 bits per byte. Optimum compression would reduce the size of this 921654 byte file by 15 percent. Chi square distribution for 921654 samples is 2744487.23, and randomly would exceed this value 0.01 percent of the times. Arithmetic mean value of data bytes is 40.3445 (127.5 = random). Monte Carlo value for Pi is 3.819698065 (error 21.58 percent). Serial correlation coefficient is 0.843178 (totally uncorrelated = 0.0). 15 procent of 900 KB = 135 KB Clearly WinRar compressess better than that. Bye, Skybuck. > Simply put I don't believe you. Can you please upload a sample avi and > compressed archive to a service like rapidshare. Here is a 10k file filled with random noise from delphis random number > generator: http://rapidshare.de/files/38183629/rand.bin.html Try and compress it ;), can't be done! Files with high entropy can't be compressed for the same reason you when > you zip a zip file it won't get smaller. Think about it. > Well something is wrong with the program or the theory. > I run ent.exe in a dos box on Windows XP x64 Pro Edition. > I tried two files: > 1. 212 MB AVI (video only) > Entropy: 6.211472 bits per byte. > Reduction would be 22 percent. > The same file compressed with WinRar: > 79.2 MB, that's clearly more than 50% compression. > 2. 900 KB BMP (Picture) > Reduction would be something like 15 procent. > It was way over 50 procent > WinRar file only 300 KB or so. > Try it yourself I would say ;) > Bye, > Skybuck. > No. Your dead wrong there. Have you even tried this? Optimum compression means the theoretical maximum you could (losslessy) > compress a file. No program could compress file a file filled with random bytes. If it > could then by definition the data would not be random. That's how compression works - by finding patterns! > What is ment with optimum compression ? > Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. > WinZip and WinRar for example compress much better than ent.exe > indicates should be theoretically possible. > Bye, > Skybuck. > === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) I stand corrected. This goes against what I thought I knew about compression! http://en.wikipedia.org/wiki/Information_entropy > I have my own webdrive, I put a BMP on it for you, and the compressed RAR > file and the TEXTENT.TXT which contains the output of the ent.exe TEST.BMP http://members.home.nl/hbthouppermans/EntropyTest/ Test.bmp is 900 KB > Test.rar is 347 KB Ent.exe Test.bmp output: Entropy = 6.723972 bits per byte. Optimum compression would reduce the size > of this 921654 byte file by 15 percent. Chi square distribution for 921654 samples is 2744487.23, and randomly > would exceed this value 0.01 percent of the times. Arithmetic mean value of data bytes is 40.3445 (127.5 = random). > Monte Carlo value for Pi is 3.819698065 (error 21.58 percent). > Serial correlation coefficient is 0.843178 (totally uncorrelated = 0.0). 15 procent of 900 KB = 135 KB Clearly WinRar compressess better than that. Bye, > Skybuck. Simply put I don't believe you. Can you please upload a sample avi and > compressed archive to a service like rapidshare. > Here is a 10k file filled with random noise from delphis random number > generator: > http://rapidshare.de/files/38183629/rand.bin.html > Try and compress it ;), can't be done! > Files with high entropy can't be compressed for the same reason you when > you zip a zip file it won't get smaller. Think about it. > Well something is wrong with the program or the theory. I run ent.exe in a dos box on Windows XP x64 Pro Edition. I tried two files: 1. 212 MB AVI (video only) Entropy: 6.211472 bits per byte. Reduction would be 22 percent. The same file compressed with WinRar: 79.2 MB, that's clearly more than 50% compression. 2. 900 KB BMP (Picture) Reduction would be something like 15 procent. It was way over 50 procent WinRar file only 300 KB or so. Try it yourself I would say ;) Bye, > Skybuck. > No. Your dead wrong there. Have you even tried this? > Optimum compression means the theoretical maximum you could (losslessy) > compress a file. > No program could compress file a file filled with random bytes. If it > could then by definition the data would not be random. > That's how compression works - by finding patterns! > What is ment with optimum compression ? Whatever the case may be, the program is useless to determine what the > maximum compressed file size would be. WinZip and WinRar for example compress much better than ent.exe > indicates should be theoretically possible. Bye, > Skybuck. > === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) says... > I stand corrected. This goes against what I thought I knew about > compression! > http://en.wikipedia.org/wiki/Information_entropy > I have my own webdrive, I put a BMP on it for you, and the compressed RAR file and the TEXTENT.TXT which contains the output of the ent.exe TEST.BMP http://members.home.nl/hbthouppermans/EntropyTest/ The math is over mine as welll, but understanding what's going on in a real-world implementation of a compression algorithm doesn't require much math. Just look at how modern compressors work at the bit and byte level. All they do is look for repeated patterns of bits and bytes. To take a simple case, if you fill a file with (truly) random 32-bit unsigned numbers, a fairly large proportion of them will have the top byte be 0, which is a string of 8 repeated 0 bits. That common value will be represented by a shorter symbol. The same type of thing applies to other patterns it may find in the raw bits and bytes, including patterns which run from one value in the file to the next. Many long repeating patterns give high compression ratios, while fewer and shorter patterns give lower compression ratios, but there are always going to be compressible blocks in any list of random numbers. Test.bmp is 900 KB Test.rar is 347 KB Ent.exe Test.bmp output: Entropy = 6.723972 bits per byte. Optimum compression would reduce the size of this 921654 byte file by 15 percent. Chi square distribution for 921654 samples is 2744487.23, and randomly would exceed this value 0.01 percent of the times. Arithmetic mean value of data bytes is 40.3445 (127.5 = random). Monte Carlo value for Pi is 3.819698065 (error 21.58 percent). Serial correlation coefficient is 0.843178 (totally uncorrelated = 0.0). 15 procent of 900 KB = 135 KB Clearly WinRar compressess better than that. Bye, Skybuck. > Simply put I don't believe you. Can you please upload a sample avi and > compressed archive to a service like rapidshare. Here is a 10k file filled with random noise from delphis random number > generator: http://rapidshare.de/files/38183629/rand.bin.html Try and compress it ;), can't be done! Files with high entropy can't be compressed for the same reason you when -- Remove the ns_ from if replying by e-mail (but keep posts in the newsgroups if possible). === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) <52d3c$477aeb5f$541983fa$24370@cache6.tilbu1.nb.home.nl> posting-account=J1hvvAkAAABbYk-yMwbrJlT5vWciLpKU 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.2),gzip(gfe),gzip(gfe) > Many long repeating patterns give high compression ratios, while fewer > and shorter patterns give lower compression ratios, but there are always > going to be compressible blocks in any list of random numbers. Even if chosen subsets can be compressed, it is easy to prove the existence of lists that can not be compressed if taken in full: 1. generate a list of random numbers 2. compress the list 3. take sequential bits from the compressed file as a new list of random numbers 4. repeat 2-4 You will soon have a list that resists compression. If you want your own private set of random numbers, just compress usenet postings from any given period and extract binary numbers from the result, throwing away the first and last few blocks which may contain structural info. The software equivalent of taking static from the air :-) P. Kline === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) > I stand corrected. This goes against what I thought I knew about > compression! > Skybuck is going off on a tangent. The subject is if a file contains random like data or not. The ent program correctly identifies the avi and bmp as non random. That is all it has to do. A small amount of compression proves the file is non random - a simple compression algorithm can do this. It does not need a sophisticated compression algorithm. That more sophisticated programs can compress further is irrelevant - all that they prove is that yes ent got it right - the file is non-random. http://en.wikipedia.org/wiki/Information_entropy I have my own webdrive, I put a BMP on it for you, and the compressed > RAR file and the TEXTENT.TXT which contains the output of the ent.exe > TEST.BMP > http://members.home.nl/hbthouppermans/EntropyTest/ > Test.bmp is 900 KB > Test.rar is 347 KB > Ent.exe Test.bmp output: > Entropy = 6.723972 bits per byte. > Optimum compression would reduce the size > of this 921654 byte file by 15 percent. > Chi square distribution for 921654 samples is 2744487.23, and randomly > would exceed this value 0.01 percent of the times. > Arithmetic mean value of data bytes is 40.3445 (127.5 = random). > Monte Carlo value for Pi is 3.819698065 (error 21.58 percent). > Serial correlation coefficient is 0.843178 (totally uncorrelated = 0.0). > 15 procent of 900 KB = 135 KB > Clearly WinRar compressess better than that. > Bye, > Skybuck. > Simply put I don't believe you. Can you please upload a sample avi > and compressed archive to a service like rapidshare. Here is a 10k file filled with random noise from delphis random > number generator: http://rapidshare.de/files/38183629/rand.bin.html Try and compress it ;), can't be done! Files with high entropy can't be compressed for the same reason you > when you zip a zip file it won't get smaller. Think about it. > Well something is wrong with the program or the theory. > I run ent.exe in a dos box on Windows XP x64 Pro Edition. > I tried two files: > 1. 212 MB AVI (video only) > Entropy: 6.211472 bits per byte. > Reduction would be 22 percent. > The same file compressed with WinRar: > 79.2 MB, that's clearly more than 50% compression. > 2. 900 KB BMP (Picture) > Reduction would be something like 15 procent. > It was way over 50 procent > WinRar file only 300 KB or so. > Try it yourself I would say ;) > Bye, > Skybuck. > No. Your dead wrong there. Have you even tried this? Optimum compression means the theoretical maximum you could > (losslessy) compress a file. No program could compress file a file filled with random bytes. If > it could then by definition the data would not be random. That's how compression works - by finding patterns! > What is ment with optimum compression ? > Whatever the case may be, the program is useless to determine what > the maximum compressed file size would be. > WinZip and WinRar for example compress much better than ent.exe > indicates should be theoretically possible. > Bye, > Skybuck. > === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) The ent program also mentions: Optimum compression What's that suppose to mean huh ? :) ;) =D Either it's optimal or not, could have fooled me =D Bye, Skybuck. === Subject: Re: Skybuck's Racing Random Number Generator V3 (algorithm fixed, should be no more many duplicates) With optimum compression maybe huffman compression is ment (?), which is ofcourse not optimal but could still be interesting... Bye, Skybuck. === Subject: Re: Balloon inflation (open problem... as far as I know) <-OadnRuG-L8rZe7aRVnyjwA@pipex.net> posting-account=mMlFNwkAAAB4mlUHsL9lydZIKUPXmAkO I'd like to know whether there's any fast algorithm to solve this problem, or whether the problem is known to be NP-complete (as it is obviously in NP). Erm. The problem is just in P. Given your starting position, it is > straightforward to state a finite upper bound on the number of steps > than can answer the question. It can easily be reduced to a choice of inflating one side of oneballoonby one unit at a time. For eachballoon, there is a limit, per > side, to the number of inflations possible. In fact, to avoid any > quibbling, one could give the net upper bound for each as M+N (for an > initial position, with zero size. Hence (K*(M+N))! is a reasonable coarse, finite, upper bound, I guess. As to whether there is a fast algorithm... that's another question. -- > Lau AS! d-(!) a++ c++++ p++ t+ f-- e++ h+ r--(+) n++(*) i++ P- m++ > ASC Decoder at When I say that the program in in NP, I mean that it is easy to guess a solution and then verify it rigorously in polynomial time. For instance, one could guess a complete paving of the grid and then verify that it does indeed lead to a positive answer to the question asked (by making sure that each piece of the paving covers completely exactly one balloon). I'm not saying that the problem is NP-complete, because I have no proof of that. The problem feels intuitively too limited for that to seem likely, but intuition can be pretty deceptive in such matters. One would have to come up with an algorithm in polynomial time (a fast one) to discard that possibility (unless of course P=NP). I didn't find any such algorithm in your answer. I'll grant you that there are finitely many ways to inflate a balloon, as you pointed out, and that a systematic search would find all conforming pavings, if any. However, it would run in exponential time, unless I missed something. Yann David NB: Sorry about answering so late, I hadn't spotted your post. sci.math.symbolic === Subject: Re: Call For Papers: WORLDCOMP'08: Computer Science & Computer Engineering Conferences, USA, July 2008 posting-account=ubyIWAkAAABW-OTbVB1QiN1oZlu0qUgw http://en.wikipedia.org/wiki/Internet sock puppet A sockpuppet is an online identity used for purposes of deception within an Internet community. In its earliest usage, a sockpuppet was a false identity through which a member of an Internet community speaks while pretending not to, like a puppeteer manipulating a hand puppet. In current usage, the perception of the term has been extended beyond second identities of people who already post in a forum to include other uses of misleading online sock-puppeting is defined as the act of creating a fake online identity to praise, defend or create the illusion of support for one's self, allies or company. The key difference between a sockpuppet and a regular pseudonym (sometimes termed an alt) is the pretense that the puppet is a third party who is not affiliated with the puppeteer. > According to yahoo groups, the person sending the message below, On Dec 28, 11:55 am, ross ...@yahoo.com in defense of WorldComp, > has never participated in any of the targeted newsgroups except to > send this one message. My working hypothesis is that this is a sock puppet. See > en.wikipedia.org/wiki/Internet sock puppet The author failed to reveal his/her name and papers titles, and > institution, etc. and so he may very well be the same person who > posted the original Call for Papers or his confederate. === Subject: M.I 5`Persec ution ` th eir meth ods an d tact ics -=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -= MI5: methods. and tactics -= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-= They deliberately set out to harass in. a way that would resemble the symptoms of schizophrenia, so that. any report of the harassment would be taken as indicating mental. illness and treated accordingly. They never show their own faces; they only. work through proxies, in the media, among the public, and by manipulating people in the workplace. Since they. do not declare their identity there is no evidence to. initiate legal action against the security services or. anyone else. The only people you can prosecute are the proxies and they will deny knowledge of. any conspiracy. By repeatedly. humiliating and abusing the victim, they induced mental illness. This is the worst form of human rights violation:. making any statement of the harassment appear to be. symptomatic of the illness which they cause through the harassment. That. this can happen, and people collude by silence, is. absolutely horrifying. have followed without change for. the last six years. They paint me as a threat to which people. must react (shades of Nazi persecution methods), while simultaneously portraying their hate. campaign on which they have spent over a million pounds of taxpayers.89 money as a. joke. The MI5 that breaks the law with the silent complicity of. the police is the same agency. that is now seeking a role in the fight against crime. Perhaps the real joke is the proposed. involvement in the implementation of justice of an organisation which. commits criminal acts with secrecy and disinterest for the. legal process. 1104 === Subject: M`I'5`Persecution - wh y t he securi ty services ? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -= why. the security services? -= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= You may ask, why do I think the they referred to are the. security services? Is there any evidence that. there is a single source, as opposed to a loosely based whispering campaign. amongst many people? Even if there is a single source, is there. any evidence that they are professional buggers as opposed to amateurs,. or perhaps people working for a privately funded. organization? a) As to the question of a single source versus something. more fragmented; it is quite obvious that there is a single source from the way the. campaign has. been carried out. Since things have been repeated verbatim which were said in my home, there must be one group. which does the watching and listening. Since on several occasions (mainly during. travel) people have been planted in close proximity and rehearsed in. what they were to say, it follows that someone must have done the planning for. that, and again a single source. is indicated. b) So why. couldn't it be amateurs? Why couldn't it be a private organisation, for example a private detective agency paid to manage. the campaign and undertake the. technical aspects? Some detective agencies are unscrupulous as. has been proved on the occasions in the past when they've been exposed or. caught; they too can have access to the bugging technology deployed; and there are reported cases of MI5. paying private eyes to do their dirty work. (against peace campaigners and similar enemies of the state) on the understanding that if. they were caught then they could deny all knowledge. Why. couldn't that be the case? The main factor pointing to direct security service. involvement (as opposed to amateurs or MI5 proxies). is the breadth of their access to the media in particular,. and the fact that the television companies are so involved in the campaign. The. BBC would not directly invade someone's home themselves, since it would not. be within their remit to allocate personnel or financial resources to do so. An organisation of their stature. would not take part in a campaign. set up by private sources. The only people they would take material. from would be the security services, presumably on the assumption that if the cat. ever flew out of the bag yowling it would be MI5 who would take. the consequences. State sponsorship for these acts. of psychological terrorism is also indicated by duration;. support for over six years for a team of three or four people would be beyond the means and will of most private. sources. The viciousness of the slanders. and personal denigration also points to MI5; they. traditionally protect the British state from politicians of the wrong. hue by character assassination, and in this case are using their tried and tested methods to murder with words. an enemy they have invented for. themselves. And there. are precedents. Diana and Hewitt were alleged to have been filmed at it by an Army intelligence team. which had operated in Northern Ireland, these allegations were made by someone called Jones. who had been on the team.. His statements were denied by the defence establishment who tried to character-assassinate by describing him as. the Jones twins. Funny how if. you tell the truth, then you must be ill, isn't it? Thought only communists behaved like. that? Hewitt later said that he'd been spoken to. by someone in the army who revealed the existence of videotapes of him and Diana, and. that the tapes would be published. if any attempt was made by them to resume their association. 1104 === Subject: M.I 5-Persecuti on - w hy t he se curity serv ices? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -= why. the security services? -= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= You may ask,. why do I think the they referred to are the security services? Is. there any evidence that there is a single source, as opposed to a loosely based whispering campaign amongst many people? Even if. there is a single source, is there. any evidence that they are professional buggers as opposed to amateurs, or perhaps people working for. a privately funded. organization? a) As to the question of a. single source versus something more fragmented; it is quite obvious that there is a single source. from the way the campaign has been carried out. Since things have been repeated verbatim which. were said in my home, there must be. one group which does the watching and listening. Since on several. occasions (mainly during travel) people have been planted in close proximity. and rehearsed in what they were to say, it follows that someone must have. done the planning for that, and again a single. source is indicated. b) So why. couldn't it be amateurs? Why couldn't it be a private organisation, for. example a private detective agency paid to manage the campaign and undertake the. technical aspects? Some detective agencies are unscrupulous as has been proved on the occasions in the. past when they've been exposed or. caught; they too can have access to the bugging technology deployed; and there are reported cases of MI5 paying private eyes to. do their. dirty work (against peace campaigners and similar enemies of the state) on the understanding that if they were caught then. they could deny all. knowledge. Why couldn't that be the case? The main factor pointing. to direct security service involvement (as opposed to amateurs or MI5 proxies) is the breadth of their access. to the media in particular, and the fact. that the television companies are so involved in the campaign. The. BBC would not directly invade someone's home themselves, since it would not. be within their remit to allocate personnel or financial resources to. do so. An organisation of their stature would not take part in a campaign set up by private. sources. The only people they would take material from would be the security services,. presumably on the assumption that if the cat ever flew out of. the bag yowling it would be MI5 who would take. the consequences. State. sponsorship for these acts of psychological terrorism is also indicated by duration; support for over six years for a. team of three or four people would be beyond the means and will of most private. sources. The viciousness of. the slanders and personal denigration also points to MI5; they traditionally protect. the British state from politicians of the wrong hue by character assassination, and in this case. are using their tried and tested methods. to murder with words an enemy they have invented for. themselves. And there are precedents. Diana and Hewitt were alleged to. have been filmed at it by an Army intelligence. team which had operated in Northern Ireland, these allegations were made by someone called Jones who. had been on the team. His statements were denied by the. defence establishment who tried to character-assassinate by describing him as the Jones. twins. Funny how if. you tell the truth, then you must be ill, isn't it? Thought only communists behaved like. that? Hewitt later said that he'd. been spoken to by someone in the army who revealed the. existence of videotapes of him and Diana, and that the tapes would be published. if any attempt was made by them to resume their association. 1104 === Subject: Re: The Halting Problem Oracle posting-account=n4TzyQkAAADLWxrRHqyiUZ-1SZdOB4vv Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > I would like to have a comment on this one: A computer runs a loop checking the decimal form of pi for a zero cipher. When it finds a zero, it starts the next loop looking for two consecutive zeroes. So it always increases the number of consecutive zeroes by one, once it has found a number of them. Will this computer come to a stop, considering ( from us, not the computer) that pi is not rational? since it is always searching for some run of zeros. If you are asking whether the decimal representation of pi has > arbitrarily long runs of zeros, then AFAIK this question is still open. > Informed opinion is that the decimal representation of pi does have > arbitrarily long runs of zeros. > The number of zeroes is either a natural number, thus finite, or of the cardinality of the set of naturals, infinite. What is an arbitrarily long number? It is a number from the naturals, greater than a given one, let's say greater one. But not a specific one. So we might be taking to Your expression an arbitrary long run of zeroes. This is not finite or infinite, but what is it in math? In Your setting of the problem, there is a difference between the program and the output, between the algorithm and the values it delivers. Now hackers and these Daedalus-programmers know, that You can feed the output into a change of the memory cells, where the program is stored. So an algorithm in a computer can change itself. With this feature, there might be a program, which will come to a halt. Or is there too much phantasy in my reasoning? With friendly greetings Hero === Subject: Re: The Halting Problem Oracle Phil Carmody a .8ecrit : > The halting problem was the first decision problem shown to be > undecidable by any algorithm. It can be stated as follows: > Given a description of a program and a finite input, decide whether > the program finishes running or will run forever, given that input. > Alan Turing proved that the halting problem is undecidable in 1936 > using a bit of Logistic Judo. He showed that if there was an algorithm > A that solves the halting problem, then one could use A to construct > an algorithm B such that B halts if and only if B does *not* halt! > This is the first example of an undecidable problem presented in most > textbooks on computability theory. Since many students are surprised > to learn that there are problems that cannot be solved by any > algorithm, introductory texts often make the point that an algorithmic > solution to the halting problem would be just too good to be > true. Such an algorithm could automatically solve nearly any > Mathematical problem. Before Wiles proved Fermat's Last Theorem, it > was frequently pointed out that the FLT could be viewed as an instance > possible integers x>0, y>0, z>0, and n>2 and halts when x^n + y^n = > z^n; clearly this program halts if and only if FLT is false. But even > after FLT was proved, there were no shortage of open Mathematical > problems that could be reduced to an instance of the halting problem: > Waring's conjecture, Goldbach's conjecture, the twin primes > conjecture, the existence of an odd perfect number, etc. > Just for fun, assume that there exists an Oracle that can give you the > solution to as many as 3 instances halting problems. Which problems > would you choose? > I'm not sure what my third choice would be, but I think the Riemann > hypothesis is so important that my first two choices would be the > Riemann hypothesis and the generalized Riemann hypothesis, restated as > halting problems. My choice would be your 'B' above :-) Doesn't work : it is not possible to construct B given an oracle, but only given an universal algorithm A. > That should teach the oracle to be such a smartarse. Phil === Subject: Re: The Halting Problem Oracle posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG > I would like to have a comment on this one: > A computer runs a loop checking the decimal form of pi for a zero > cipher. When it finds a zero, it starts the next loop looking for two > consecutive zeroes. So it always increases the number of consecutive > zeroes by one, once it has found a number of them. Will this computer > come to a stop, considering ( from us, not the computer) that pi is > not rational? since it is always searching for some run of zeros. If you are asking whether the decimal representation of pi has > arbitrarily long runs of zeros, then AFAIK this question is still open. > Informed opinion is that the decimal representation of pi does have > arbitrarily long runs of zeros. Making it a conjecture that there is a maximal run of zeroes somewhere in the decimal expansion of pi? If pi is normal, wouldn't a run of m consecutive digits be present with probability P(m) = P(m-1)/10, so that longer and longer runs approach (but never reach) a probability of zero? (But, as you say, the searching algorithm would never find out for us if that is true.) === Subject: Re: The Halting Problem Oracle posting-account=n4TzyQkAAADLWxrRHqyiUZ-1SZdOB4vv Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Drizzle, Drazzle, Drozzle, Drome, > Time for this one to come home! > - Mr. Wizard from Tooter Turtle Can You give a comment on this too, please? I post to a lot of animation newsgroups. A lot of my fellow animation > fans are amused by my connection of a baby boomer kid's cartoon Tooter > Turtle with a more contemporary adult Anime series. I must concede that > this signature is not appropriate for math groups. My apologies for any > confusion this might have caused. > Is this confusion? You do not have to apologize, anyhow. My computer had a Mr.Wizard, a reset buttom. And once i have done a machine code, i built in every loop a request for a memory cell with the obligation to jump out of the loop, if the memory cell contained a one. So with One Laptop Per Child one can build in some kind of a switch, so when the child says > Drizzle, Drazzle, Drozzle, Drome, > Time for this one to come home! it will stop the running process and goes back to start. With friendly greetings Hero === Subject: M-I,5.Pe rsecution . harassme nt at w ork -=-=-=-=-=-=-=-=-=-=-=-= -= harassment. at work -= -=-=-=-=-=-=-=-=-=-=-=-= Once I stopped watching television. and listening to the radio at the end of 1990, they had to find other ways of committing abuses.. So they took what must be for them a tried and tested. route; they get at you by subversion of those around you. Since they wouldn't be able to do that with. my family or friends, that meant getting. at people in the workplace to be their mouthpieces and do their dirty. work for them. They supplied my employers in Oxford with. details from what was going on in my private life, and what I. and other people had said at my home and accommodation in Oxford.. So people at work repeated verbatim words which had been said. in my home, and repeated what I'd been doing recently. Often the most trivial things, the ones from your domestic. life, are the ones which hurt most. One manager in particular. at Oxford continuously abused me for ten months with verbal sexual abuse, swearing,. and threats to terminate my employment. After ten months I was forced. to seek psychiatric help and start. taking medication, and was away from work for two months. I spoke later with a solicitor about what had happened at that. company; he advised it. was only possible to take action if you had left the company as a result of harassment, and such an. action would have to be started very soon after leaving. Over a year later the. same manager picked on another new worker, with even more serious results; that employee tried to commit suicide with. an overdose as a result of the. ill-treatment, and was forced to leave his job. But he didn't take action against the company,. either. Abuse at work is comparable to that. elsewhere in that tangible evidence is difficult to produce, and the abusers will always have their denials ready. when challenged. And even if a court accepts. what you say happened, it still remains to prove that abuse causes the type of breakdown I had at the. end of 1992. In. a recent case before a British court, a former member of the Army brought a case against others. who had maltreated him ten years previously. Although the court accepted that abuse had occurred,. it did not agree that depressive illness necessarily. followed, and denied justice to the. plaintiff. 3525 === Subject: basic algebra Any good websites for basic algebra? === Subject: Re: Question about pi >Not too long ago I heard that someone had come up with a method for >determining the Nth digit of pi, so that if I asked for the 3,240,077,555th >digit, there is a formula that could somehow determine what that digit would >be without actually iterating pi. > On the computation of the n'th decimal digit of various transcendental numbers. by Simon Plouffe November 30, 1996 > Is this true? If it is true, how is it >possible? The observation is that a fraction 1/(a*b) can be split into k1/a + k2/b by using the continued fraction algorithm of a/b. Here a and b are two prime powers. This is equivalent to having to solve a diophantine equation for k1 and k2 - it is always possible to do so if (a,b) = 1 , see [HW] if they have no common factor. If we have more than 2 prime factors then it can bedone by doing 2 at the time and then using the result to combine with the third element. This way an arbitrary big integer M can be split into small elements. If we impose the conditions on M of having only small factors (meaning that the biggest prime power size is of the order of a computer word), then an arbitrary M can be represented. If this is true then a number of known series and numbers can then be evaluated. For example the expression 1/C(2*n,n), the central binomials satisfies that : the prime powers of this number are small when n is big. and: Finally, it is interesting to observe that we can then compute Pi to the 10000'th digit without having to store (hardly) any array or matrix, so it can be computed using a small pocket calculator. We also note that, in some way we have a way to produce the digits of Pi without using memory, this means that the number is compressible , if we consider that we could use the algorithm to produce a few thousands digits of the number. We think that other numbers are yet to come and that there is a possibility (?) of having a direct formula for the n'th digit (in any base) of a naturally occuring constant like log(2). Plouffe's posting to sci.math.symbolic outlining Bailey and Borwein's contributions to the BBP algorithm is at: === Subject: Re: Question about pi > Not too long ago I heard that someone had come up with a method for > determining the Nth digit of pi, so that if I asked for the > 3,240,077,555th digit, there is a formula that could somehow determine > what that digit would be without actually iterating pi. Is this true? > If it is true, how is it possible? > > Intuitively the answer must be no. Sorry, but your intuition has failed. There are a number of formulas, the most well known beinghte BBP > formula, > for determining a specific digit in pi. AFAIK all report a value in some > power of two ---- BBP reports in jex. Breifly, these ormulas compute pi as an infinite sum, and by choosing > which > term you want to start with yo ignore all previous digits. > However that term is meaningless without the terms before it ,you cannot > get the nth digit because it depends on the value of previous terms. No, it doesn;t > I don't fail. Miserably > For example > > the term you calulate = 0.000000000000003342493370000002300 > So what is the 19th digit?????? > > Bad math. BBP and the like are a class called spigot algorithms, algorthms that > compute single digits without reliance on previous diigits int he number, > useful in mumerical analysis and related fields > http://mathworld.wolfram.com/SpigotAlgorithm.html The BBP formula is here > http://en.wikipedia.org/wiki/Bailey-Borwein-Plouffe_formula along with an axplanation of how it works. No it admits it is akin to partially doing a long multiplication and adding up some of the colums and hoping there are no carries to affect the result (pretty unlikely IMO). Might as well pick the number out of a hat. Larry > Larry > Nice idea though. > I mean it is probaly done through calculus or the sum of a series or > whatever. > You will be adding all the bits togeather in the end to get the > answer/aproximation. > The size of the 'bigger lumps' (terms) will affect the overall answer > so > with out > them you cannot get the answer. > It proably help to forget about maths and number bases etc......they > are > just a method > to represent the size of those lumps. You might know the method but you > won't > know the size so you are undone. > This lesson was brought to you by the letters P and I. > You might be able to calculate the value using some fancy maths > but that is only because you have made a mistake :O) > > LTC <------- Knows it all. > > === Subject: Request posting-account=cTF5XwoAAACZy28SDMLmdhDOZPTNanBC CLR 1.1.4322; MEGAUPLOAD 2.0),gzip(gfe),gzip(gfe) Could you send me Solutions manual of Concepts of Modern Physics by === Subject: Re: Request > Could you send me Solutions manual of Concepts of Modern Physics by > Hell no. Here's my request. Quit bothering us for the answers to all of your problems. Grow up, be a student, study, learn and solve your own problems. You are your own best solution manual. === Subject: Re: Solution manual of textbooks in ebook format! Get it in hours! <74b83bbfc90ff842428611fda224ba43@localhost.talkabouteducation.com> posting-account=cTF5XwoAAACZy28SDMLmdhDOZPTNanBC CLR 1.1.4322; MEGAUPLOAD 2.0),gzip(gfe),gzip(gfe) Could you send me Solution manual of Concepts of modern physics by Arthur Beiser ?(6th edition if available) === Subject: Probability: Weighted Mean (or Expected Value) Expected Value of a Discrete Random Variable 100 investment managers asked about their short-term investment outlook in which they respond 5% were very bullish, 30% were bullish, 40% were neutral, 5% were bearish, and 20% were very bearish. Let x represents the random variable of optimism level. Let x = 5 for very bullish and let x = 1 for very bearish. Compute the expected value. E(x) = (5)(0.05) + (4)(0.30) + (3)(0.40) + (2)(0.05) + (1)(0.20) = 2.95 Let x = 1 for very bullish and let x = 5 for very bearish. Compute the expected value. E(x) = (1)(0.05) + (2)(0.30) + (3)(0.40) + (4)(0.05) + (5)(0.20) = 3.05 __________________________________________________________ The second part of the question, I made it up by rearranging the random variable settings. It was not asked in the question. This is the conclusion I came up with. But I need to verify it especially the subjective word used in this context. Expected values differs because setting x = 5 for very bullish and x = 1 for very bearish is subjective. On the other hand, we could have set x = 1 for very bullish and x = 5 for very bearish, but it still be subjective. - Do you agree with the above comment? Please explain. - Do you agree that weighted mean can be subjective? Variance and standard deviation are different when the expected value changes. - How can we make such statistical inference when the standard deviation and variance are different despite having the same raw data? Explain. I stumbled upon this reality when I first encountered the question. When I was reading previous chapters, even though it wasn't clearly stated, it said weights are the level of importance / priority. It did not say clearly if it was subjective or not. I basically want to know besides the other questions if Weighted Mean is subjective? That is, if Weighted Mean depends on each individual's opionion of weight. === Subject: Re: Probability: Weighted Mean (or Expected Value) > Expected Value of a Discrete Random Variable 100 investment managers asked about their short-term investment outlook in which they respond 5% were very bullish, 30% were bullish, 40% were neutral, 5% were bearish, and 20% were very bearish. Let x represents the random variable of optimism level. Let x = 5 for very bullish and let x = 1 for very bearish. Compute the expected value. E(x) = (5)(0.05) + (4)(0.30) + (3)(0.40) + (2)(0.05) + (1)(0.20) = 2.95 Let x = 1 for very bullish and let x = 5 for very bearish. Compute the expected value. E(x) = (1)(0.05) + (2)(0.30) + (3)(0.40) + (4)(0.05) + (5)(0.20) = 3.05 > __________________________________________________________ The second part of the question, I made it up by rearranging the random variable settings. It was not asked in the question. This is the conclusion I came up with. But I need to verify it especially the subjective word used in this context. Expected values differs because setting x = 5 for very bullish and x = 1 for very bearish is subjective. On the other hand, we could have set x = 1 for very bullish and x = 5 for very bearish, but it still be subjective. > - Do you agree with the above comment? Please explain. > - Do you agree that weighted mean can be subjective? Variance and standard deviation are different when the expected value changes. > - How can we make such statistical inference when the standard deviation and variance are different despite having the same raw data? Explain. I stumbled upon this reality when I first encountered the question. When I was reading previous chapters, even though it wasn't clearly stated, it said weights are the level of importance / priority. It did not say clearly if it was subjective or not. I basically want to know besides the other questions if Weighted Mean is subjective? That is, if Weighted Mean depends on each individual's opionion of weight. > Yes very much it depends on how you view the weights (mathematically referred to as the measure). If you are playing with risk measures (as they do in finance or calculating horse racing odds) you have it the wrong way round it is the 5%, 30% 40%, 5% and 40% that changes depending on how you look at things. eg how you measure the weights you give to each value. === Subject: Re: The Halting Problem Oracle posting-account=n4TzyQkAAADLWxrRHqyiUZ-1SZdOB4vv Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > I would like to have a comment on this one: A computer runs a loop checking the decimal form of pi for a zero cipher. When it finds a zero, it starts the next loop looking for two consecutive zeroes. So it always increases the number of consecutive zeroes by one, once it has found a number of them. Will this computer come to a stop, considering ( from us, not the computer) that pi is not rational? since it is always searching for some run of zeros. If you are asking whether the decimal representation of pi has > arbitrarily long runs of zeros, then AFAIK this question is still open. > Informed opinion is that the decimal representation of pi does have > arbitrarily long runs of zeros. > The number of zeroes is either a natural number, thus finite, or of the cardinality of the set of naturals, infinite. What is an arbitrarily long number? It is a number from the naturals, greater than a given one, let's say greater one. But not a specific one. So we might be taking to Your expression an arbitrary long run of zeroes. This is not finite or infinite, but what is it in math? In Your setting of the problem, there is a difference between the program and the output, between the algorithm and the values it delivers. Now hackers and these Daedalus-programmers know, that You can feed the output into a change of the memory cells, where the program is stored. So an algorithm in a computer can change itself. With this feature, there might be a program, which will come to a halt. Or is there too much phantasy in my reasoning? With friendly greetings Hero === Subject: Re: The Halting Problem Oracle Phil Carmody a .8ecrit : > The halting problem was the first decision problem shown to be > undecidable by any algorithm. It can be stated as follows: > Given a description of a program and a finite input, decide whether > the program finishes running or will run forever, given that input. > Alan Turing proved that the halting problem is undecidable in 1936 > using a bit of Logistic Judo. He showed that if there was an algorithm > A that solves the halting problem, then one could use A to construct > an algorithm B such that B halts if and only if B does *not* halt! > This is the first example of an undecidable problem presented in most > textbooks on computability theory. Since many students are surprised > to learn that there are problems that cannot be solved by any > algorithm, introductory texts often make the point that an algorithmic > solution to the halting problem would be just too good to be > true. Such an algorithm could automatically solve nearly any > Mathematical problem. Before Wiles proved Fermat's Last Theorem, it > was frequently pointed out that the FLT could be viewed as an instance > possible integers x>0, y>0, z>0, and n>2 and halts when x^n + y^n = > z^n; clearly this program halts if and only if FLT is false. But even > after FLT was proved, there were no shortage of open Mathematical > problems that could be reduced to an instance of the halting problem: > Waring's conjecture, Goldbach's conjecture, the twin primes > conjecture, the existence of an odd perfect number, etc. > Just for fun, assume that there exists an Oracle that can give you the > solution to as many as 3 instances halting problems. Which problems > would you choose? > I'm not sure what my third choice would be, but I think the Riemann > hypothesis is so important that my first two choices would be the > Riemann hypothesis and the generalized Riemann hypothesis, restated as > halting problems. My choice would be your 'B' above :-) Doesn't work : it is not possible to construct B given an oracle, but only given an universal algorithm A. > That should teach the oracle to be such a smartarse. Phil === Subject: Re: The Halting Problem Oracle posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG > I would like to have a comment on this one: > A computer runs a loop checking the decimal form of pi for a zero > cipher. When it finds a zero, it starts the next loop looking for two > consecutive zeroes. So it always increases the number of consecutive > zeroes by one, once it has found a number of them. Will this computer > come to a stop, considering ( from us, not the computer) that pi is > not rational? since it is always searching for some run of zeros. If you are asking whether the decimal representation of pi has > arbitrarily long runs of zeros, then AFAIK this question is still open. > Informed opinion is that the decimal representation of pi does have > arbitrarily long runs of zeros. Making it a conjecture that there is a maximal run of zeroes somewhere in the decimal expansion of pi? If pi is normal, wouldn't a run of m consecutive digits be present with probability P(m) = P(m-1)/10, so that longer and longer runs approach (but never reach) a probability of zero? (But, as you say, the searching algorithm would never find out for us if that is true.) === Subject: Re: The Halting Problem Oracle posting-account=n4TzyQkAAADLWxrRHqyiUZ-1SZdOB4vv Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Drizzle, Drazzle, Drozzle, Drome, > Time for this one to come home! > - Mr. Wizard from Tooter Turtle Can You give a comment on this too, please? I post to a lot of animation newsgroups. A lot of my fellow animation > fans are amused by my connection of a baby boomer kid's cartoon Tooter > Turtle with a more contemporary adult Anime series. I must concede that > this signature is not appropriate for math groups. My apologies for any > confusion this might have caused. > Is this confusion? You do not have to apologize, anyhow. My computer had a Mr.Wizard, a reset buttom. And once i have done a machine code, i built in every loop a request for a memory cell with the obligation to jump out of the loop, if the memory cell contained a one. So with One Laptop Per Child one can build in some kind of a switch, so when the child says > Drizzle, Drazzle, Drozzle, Drome, > Time for this one to come home! it will stop the running process and goes back to start. With friendly greetings Hero === === Subject: Re: Product of orders of generators of a finite group Reply-to: weu_rznvy-hfrarg@lnubb.pbz.invalid On 20-Nov-2007, magidin@math.berkeley.edu (Arturo Magidin) > Hi all, I have a question about finite groups: is it true or false that, for each finite group G, there is some set {g_1,...,g_n} of generators of G such that the order of G is the product of the orders of the g_i's? I wanted to follow up on this... Let G be a finite group. Let us say that a generating set for G is > order pefect if the product of the orders of the elements of the set > is equal to the order of G, order abundant if it is greater, and > order deficient if it is less than. Let us say G is > generator-order-perfect if it has an order perfect generating set. I noted that Q_8 has the property that every generating set is order > abundant. Abelian groups and finite regular nilpotent groups are generator order > perfect. As Jack said, if each p-Sylow subgroup of G is generator order > perfect, then G itself is generator order perfect. Also: If G = A x B, and gcd(|A|,|B|)=1, then G is generator order > perfect if and only if each of A and B is generator order perfect. To > see this, note that every element (a,b) in a generating set for G can > be replaced with two elements (a,e) and (e,b), with > |(a,b)|=|(a,e)||(e,b)|. As a consequence, we have that for a finite nilpotent group G, G is > generator order perfect if and only if its p-Sylow subgroups are > generator order perfect. I am wondering if we can extend this to solvable groups. Suppose G = > AB, with A and B subgroups, gcd(|A|,|B|)=1. If each of A and B is > generator order perfect, than G is generator order perfect. Does the > converse hold? No. Consider Q_8 extended upward by its outer automorphism of order 3, i.e., the semidirect product G = Q_8 x| C_3, of order 24, with presentation . G satisfies your criteria with A = ~= Q_8 and B = ~= C_3, and is generator order perfect since it's generated by any two elements of orders 4 and 6, say, G = . But as you point out above, A ~= Q_8 isn't generator order perfect. > (If it does, then Hall's Theorem allows us to extend the p-Sylow > subgroup result to all solvable groups: suppose that G is a minimal > solvable counterexample; it cannot be a p-group, so |G| is divisible > by at least two primes, p and q. If |G| = p^a*m with gcd(m,p)=1, and A > is a p-Sylow subgroup, then by Hall's Theorem there is a subgroup B of > order m, and AB = G; then both A and B would be generator order > perfect by the conjectured result, hence all q-Sylow subgroups of B > would be generator order perfect since G is a minimal counterexample, > but all such are q-Sylow subgroups of B, and A is the p-Sylow subgroup > and also generator order perfect by the conjectured converse). Some non-solvable groups have the property: S_5 is generated by > (1,2,3,4,5) and (1,2). The product of the orders is 10, and we add > two other element of order 2 and one of order 3 to get a (superfluous) > order perfect generating set. Or just A_5, generated by any two elements of orders 3 and 5. Then, following your prescription, add any two (superfluous) elements of order 2 to the generating set. -- Jim Heckman === Subject: Re: Product of orders of generators of a finite group days. My association with the Department is that of an alumnus. On 20-Nov-2007, magidin@math.berkeley.edu (Arturo Magidin) [...] > I am wondering if we can extend this to solvable groups. Suppose G = > AB, with A and B subgroups, gcd(|A|,|B|)=1. If each of A and B is > generator order perfect, than G is generator order perfect. Does the > converse hold? No. Consider Q_8 extended upward by its outer automorphism of >order 3, i.e., the semidirect product G = Q_8 x| C_3, of order 24, >with presentation z^3 = 1, zxz^{-1} = y, zyz^{-1} = xy>. G satisfies your criteria >with A = ~= Q_8 and B = ~= C_3, and is generator order >perfect since it's generated by any two elements of orders 4 and 6, >say, G = . But as you point out above, A ~= Q_8 isn't >generator order perfect. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: #346 MathWorld's silly definition of P-adic and less flexible than even Wikipedia ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) Some of my posts are out of number for I seem to have bypassed #244, but no harm done, for it is only an aid to retrieval. I an earlier post today I mentioned the clouded definition of MathWorld's P-adic definition: and here they are: --- quoting MathWorld definitions on P-adic number and P-adic integer --- p-adic Number A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called p-adic metric. Any nonzero rational number x can be represented by x==(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. Then define the p-adic norm of x by |x|_p==p^(-a). (2) Also define the p-adic norm |0|_p==0. (3) The p-adics were probably first introduced by Hensel (1897) in a paper which was concerned with the development of algebraic numbers in power series. p-adic p-adic Integer A p-adic integer is a p-adic number of the form sum_(k==m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. Equivalently, a p-adic integer is an element of the inverse limit of the rings Z/p^kZ for k>=0. The same ring is obtained by taking the a_k to be any rationals with denominator coprime to p. --- end quoting MathWorld --- It should be obvious to anyone reading my textbook that I can teach a bright six year old with his helping parents what an Infinite Integer is because all of them can grasp All Possible Digit Arrangements and all of them can grasp an infinite string whether leftward or whether rightward. And all of them can grasp multiplying or dividing or adding or subtracting Infinite Integers so long as they know how to multiply and divide and add and subtract with Reals. But at what level of education would one have to have in order to even grasp what a P-adic is from reading MathWorld. I would dare say that only one who already knows and has used p-adics does the MathWorld definition make any sense. Also, it is funny and hilarous to me that Wikipedia is more flexible in correcting their mistakes than is MathWorld for that Wikipedia has now a valid Euclid Infinitude of Primes proof whereas MathWorld still has a muddleheaded and phony spiel and invalid Euclid Infinitude of Primes. The editors of MathWorld do not get it. They do not get it that there are two methods to proving IP where one is Direct and the other is Indirect and where MathWorld mixes the two and fobbs that mixture off as a valid proof when it is a sham. Maybe the editors of MathWorld never read the posts of Archimedes Plutonium, but they should, for the eggs are in their faces. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #347 does our education system still have room to teach us how to properly type ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) > Some of my posts are out of number for I seem to have bypassed #244, > but no harm done, for it is > only an aid to retrieval. > What can I say for my brain when I make a mistake in the process of trying to correct an earlier mistake. That should read above as #344 not #244. Is it a harbinger of Alzheimers? Or is it typing too fast? Also, I want to comment on education that the finest schools in the country can afford to teach young people how to properly type and the rest of the schools leave people to hen peck typing. Some may say that proper typing is a matter of speed for hen peckers can never catch up but there is another facet between hen peckers (those that use one finger on each hand rather than all ten fingers.) There is the etiquette that hen peckers are loud and some people just cannot bear being around hen pecker typers for the noise. So I think the best schools in the land still teach young people the proper way to type even though typewriters are no longer with us but the keyboard is still with us. And I found out the reasoning behind where the letters were placed on the keyboard because typing with 10 fingers became so fast that the mechanics of the keyboard would jam up so they made the a e i o and u in rather hard to reach places because if they had streamlined the keyboard with allowing the ten fingers of maximum speed, well, the a e i o u would have been situated to increase speed and not decrease the speed for mechanical reasons. I happened to have been fortunate in going to one of the best High Schools in the country of Wyoming High where typing was taught and where I did not make a nuisance of myself by loud noises in typing that would drive away people around me. And a great education should sometimes be of a sort that includes doing something that is the most proficient way of doing it, such as using all ten fingers to type rather than these hen peckers. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #348 position the letters to maximize speed in typing ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) There is another advantage and a major advantage to proper typing is that I can actually read a book and type in what I am reading with the proper way to type rather than the hen-peckers who have to interrupt their eyes in reading and hen peck their typing. So proper typing allows one to do two things simultaneously whereas hen-peckers can only do one thing. And it will be interesting to see if the keyboard remains during advances in technology of the computer. I cannot envision a total elimination of the keyboard. What I do envision is that since typewriters are no longer culturally significant that we revise the positioning of the letters of the alphabet since electronics no longer jams up the keys, that we position the letters to maximize speed in typing. I suppose the e and a and i o u would be positioned closer to the index finger and where the e and i o u are not above the fingers in a different row but in the same row as the a s d f j k l. I would bet someone already figured out the maximum speed positioning of the letters of the alphabet, and should make them available to the marketplace for people who want to use a keyboard that allows for greater speed in typing. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #349 World's smallest nonzero Real Number 1 x 10^(-)999...9998 ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) I did not spend much time discussing the ramifications of AP-adics to the Reals and I should spend some time doing that. Notice that in the Infinite Integers there is a largest one which is 999....99999 and when people speak of infinity, they can substitute this number for infinity itself. And in decimal notation it is 9 x 10^999...999998 + 9 x 10^9999....99997 + .... + And since both Reals and AP-adics are All Possible Digit Arrangements for infinite strings rightward and infinite strings leftward respectively, that the Reals should have a symmetrical opposite of 9999....99999 and it happens to be 0.0000.....0000010 where the 1 digit is in the 10^(-)999...9998 place value. So now what happens when we add this world's smallest nonzero number to that of 0.9999...9999 and to 1.0000.....000000 since 0.9999.... = 1.0000.... So we have 1.0000.....000000 where the rightmost 0 is in the 10^9999...9999 place value +.0000.....000010 where the 1 digit is in the 10^999....99998 place value which gives us 1.000....00010 And we have 0.9999.....999999 where the rightmost 9 is in the 10^9999....9999 place value +.0000.....000010 where the 1 digit is in the 10^9999...9998 place value which gives us 1.0000....000009 where the 9 is in the 10^9999....99999 place value and we have 1.0000.....000010 = 1.0000....000009 So we have agreement. And thus the world's smallest nonzero number possible is 1 x 10^(-)9999....99998 Now some may ask well what about 1 x 10(-)9999....99999 or 2 x 10^(-)999...9999 or 3 or 4 or 5 or 6 or 7 or 8 or 9. And we look back to the world's largest integer of 999....999999 and since it cannot be 9 x 10^999....999 for that would be beyond the South Pole point of imaginary pi. Now one begins to question the definition of P-adics such as 10-adics that we know 3 x ....33333 in 10-adics is .....999999 but why should 1 +....9999 in 10-adics be 0 for it should be 1 with the carryover. What I suspect is that Frontview concept is so new that the old mathematics has not even understood the shortcomings of their old definitions on P-adics. Now does it make sense that the world should have a smallest nonzero number? Of course it does, since the world has a smallest number in 0 itself, then it is reasonable to suspect the next smallest number. and the world's third smallest number is then of course 2 x 10^(-)999...9998 Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #351 World's smallest nonzero positive Real Number 1 x 10^(-)999...9998 and Continuity on Reals ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) > I did not spend much time discussing the ramifications of AP-adics to > the Reals and I should spend > some time doing that. Notice that in the Infinite Integers there is a > largest one which is > 999....99999 and when people speak of infinity, they can substitute > this number for infinity itself. > And in decimal notation it is 9 x 10^999...999998 + 9 x > 10^9999....99997 + .... + And since both Reals and AP-adics are All Possible Digit Arrangements > for infinite strings rightward > and infinite strings leftward respectively, that the Reals should have > a symmetrical opposite of > 9999....99999 and it happens to be 0.0000.....0000010 where the 1 > digit is in the 10^(-)999...9998 > place value. So now what happens when we add this world's smallest nonzero number > to that of 0.9999...9999 > and to 1.0000.....000000 since 0.9999.... = 1.0000.... So we have > 1.0000.....000000 where the rightmost 0 is in the 10^9999...9999 > place value > +.0000.....000010 where the 1 digit is in the 10^999....99998 place > value > which gives us 1.000....00010 And we have > 0.9999.....999999 where the rightmost 9 is in the 10^9999....9999 > place value > +.0000.....000010 where the 1 digit is in the 10^9999...9998 place > value > which gives us 1.0000....000009 where the 9 is in the 10^9999....99999 > place value > and we have 1.0000.....000010 = 1.0000....000009 So we have agreement. And thus the world's smallest nonzero number > possible is > 1 x 10^(-)9999....99998 Now some may ask well what about 1 x 10(-)9999....99999 or 2 x > 10^(-)999...9999 > or 3 or 4 or 5 or 6 or 7 or 8 or 9. And we look back to the world's > largest integer > of 999....999999 and since it cannot be 9 x 10^999....999 for that > would be beyond the > South Pole point of imaginary pi. Now one begins to question the definition of P-adics such as 10-adics > that we know > 3 x ....33333 in 10-adics is .....999999 but why should 1 +....9999 in > 10-adics be > 0 for it should be 1 with the carryover. What I suspect is that > Frontview concept is so new > that the old mathematics has not even understood the shortcomings of > their old definitions > on P-adics. Now does it make sense that the world should have a smallest nonzero > number? Of course it does, > since the world has a smallest number in 0 itself, then it is > reasonable to suspect the next > smallest number. and the world's third smallest number is then of > course 2 x 10^(-)999...9998 > One small error of neglect in the above where it should read world's smallest nonzero POSITIVE Real Number Prior to these discoveries, mathematicians thought that between any two Real Numbers exist another Real Number and that prevented them from finding a world's smallest nonzero positive Real Number. Also I made a mistake in earlier posts that since betweenness on Reals is gone since there is no Real between that of 0.555555.....555555 and 0.55555...555554 that although betweenness is lost, does not imply continuity or continuum is lost. The Reals are still a dense set between any two consecutive integral- Real. So I think density implies continuity even though there is no longer betweenness. I believe the Reals are continuous because there are an infinity of Reals between integral consecutive Reals and this infinity supply forms continuity. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #353 lovers of P-adics have to clean up their house-- is 1+...9999 = 0 or equal to 1000...0000 ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) Alright then, we know the lovers of P-adics never had the concept of Frontview. For I discovered that new concept in 2007. And the Frontview concept puts questions and doubts as to the old school of P-adics. It asks why they believe 3 x ....3333 in 10-adics is ....999999 yet when they add 1 to ....99999 they arrive at an answer of 0 but with FrontView they should have an answer of 10000....000000 So is this just sloppy mathematics and sloppy logic and sloppy definitions on the part of old math? Another pitfall is when they have 3 x .....66666 in 10-adics where their old answer was ....88888 but with FrontView their answer should have been 18888....888888. So were the old math being sloppy and inconsistent and capricious? Where their answer is what they please it to be. They constantly say that ....99999 is equal to -1 but when you add 1 to -1 you should end up with 0 but when you add 1 to ....99999 you end up with 10000.....000000. So the old math really did not solve much with their P-adics and their sloppy capricious definitions, did they? I guess the theme of this post is that when math has new true concepts in their midsts such as FrontView that all of a sudden, alot of the old math is seen as decrepit and deficient and outright false. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #354 mistakes corrected, lovers of P-adics have to clean up their house-- is 1+...9999 = 0 or equal to 1000...0000 ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) > Alright then, we know the lovers of P-adics never had the concept of > Frontview. For I discovered > that new concept in 2007. And the Frontview concept puts questions and > doubts as to the old > school of P-adics. It asks why they believe 3 x ....3333 in 10-adics > is ....999999 yet when they > add 1 to ....99999 they arrive at an answer of 0 but with FrontView > they should have an answer > of 10000....000000 So is this just sloppy mathematics and sloppy logic and sloppy > definitions on the part of > old math? > correcting this paragraph Another pitfall is when they have 3 x .....66666 in 10-adics where their old answer was ....99998 but with FrontView their answer should have been 19999....99998. > So were the old math being sloppy and inconsistent and capricious? > Where their answer > is what they please it to be. They constantly say that ....99999 is > equal to -1 but when you > add 1 to -1 you should end up with 0 but when you add 1 to ....99999 > you end up with > 10000.....000000. So the old math really did not solve much with their P-adics and their > sloppy capricious > definitions, did they? I guess the theme of this post is that when math has new true concepts > in their midsts such as > FrontView that all of a sudden, alot of the old math is seen as > decrepit and deficient and outright > false. Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: Re: Differential equation (sort of) > I recently came across a function defined as the limit of a > recursively-defined sequence of functions. I was trying to find a > closed form for the limit, and I found that the limit function f(x) > satisfies an equation something like f'(x) = f(2x). Are there any > known techniques for dealing with an equation like this? Can anyone > point me to a book or some other reference that discusses problems > like this? I tried writing f as a power series, but ended up with a > contradiction, so it seems a non-zero solution to this equation cannot > be real-analytic. The Fabius function satisfies Fb'(x) = 2Fb(2x) . It is everywhere C^infinity, but nowhere real-analytic. So for your equation, use f(x) = Fb(x/2) , right? 029/1e57fc37d5202134?lnk=st&q=#1e57fc37d5202134> -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Differential equation (sort of) > I recently came across a function defined as the limit of a > recursively-defined sequence of functions. I was trying to find a > closed form for the limit, and I found that the limit function f(x) > satisfies an equation something like f'(x) = f(2x). Are there any > known techniques for dealing with an equation like this? Can anyone > point me to a book or some other reference that discusses problems > like this? I tried writing f as a power series, but ended up with a > contradiction, so it seems a non-zero solution to this equation cannot > be real-analytic. The Fabius function satisfies Fb'(x) = 2Fb(2x) . > It is everywhere C^infinity, but nowhere real-analytic. > So for your equation, use f(x) = Fb(x/2) , right? > Not sure about the source quoted in this reference!! http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=eu clid.rae/1184700035 Looks like it should be in another type of newsgroup. === Subject: Re: Galois group of a polynomial is cyclic ><20300506.1195759868120.JavaMail.jakarta@nitrogen.mathforum.org>, jane <25068525.1195753159031.JavaMail.jakarta@nitrogen.math > forum.org>, jane > Suppose i have a polynomial p(x) in Q[x], Q > -rationals of degree 5, which is irreducible, such that it's Galois group is cyclic. How can i prove that all the roots of p are real. Message was edited by: jane If it has a non-real root, then complex conjugation > is a non-identity > automorphism for the splitting field, so the Galois > group has an > element of order 2. The cyclic group of order 5 has > no element of > order 2. How do you know that the Galois group has order 5 ? He said it is cyclic. But why a cyclic group of order 5? Why not a cyclic group of order 20, say? I think that takes an ounce more reasoning ... Firstly, we know the order of G must be a multiple of 5 (since the degree of the irreducible polynomial is 5). If G = , represent g as a product of disjoint cycles in S_5. Since the order of g is a multiple of 5, g must be a 5-cycle, hence G is a cyclic group of order 5. quasi === Subject: Re: Galois group of a polynomial is cyclic ><20300506.1195759868120.JavaMail.jakarta@nitrogen.mathforum.org>, jane > <25068525.1195753159031.JavaMail.jakarta@nitrogen.math > forum.org>, jane > Suppose i have a polynomial p(x) in Q[x], Q > -rationals of degree 5, which is > irreducible, such that it's Galois group is cyclic. How can i prove that all the roots of p are real. Message was edited by: jane > If it has a non-real root, then complex conjugation > is a non-identity > automorphism for the splitting field, so the Galois > group has an > element of order 2. The cyclic group of order 5 has > no element of > order 2. How do you know that the Galois group has order 5 ? >He said it is cyclic. But why a cyclic group of order 5? Why not a cyclic group of order 20, >say? I think that takes an ounce more reasoning ... Firstly, we know the order of G must be a multiple of 5 (since the >degree of the irreducible polynomial is 5). If G = , represent g as a product of disjoint cycles in S_5. Since the order of g is a multiple of 5, g must be a 5-cycle, hence G >is a cyclic group of order 5. Alternatively, we know a galois group must be transitive. But a cyclic subgroup of S_n is never transitive unless the generator is a cycle. To see that, write the generator as a product of disjoint cycles. A power of that disjoint cycle can't map elements from one disjoint cycle into a different one, hence no transitivity (unless the generator is a cycle). quasi === Subject: Re: Galois group of a polynomial is cyclic <20300506.1195759868120.JavaMail.jakarta@nitrogen.mathforum.org>, jane <25068525.1195753159031.JavaMail.jakarta@nitrogen.math > forum.org>, jane Suppose i have a polynomial p(x) in Q[x], Q > -rationals of degree 5, which is > irreducible, such that it's Galois group is cyclic. How can i prove that all the roots of p are real. Message was edited by: jane If it has a non-real root, then complex conjugation > is a non-identity > automorphism for the splitting field, so the Galois > group has an > element of order 2. The cyclic group of order 5 has > no element of > order 2. How do you know that the Galois group has order 5 ? He said it is cyclic. >But why a cyclic group of order 5? Why not a cyclic group of order 20, >say? >I think that takes an ounce more reasoning ... >Firstly, we know the order of G must be a multiple of 5 (since the >degree of the irreducible polynomial is 5). >If G = , represent g as a product of disjoint cycles in S_5. >Since the order of g is a multiple of 5, g must be a 5-cycle, hence G >is a cyclic group of order 5. Alternatively, we know a galois group must be transitive. But a cyclic subgroup of S_n is never transitive unless the generator >is a cycle. I meant n-cycle. >To see that, write the generator as a product of disjoint >cycles. A power of that disjoint cycle can't map elements from one >disjoint cycle into a different one, hence no transitivity (unless the >generator is a cycle). Again, I meant: unless the generator is an n-cycle. quasi === Subject: Re: Why real numbers and points can't model continuum posting-account=i1MELAoAAADwo_-GGwN3NKKSXm8aSdBN SV1),gzip(gfe),gzip(gfe) > mirage. We still did not link up the related sciences such as math and > physics in such a way that both have the same perspectives of the > nature and abstract spaces. > > Also, the modern advances in math, I think, are enough to give > approxiamtely correct results for practical applications, but not > logically or philosophically correct results that are needed to really > understand the nature. > > - venkat- Hide quoted text - > > - Show quoted text - > I tend to agree. Except wrt to the 'mirage' of the practical success of calculus. It's a real success. > But for instance, it's hard to accept the physical existence of point- like time extensions. But physical existence of abstractions like points is not what is > assumed when considering physics. Instead we consider properties of > things that exist as being represented by a mathematical model, which > reflects our measurements and observations. > Suppose a body A could exert a force on a body B during a point-like time extension t. But that is not what physical theories claim can occur. Of course not! That's what I'm saying. It would be a physical impossibility B's induced acceleration (v-v')/t would seemingly be infinite and, consequently, the force applied would also be so, which is nonsense. You're putting the cart before the horse. It's not that it's > nonsense; it's simply not what we observe happening in the physical > realm. Not just that. It would be a logical nonsense. > This is consistent with the philosophy that what is important is what > we /observe/ to occur, regardless of whether it /should/ or / > shouldn't/ occur according to our innate intuitions about space and > time. > Consider two bodies A and B approaching each other along a straight line with speed v and -v. Imagine a fly goes from A to B with speed 2v and from B to A with speed -2v until A and B collide. > Now, if you assume that the fly can stay on A or B for just a point- like extension of time... Well, it's an /idealized/ fly. We need only allow that there exists a > time t (not an extent (t..t')) such that the (idealized) fly is at A; > just as we allow that there is a time t before collision when the > (idealized) fly is at the midpoint between A and B. No. t must have duration. If it hadn't, the fly would live. , it's easy to show it will never be crushed and A and B will never collide: since the fly is more rapid than A and than B, neither body can follow the fly and reach the other body at the same time the fly does; so the fly will never be crushed. But this is just the paradox of Zeno's arrow, dressed up a bit. It is > resolved by the theory of limits: the (idealized) fly's position at > the time of collision is consistent with the limit of a sequence of > positions and times. I don't think so. Limit theory misses the point of the paradox. It can compute how long it will take for the bodies to crash but it does not show why the reasoning to the effect that no collision an happen is wong, and that's what we need from a logical point of view. > At each time t, we speak of the position of the (idealized) fly. It is > true that at no time t before collision that the (idealized) fly is > being crushed. It does not follow that at the time t_0 of collision, > the (idealized) fly is not crushed (i.e., coincident with both A and > B). If you suppose the fly consumes no time extension in bouncing on A and B, the model cannot account for the real fact that the fly gets crushed. If you assert that it is not reasonable to speak of the (idealized) > fly's position at each time t, then the paradox is not a paradox of > the real numbers or of physics, but instead is a result of your > adherence to this intuition. Your are observing is that if we accept your inuitions regarding > points and times, then Zeno's arrow does not reach its target and yet > it must reach the target. So the paradox suggests to me that your > intuition does not reflect physical reality very well, as we observe > it. Accepting point-like space and time units is what makes the arrow miss the target: in a point-like space unit it would stand still, provoking the paradox. Facts agree with my intuition that it can reach its target. The fact is that any /real/ fly has very little influence on whether A > and B collide (depending on the relative momenta of A, B, and the > fly); It's the reasoning, not the fly what has big momentum! > because there is no such thing as a real fly having the > idealized properties you describe. That's what I claim. And physics doesn't claim otherwise for /any/ things that have > physical existence. For example, suppose A and B are mirrors, and > the fly is a photon. Photons (unlike idealized flies or points) still > have momentum, and interactions such as reflection are always observed > to occur over some finite non-zero duration delta t (by the > uncertainty principle). So photons are always /observed/ as being > arbitrarily near A for some real duration, not at A for only a > point-like extent of time. These durations and momenta are small enough that they are often > ignored because their numerical impact on calculations is negligible; > but that is not the same as claiming they don't exist! Again what I claim! As fas as I can see, this all suggests the necessity of admitting non- null quantities that are less than any number... I don't see why. There is no apparent conflict between observed > reality and our physical models using the usual mathematics of the > reals: after all, Zeno's arrow /does/ actually reach the target, just > as we expect from the mathematical model. Subnumerical quantities may be required for the logical coherence of the mathematical analysis of the continuum: you can make the time the fly takes to bounce less than any number, but it should not become point-like, for the sake of coherence. > Nor do I see how adding infinitesimals resolves the issues: if you > still believe that we cannot speak of a position at a time, I think > you'll still have your Thompson's lamp problems. Well, yes. Really Thompson's is another problem, the problem of admitting a(n actual) physical ordinal infinity. === Subject: Re: Question bout SVD and eigenvalue decomposition > Hi everyone, I was playing around with Matloab and trying to understand SVD and > Eigenvalue decomposition. If the matrices are square and can have an eigen value decomposition, > are the SVD and eigenvalue decomposition producing the same results? No. If A is your matrix, the singular values are the square roots of the eigenvalues of AA^*. > Under what conditions would SVD and eigen value decomposition produce > different results? If A is positive semidefinite. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Question bout SVD and eigenvalue decomposition On 2007-11-22 16:09:00 -0500, Robert Israel said: Hi everyone, I was playing around with Matloab and trying to understand SVD and > Eigenvalue decomposition. If the matrices are square and can have an eigen value decomposition, > are the SVD and eigenvalue decomposition producing the same results? No. If A is your matrix, the singular values are the square roots of the > eigenvalues of AA^*. Under what conditions would SVD and eigen value decomposition produce > different results? If A is positive semidefinite. Huh? The OP asked when SVD and eigen-decomposition yield *different* results. I think you mean in the positive semidefinite case, they do yield the same result. Otherwise, they do not. And if the ground field is not algebraically-closed, you may not even have an eigen decomposition. -- -kira === Subject: Re: Question bout SVD and eigenvalue decomposition > On 2007-11-22 16:09:00 -0500, Robert Israel > said: > > Hi everyone, I was playing around with Matloab and trying to understand SVD and > Eigenvalue decomposition. If the matrices are square and can have an eigen value decomposition, > are the SVD and eigenvalue decomposition producing the same results? No. If A is your matrix, the singular values are the square roots of the eigenvalues of AA^*. > Under what conditions would SVD and eigen value decomposition produce > different results? If A is positive semidefinite. Huh? The OP asked when SVD and eigen-decomposition yield *different* > results. I think you mean in the positive semidefinite case, they do > yield the same result. Otherwise, they do not. Sorry, of course that's what I meant. > And if the ground field is not algebraically-closed, you may not even > have an eigen decomposition. > -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Question bout SVD and eigenvalue decomposition <2007112217365916807-kirakun@earthlinknet> posting-account=mYmveAoAAAA6m8p7tyKTuI-_Mp56JWnf Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > On 2007-11-22 16:09:00 -0500, Robert Israel > said: > Hi everyone, I was playing around with Matloab and trying to understand SVD and > Eigenvalue decomposition. If the matrices are square and can have an eigen value decomposition, > are the SVD and eigenvalue decomposition producing the same results? > No. If A is your matrix, the singular values are the square roots of the eigenvalues of AA^*. Under what conditions would SVD and eigen value decomposition produce > different results? > If A is positive semidefinite. Huh? The OP asked when SVD and eigen-decomposition yield *different* > results. I think you mean in the positive semidefinite case, they do > yield the same result. Otherwise, they do not. And if the ground field is not algebraically-closed, you may not even > have an eigen decomposition. -- -kira I for one agree with you. === Subject: Re: Question bout SVD and eigenvalue decomposition posting-account=D3FzDwoAAABdMDXitkUrPM9nBOvcbWaj Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) On Nov 22, 9:09 pm, Robert Israel Hi everyone, > I was playing around with Matloab and trying to understand SVD and Eigenvalue decomposition. > If the matrices are square and can have an eigen value decomposition, are the SVD and eigenvalue decomposition producing the same results? No. If A is your matrix, the singular values are the square roots of the > eigenvalues of AA^*. > Under what conditions would SVD and eigen value decomposition produce different results? If A is positive semidefinite. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada the eigenvalue decomposition and SVD produce the same result? Luca === Subject: Non-finitive SLAE solution posting-account=gEWROwoAAAC4fgIrtkB5utuwf46mmFU- SV1),gzip(gfe),gzip(gfe) i have to find a solutoin for a non-finitive SLAE. As far as i know, there is a method of reduction for such systems. Could you please provide me more information on that topic? Is there any kind of standart soluiotn? ( I don't want to write a program, just use the existiong framework). My SLAE look like the following one: (1): A(l, s) + summ(summ(A(p, j) * Z0(l, p, s, j), p=-inf .. +inf), j=1..N, j!=s) = c0(s) + summ(c(1) * W(n,s), n=-ing..+inf) (2): A(l, s) + summ(summ(A(p, j) * Z1(l, p, s, j), p=-inf .. +inf), j=1..N, j!=s) = c1(s) + W(s) A, W - variables, Z and C - koeficients, s=1..N (fixed apriori) Alexander Maystrenko === Subject: The missing dollar paradox Can't we describe the 'solution' to the missing dollar paradox as what Deep Throat told Woodward and Bernstein in 'All the President's Men' (for those of you old enuf to remember that :-) viz, Follow the money? I'm not sure it wouldn't be a 'spoiler' if I said what I mean, so I'll just leave it at that. Somebody might prefer a different approach. === Subject: Re: The missing dollar paradox > Can't we describe the 'solution' to the missing dollar paradox as what > Deep Throat told > Woodward and Bernstein in 'All the President's Men' (for those of you > old enuf to > remember that :-) viz, > Follow the money? > I'm not sure it wouldn't be a 'spoiler' if I said what I mean, so I'll > just leave it at that. > Somebody might prefer a different approach. Why is it that no one ever asks about the found dollar paradox? Two guys check into a hotel and pay $30 for the room. The desk man decides to refund $5, which he gives to the bellhop. The bellhop keeps $3 for himself and gives $2 to the two men. So the men wound up paying $14 apiece for the room, and the bellhop kept $3, making a total of $31. Where did the other dollar come from? Obviously, it's the same dollar that went missing in the first puzzle. Problem solved. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === Subject: Re: The missing dollar paradox On 2007-11-22 17:46:01 -0500, Dave Seaman said: > Can't we describe the 'solution' to the missing dollar paradox as what > Deep Throat told > Woodward and Bernstein in 'All the President's Men' (for those of you > old enuf to > remember that :-) viz, Follow the money? I'm not sure it wouldn't be a 'spoiler' if I said what I mean, so I'll > just leave it at that. > Somebody might prefer a different approach. Why is it that no one ever asks about the found dollar paradox? Two guys check into a hotel and pay $30 for the room. The desk man > decides to refund $5, which he gives to the bellhop. The bellhop keeps > $3 for himself and gives $2 to the two men. So the men wound up paying > $14 apiece for the room, and the bellhop kept $3, making a total of $31. Where did the other dollar come from? Obviously, it's the same dollar > that went missing in the first puzzle. Problem solved. These paradoxes are great because of the way they lead you down the wrong path. If you apply 'follow the money' as greek_candy_man did above, then the $30 ends up: $25 w/ the desk man, $3 to the bellhop, and $2 back to the guys renting the room. So there's no extra $. However if you insist on attempting to disentangle the puzzle from the point of view of the puzzle: for example, the $14 each went to pay for the room AND the bellhop, since the room only cost $25. In other words, $28 actually ended up in different hands. I was originally going to say a dollar was counted twice, but actually $3 ends up getting counted twice. That sound right? That's a clever variant of the original! === Subject: Re: The missing dollar paradox posting-account=u8_ddgoAAADEnjcEJ4lflyn5ygFN0Cdb SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.590),gzip(gfe),gzip(gfe) what missing money? there was $25 in the bill, $2 in the waiters pocket, and $3 given back to the ladies. That's $30! Nothing missing! Jay's World http://jaysmoney.blogspot.com === Subject: Re: The missing dollar paradox On 2007-11-22 17:07:37 -0500, greek_candy_man@yahoo.com said: > what missing money? there was $25 in the bill, $2 in the waiters > pocket, and $3 given back to the ladies. That's $30! Nothing missing! > Jay's World service---assuming the customer in service does not allow a friend to > cut in). We have X(t+1) = -1 + X(t) + sum{Y_i,i=1..X(t)}, where the > Y_i are iid Bernoulli random variables, with P{Y_i = 0} = q (= 0.95) > and P{Y_i = 1} = p (= 0.05). (Note: if X(t) = 0 the sum is 0 by > definition. This well lead to a correct evaluation later on.) Letting > M_t(z) denote the mgf of X(t), so M_t(z) = > sum{z^k*P{X(t)=k},k=0..infinity}, we can get a recursion for the M_t > as follows: M_{t+1}(z) = sum{P{X(t)=k}*z^(k-1) * (q + p*z)^k, > k=0..infinity} = M_t(qz+pz^2)/z. I think you want to drop the z^(-1) term, so make it M_{t+1}(z) = (M_t(qz+pz^2) - M_t(0))/z. The probability that you're still in the queue (either waiting or being served) at time t is then M_t(1). -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Queue waiting times posting-account=zKSjoQoAAAC5wIsHKdIzIXzOHEFPgaXy Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) On Nov 22, 1:42 pm, Robert Israel > Imagine you're waiting in a long queue of people. For each minute, > there is a 5% chance that any given person in the queue will spot > someone they know and let them cut in line. At the front of the > queue, each person takes a minute to get served their pierogies (you > can tell I thought this up while waiting in an interminable queue at a > local Polish festival). What is the average wait time based on a > person's current position in the queue? > > It would seem to me that beyond the 20th position in line, the wait > time would start to average infinity, as the odds are that someone in > front of you will let someone cut in line each minute, and so your > wait will be getting longer and longer instead of shorter. Not only > that, your position will be accelerating backwards -- the more people > you have in front of you, the more places you will move back each > minute. But it's hard to imagine a formula based on line position > that would suddenly jump to infinity. Does it make more sense to ask, > what are the odds that a person at position n in the queue will EVER > get served? > > --Mark > Suppose X(t) is the number in front of you (excluding the customer in service---assuming the customer in service does not allow a friend to cut in). We have X(t+1) = -1 + X(t) + sum{Y_i,i=1..X(t)}, where the Y_i are iid Bernoulli random variables, with P{Y_i = 0} = q (= 0.95) and P{Y_i = 1} = p (= 0.05). (Note: if X(t) = 0 the sum is 0 by definition. This well lead to a correct evaluation later on.) Letting M_t(z) denote the mgf of X(t), so M_t(z) = sum{z^k*P{X(t)=k},k=0..infinity}, we can get a recursion for the M_t as follows: M_{t+1}(z) = sum{P{X(t)=k}*z^(k-1) * (q + p*z)^k, k=0..infinity} = M_t(qz+pz^2)/z. I think you want to drop the z^(-1) term, so make it > M_{t+1}(z) = (M_t(qz+pz^2) - M_t(0))/z. The probability that you're > still in the queue (either waiting or being served) at time t is then > M_t(1). RGV > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada === Subject: i ^ 1/2? Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or some other kind of thing? === Subject: Re: i ^ 1/2? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? It's a complex number, equal to (1 + i)/sqrt(2) (and of course the negative of that). There are two methods of solution: Method 1: First we expand (x + yi)^2: (x + yi)^2 = (x^2 - y^2) + (2xy)i. So we want to find x and y such that x^2 - y^2 = 0 (since i has no real part), and that 2xy = 1 (since 1i = i): x^2 - y^2 = 0 2xy = 1. We solve the first equation for x: x^2 = y^2, so x = sqrt(y^2) = |y|. Plugging that into the second yields 2|y|y = 1, or |2y^2| = 1.Since y^2 is always positive for all reals y, we can drop the absolute value signs. Then y^2 = 1/2, and so y = sqrt(1/2) = 1/sqrt(2). So x = |y| = 1/sqrt(2) also. Thus, sqrt(i) = x + yi = 1/sqrt(2) + i/sqrt(2) = (1 + i)/sqrt(2) (and, of course, (-1 - i)/sqrt(2)). Method 2: We express i in polar form, r cis(theta), where cis(theta) = cos(theta) + i sin(theta). One can prove using trigonometric identities that (r cis(theta))^2 = r^2 cis(2 theta). i equals 1 cis((2n + 1)pi), where n is any integer. For convenience, we'll let n = 0 (taking the smallest polar angle), so we get i = 1 cis(pi). Then we need to find r such that r^2 = 1 and theta such that 2 theta = pi. That's easy -- r = 1, theta = pi/2. So then sqrt(i) = r cis(theta) = 1 cis(pi/2) = cos(pi/2) + i sin(pi/2) = 1/sqrt(2) + i/sqrt(2) = (i + i)/sqrt(2) (and, of course, (-1 - i)/sqrt(2)), same as before. So there's your answer. === Subject: Re: i ^ 1/2? posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? The best way to imagine i^x is to multiply the angle pi/2 with x and find the point on the unit circle with that angle. But this throws me into another thought - Is angle a conversion medium between additive and multiplicative senses? How did it acquire this property? - venkat === Subject: Re: i ^ 1/2? > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? The best way to imagine i^x is to multiply the angle pi/2 with x and > find the point on the unit circle with that angle. But this throws me into another thought - Is angle a conversion medium > between additive and multiplicative senses? How did it acquire this > property? - venkat Yes. A formula for the angle z makes to the real axis, is to take the imaginary part of log(z). (And clearly this formula is only unique up to a multiple of 2pi.) But log converts times to adds. === Subject: Re: i ^ 1/2? posting-account=eZZyEAoAAAADi5VPqB_NKqDpg4Q2X8NP VendorID/125,gzip(gfe),gzip(gfe) > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? I always thought that the coolest thing about i was that once you've defined it, you never, ever need any 'other kind of thing' for all your polynomial challenges. === Subject: Re: i ^ 1/2? >Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or >some other kind of >thing? See , section 2 (polar form), and also The two square roots of i are sqrt(2)/2 (1 + i) and -sqrt(2)/2 (1 + i) === Subject: Re: i ^ 1/2? > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? > More generally, any polynomial with coefficients from the complex numbers has a root in the complex numbers. === Subject: Re: i ^ 1/2? On 2007-11-22 18:07:08 -0500, Stephen Montgomery-Smith said: > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? > More generally, any polynomial with coefficients from the complex > numbers has a root in the complex numbers. Ah. I think this is what I was asking in a post that doesn't seem to have appeared yet. Actually not quite what I was asking. I was asking where the coefficients can be roots for closure to apply. As you'll see when my post ever appears. I'm using Unison on a MAC. === Subject: Re: i ^ 1/2? > On 2007-11-22 18:07:08 -0500, Stephen Montgomery-Smith > said: Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, > or some other kind of > thing? > More generally, any polynomial with coefficients from the complex > numbers has a root in the complex numbers. Ah. I think this is what I was asking in a post that doesn't seem to > have appeared yet. > Actually not quite what I was asking. I was asking where the > coefficients can be roots > for closure to apply. As you'll see when my post ever appears. I'm using > Unison on > a MAC. > Many years ago I also was fascinated by the question of what was i ^ 1/2. So enjoy yourself. I went on to find a general formula for the square root of any complex number, only to find out that my formula was on page 2 or so of a book by Ahlfors. And then, when I went to college, and found out the fundamental theorem of algebra, I realized that this was, in a sense, the whole point of complex numbers! (Actually I learned the fundamental theorem a few years earlier - I happened to see some Christmas Lectures by Prof Zeeman on the T.V., and he even presented a proof. This was probably 30 years ago.) There are extensions of complex numbers - the quarternians, and the octonians, but their need doesn't arise out of looking for roots of polynomials. === Subject: Re: i ^ 1/2? <2007112218252711272-kquirici@yahoocom> posting-account=Gg91ZwkAAAARyqtmT5dB5plbBnobCndP rv:1.8.1.9) Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) On Nov 22, 7:47 pm, Stephen Montgomery-Smith On 2007-11-22 18:07:08 -0500, Stephen Montgomery-Smith said: > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, > or some other kind of > thing? More generally, any polynomial with coefficients from the complex > numbers has a root in the complex numbers. > Ah. I think this is what I was asking in a post that doesn't seem to have appeared yet. Actually not quite what I was asking. I was asking where the coefficients can be roots for closure to apply. As you'll see when my post ever appears. I'm using Unison on a MAC. Many years ago I also was fascinated by the question of what was i ^ > 1/2. So enjoy yourself. I went on to find a general formula for the > square root of any complex number, only to find out that my formula was > on page 2 or so of a book by Ahlfors. And then, when I went to college, > and found out the fundamental theorem of algebra, I realized that this > was, in a sense, the whole point of complex numbers! (Actually I > learned the fundamental theorem a few years earlier - I happened to see > some Christmas Lectures by Prof Zeeman on the T.V., and he even > presented a proof. This was probably 30 years ago.) There are extensions of complex numbers - the quarternians, and the > octonians, but their need doesn't arise out of looking for roots of > polynomials. I think there are 'o's in quarternions and octonions (never heard of the latter) but you've pointed out a number of doors at the moment closed, but who knows? === Subject: Re: i ^ 1/2? > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Try multiplying (1/2)(sqrt2 + i sqrt2) by itself. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: i ^ 1/2? On 2007-11-22 17:38:54 -0500, Gerry Myerson said: Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Try multiplying (1/2)(sqrt2 + i sqrt2) by itself. Very nice. 1/2(sqrt2 +isqrt2)*1/2(sqrt2+isqrt2)= 1/4(sqrt2*sqrt2 + 2isqrt2sqrt2 + isqrt2isqrt2) = (application of (a+b)^2 = a^2 + 2ab + b^2) 1/4(2 + 4i - 2) = 1/4*4i = i So does this mean (or rather can I guess that ) the imaginary numbers are closed with respect to taking the roots of polynomials with imaginary coefficients (and does that mean the coefficients can be imaginary numbers with RATIONAL whatever you call the a and b in a + bi?). Actually why stop there. Are the imaginary numbers closed with respect to taking the roots of polynomials with imaginary coefficients where the a and b in a + bi are allowed to be roots of a polynomial etc etc.? Where does this closure end? === Subject: Re: i ^ 1/2? > On 2007-11-22 17:38:54 -0500, Gerry Myerson > said: > > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Try multiplying (1/2)(sqrt2 + i sqrt2) by itself. Very nice. 1/2(sqrt2 +isqrt2)*1/2(sqrt2+isqrt2)= > 1/4(sqrt2*sqrt2 + 2isqrt2sqrt2 + isqrt2isqrt2) = (application of > (a+b)^2 = a^2 + 2ab + b^2) > 1/4(2 + 4i - 2) = 1/4*4i = i So does this mean (or rather can I guess that ) the imaginary numbers > are closed with respect to > taking the roots of polynomials with imaginary coefficients (and does > that mean the > coefficients can be imaginary numbers with RATIONAL whatever you call > the a and b in > a + bi?). Actually why stop there. Are the imaginary numbers closed with respect > to taking the > roots of polynomials with imaginary coefficients where the a and b in a > + bi are allowed > to be roots of a polynomial etc etc.? Where does this closure end? > The complex numbers are algebraically closed. Look it up. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: i ^ 1/2? >On 2007-11-22 17:38:54 -0500, Gerry Myerson > said: Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Try multiplying (1/2)(sqrt2 + i sqrt2) by itself. Very nice. 1/2(sqrt2 +isqrt2)*1/2(sqrt2+isqrt2)= >1/4(sqrt2*sqrt2 + 2isqrt2sqrt2 + isqrt2isqrt2) = (application of >(a+b)^2 = a^2 + 2ab + b^2) >1/4(2 + 4i - 2) = 1/4*4i = i So does this mean (or rather can I guess that ) the imaginary numbers >are closed with respect to >taking the roots of polynomials with imaginary coefficients (and does >that mean the >coefficients can be imaginary numbers with RATIONAL whatever you call >the a and b in >a + bi?). Actually why stop there. Are the imaginary numbers closed with respect >to taking the >roots of polynomials with imaginary coefficients where the a and b in a >+ bi are allowed >to be roots of a polynomial etc etc.? Where does this closure end? Your original question amounted to finding the roots of z^2 - i = 0 === Subject: Re: i ^ 1/2? <200711221822268930-kquirici@yahoocom> <224ck3l2qsvtkbks81p83mdbn3fk8fhglr@4ax.com> posting-account=Gg91ZwkAAAARyqtmT5dB5plbBnobCndP rv:1.8.1.9) Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > On 2007-11-22 17:38:54 -0500, Gerry Myerson said: > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Try multiplying (1/2)(sqrt2 + i sqrt2) by itself. > Very nice. > 1/2(sqrt2 +isqrt2)*1/2(sqrt2+isqrt2)= 1/4(sqrt2*sqrt2 + 2isqrt2sqrt2 + isqrt2isqrt2) = (application of (a+b)^2 = a^2 + 2ab + b^2) 1/4(2 + 4i - 2) = 1/4*4i = i > So does this mean (or rather can I guess that ) the imaginary numbers are closed with respect to taking the roots of polynomials with imaginary coefficients (and does that mean the coefficients can be imaginary numbers with RATIONAL whatever you call the a and b in a + bi?). > Actually why stop there. Are the imaginary numbers closed with respect to taking the roots of polynomials with imaginary coefficients where the a and b in a + bi are allowed to be roots of a polynomial etc etc.? Where does this closure end? Your original question amounted to finding the roots of z^2 - i = 0 thinking was muddled. I was thinking of polynomials as having integral coefficients and was trying to expand the realm of the coefficients, which the FTA does at one fell swoop. === Subject: Re: i ^ 1/2? > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? Solve this to find out: (a + ib)^2 = i === Subject: Re: i ^ 1/2? > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? > Solve this to find out: (a + ib)^2 = i Or write i in polar form as i = r*exp(i*t), where r=1 and t=pi/4+2pi*n. Then the two square roots of i are given by i^(1/2) = r^(1/2) * exp(i*t/2) = exp(i*pi/4) or exp(i*5pi/4). where exp(i*t) = cos(t) + i*sin(t). -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === Subject: Re: i ^ 1/2? posting-account=u8_ddgoAAADEnjcEJ4lflyn5ygFN0Cdb SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.590),gzip(gfe),gzip(gfe) > Given that i = (-1)^1/2, what is i ^ 1/2? Is it an imaginary number, or > some other kind of > thing? i think its just expressed as i^1/2 i would guess it is imaginary because there is no sqaure root of -1^1/2 http://jaysmoney.blogspot.com === Subject: Re: cantor's theorem - the pieces of the puzzle In sci.math, kunzmilan In sci.math, kunzmilan > In sci.math, kunzmilan > In sci.math, David R Tribble > One fault of these discussions is, that either contributors do not > follow them, or they forget what was discussed and solved. > 1) The set of rationals 1/k, k going from 1 till infinity is > countable. It is infinite. This set does not contain all rational > numbers. Thus rational numbers can not be counted using the set of > natural numbers. > Non sequitur. Of course the rationals can be counted. > Here's a sequence I (re)discovered a few months ago > (related to Farey sequences and Stern-Brocot trees): > S(0) = 0 > I'm assuming S(1) = 1 here. > S(2n) = S(n)+1, for n > 0 > S(2n+1) = 1/S(2n) > This sequence maps every natural n to a unique rational > p/q in lowest terms. An inverse mapping is easily derived > from this. > Pedant Point: that only maps the nonnegative rationals. Of > course that's a minor detail that can easily be fixed; one > possibility is to do something like: > U(0) = 0 > U(1) = 0 > U(2) = +1 > U(3) = -1 > U(16n) = U(4n)+1 > U(16n+3) = U(4n+1)-1 > U(16n+6) = U(4n+2)+1 > U(16n+9) = U(4n+3)-1 > Not sure how well this works but the mapping should be > surjective now, at least. :-) > Another solution might be to define > S(-n) = -S(n) > for n > 0, thus establishing a bijective mapping from Z > to Q, or one can define > T(2n) = S(n) > T(2n+1) = -S(n+1) > and then T : {0,1,...} -> Q is a bijective mapping. > 2) The set of rationals j/i is is countable, and their counting > function exists. But it grows faster than n. Thus rational numbers can > not be counted using the set of natural numbers. > These arguments are quite simple. > And also quite wrong. To be correct, you'd have to find > a natural n that does not map to a unique rational p/q, or > vice versa, a rational that does not map to a unique natural. > This is not possible using the sequence I gave above. And > it is just one of many similar sequences with the same > property. > You seem to be assuming that there is some point where > you run out of naturals, which in turn implies that you think > they are a finite set or that there exist some largest natural. > I also tried to disprove Cantor. > And obviously failed. > Since he's going to have to disprove *two* arguments of > the uncountability of R (both of which are quite valid, AFAICT), > he has his work cut out for him. ;-) > For me, it is possible to count from 1 till infinity. You try to count > from 1 till 10^infinity. This is somewhat another number. > Your haphazard setup isn't helping, but 2^S or P(S) has cardinality > greater than S; this is a well known result. > I can accept this convention, but it must be explicite, and you must > keep to it. > As to the objection of existence of numbers (a - 1)/2. This > construction spans the available space twice. Your problem is > notation, how to say that there exist some number between 1 and > pointallnines spin up? Plese, say me the name of this miraculous > number. Ir it is a secret name? > I'm assuming that by pointallnines you're referring to the > infinite series s = .999... (it's a series since it's sum(i=1,+oo) 9/10^i, > given most definitions). > If there is a number between s = .999... and 1, call it d, then there > must be an uncountably infinite number of such numbers between > s and 1, since d(k) = k * d + 1 * (1 - d) for any 0 < k < 1 > is between d and 1, and d'(k) = k * d + s * (1 - d) > is between s and d. > A note to Cantor. I agree with him that rational numbers are > uncountable. > You are extremely confused. The rational numbers are quite countable, > and have been for quite some time. One method of enumerating > them is as follows: > spit out 0 > for(i = 1 to +oo) > for(j = 1 to i) > if(gcd(i,j) == 1) > { > spit out j / (i + 1 - j) > spit out -j / (i + 1 - j) > } > (This is the more or less standard diagonal scan.) > In short, Q = {0, 1/1, -1/1, 1/2, -1/2, 2/1, -2/1, 1/3, -1/3, 3/1, -3/1, > ... } and every rational number is somewhere in this sequence. > I'm not entirely sure Mister Tribble's setup enumerates the positive > rationals properly, but one can work out the first few terms: > s(0) = 0 > s(1) = 1 > s(2) = s(1) + 1 = 2 > s(3) = 1/2 > s(4) = s(2) + 1 = 3 > s(5) = 1/3 > s(6) = s(3) + 1 = 3/2 > s(7) = 2/3 > s(8) = s(4) + 1 = 4 > s(9) = 1/4 > s(10) = s(5) + 1 = 4/3 > s(11) = 3/4 > It's pretty clear that any integer n > 1 will be represented with > s(2^(n-1)) = n and any rational 1/n = s(2^(n-1) + 1). Beyond that, things > get a little murky, but it looks like it should work reasonably well; > certainly we got 1/3 and 2/3 relatively quickly. > It's also easy to generate s(2^k * (2^(n-1) + 1)) = k + 1/n for > any k > 0, n > 1. Given that, one can generate > s(2^k * (2^(n-1) + 1) + 1) = n / (kn + 1). But enough guesswork. > So let's assume that s(n) = p/q. Without loss of generality (by > dividing out factors of 2 in n) one can assume 0 < p < q. Clearly > n ends up odd, for s(n) >= 1 for all even n. Therefore s(n-1) = q/p, > s( (n-1)/2) = (q-p)/p, and at some point one will run into > 1/k for some k. Therefore given an arbitrary p/q we can calculate n, > by generating the bit sequence -- backwards. > For example, take 4/3. Writing 0 as we subtract 1, 1 if we flip, we > get: > 4/3 0 s(10) > 1/3 s(5) > 3/1 1 s(4) > 2/1 0 s(2) > 1/1 1 s(1) > and the binary expansion of the desired n can then simply > be read upwards. > Since we already knew s(10) = 4/3 anyway, this is probably > not all that interesting, but what about 15/28? > 15/28 s(775) > 28/15 1 s(774) > 13/15 s(387) > 15/13 1 s(386) > 2/13 s(193) > 13/2 1 s(192) > 11/2 0 s(96) > 9/2 0 s(48) > 7/2 0 s(24) > 5/2 0 s(12) > 3/2 0 s(6) > 1/2 s(3) > 2/1 1 s(2) > 1/1 1 s(1) > This method can easily be adapted to a computer program. > Therefore Mister Tribble's sequence generates a bijective > correspondence between N and Q+, and can be extended to > generate a bijective correspondence between Z and Q -- > which is what I was quibbling about anyway. In short, > it counts the positive rationals, and can be modified to > count all rationals. > A very clever enumeration, if a bit obscure. > Accepting 10^infinity as possible, I must use matrix R > with as many rows and columns. This will have ewen greater number of > different elements, and so on. > kunzmilan > Not sure how one generates a matrix with uncountably many rows or > columns. Did you mean a crossproduct mapping? > -- > #191, ewi...@earthlink.net > Windows Vista. It'll Fix Everything(tm). > -- > I am glad, that Mister Tribble's sequence appeared in this discussion. > As I already pointed, S(n) counts nonrepeating elements of matrix R, > thus also rationals lesser and greater than 1 as: > S(1) > R(1) = 1 > S(3) > R(2) = 1 + 2*1 > S(7) > R(3) = 1 + 2*3 > S(11) > R(4) = 1 + 2*5 > I'm not sure what you mean here. Certainly S() allows for the > ordering of Q+ in an admittedly not-all-that-useful fashion; > therefore Q+ is countable, therefore Q is countable. > S(11) = 3/4. There are counted 5 rationals: 1/2, 1/3, 2/3, 1/4, 3/4. No, there are 12. The sequence is {0, 1, 2, 1/2, 3, 1/3, 1 + 1/2, 2/3, 4, 1/4, 1 + 1/3, 3/4, ... } (The 0 adds the extra.) If you mean rationals between 0 and 1, then yes, there are 5. But the rational numbers include the integers, which means they are unbounded. > Where S(x) = 4/5, (x - 1)/2 gives count of all generated rationals > greater than 4/5. > kunzmilan > -- #191, ewill3@earthlink.net Linux. Because life's too short for a buggy OS. -- === Subject: Re: weird identity In sci.math, Andersen <47441565$0$47101$892e7fe2@authen.yellow.readfreenews.net>: > 1 / (1 - p) = 1 - p + p^2 - p^3 + p^4 ... You mean 1 + p + p^2 + p^3 ... ? That is the geometric series, right? > Hmm...OK, my bad. Still, that gives me log(1 - p) = -p - p^2/2 - p^3/3 - ... -- #191, ewill3@earthlink.net Useless C/C++ Programming Idea #12398234: void f(char *p) {char *q = strdup(p); strcpy(p,q);} -- === Subject: Re: question about primes posting-account=u8_ddgoAAADEnjcEJ4lflyn5ygFN0Cdb SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.590),gzip(gfe),gzip(gfe) > let's say i have a number N lets say I tried to divide N by all primes < K (which is < N), and > there was non-zero reminder, but N divides by K without reminder. is it enough to say that K is prime number? I mean, otherwise N would > also divde by something less than K, right? yeah. i think thats right http://jaysmoney.blogspot.com === Subject: Re: question about primes >let's say i have a number N lets say I tried to divide N by all primes < K (which is < N), and >there was non-zero reminder, but N divides by K without reminder. is it enough to say that K is prime number? I mean, otherwise N would >also divde by something less than K, right? Provided K > 1, yes K is prime. rossum === Subject: Re: Tetration and integrals posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I was wondering. Is there anything interesting about the integrals > of the tetrational power function (tower function?), that is, x > tetrated to the nth tower? > Would any of these investigations yield anything new about the > tetration operation itself? For some reason, I've noticed several threads about this new, mysterious operation of tetration in the past few weeks. Unfortunately, I doubt that the integral of x^x^x would have a simple form. Most of the tricks that work for x^x simply won't work for x^x^x. Indeed, consider the operation of finding the inverse of a powertower -- often known as a superroot. Second-order superroots (inverses of x^x) are easy to calculate, via the Lambert W function. But I don't know of any trick to find third-order superroots (inverse of x^x^x) quickly. === Subject: Re: Locus of point subtending an equal angle posting-account=33KaEgkAAAA9tz8WICNABjrkyMKXFbGS Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > Given shortest length AB = c, find the locus of C when angle ACB between variable straight lines AC and CB through C is constant = gama. A,B and C are points on a sphere of radius R > c. TIA. > > Not very well stated. > > Given shortest length AB = c > > Shortest? Shorter than what? Than AC and BC? But you haven't even > mentioned C yet in the problem. > > Also, you should state in _advance_ where the points live. > > I would have assumed the points were all in the plane until you > finally revealed that the points were on a sphere. > > But if the points are on a sphere, you need to clarify the meaning of > length. Length in R^3 or length based on distance on the sphere? > > The meaning of angle also needs to be clarified. Is angle ACB an angle > of triangle ABC regarded as a planar triangle or is it a spherical > angle? > > quasi > Agreed,there is some ambiguity about 3-D distances,even when lengths later are stated to be on 2-D. > OK, it is the usual problem in spherical trigonometry of spherical triangle ABC. AB,AC, and CB are geodesic/great circle arc segments on the surface of a sphere radius R.(They are not directly connected through the sphere by straight lines of 3-D). Angle at C (gama) between tangents CA and CB is a given constant and geodesic side length opposite to it is also given as constant c. > In plane trigonometry when (R = Infinity,the locus is the circum- circle of diameter c/sin(gama).In spherical trigonometry sin(c/R)/ sin(gama) is a (geometrically obscure?) constant. > > I'll write spherical coordinates as (phi,theta) where phi is latitude > and theta longitude, defined as on Earth. > > WLOG, let A = (0,t) and B = (0,-t). Then, according to my > calculations, C = (phi,theta) satisfies > > cos(gamma) = (Cos(2*t) - Cos(alpha) * Cos(beta))/(Sin(alpha) * > Sin(beta)) > > where > > cos(alpha) = Cos(phi) * Cos(theta - t) > cos(beta) = Cos(phi) * Cos(theta + t) > > I drew some plots, and C traces out some interesting curves, but I > don't see how to make any geometrical sense of them other than the > sense the question already implies. They certainly aren't arcs of > circles. > Can you show some plots of representative (t-gamma)? Here are some examples of what I got: http://img402.imageshack.us/img402/6987/sphericaltrianglesfv1.gif The red dots are the points A and B. The red line is the locus of C. > The grey lines are the lines of latitude and longitude, for reference. > This is the view looking directly down on one of the poles (it doesn't > matter which because the two hemispheres are mirror images). > BTW, which theorems of Euclid's Elements are known as generalized into 3-D spherical trigonometry? (geodesic arcs taken for straight lines &c.) Not sure... The loci in the neighborhood of A and B seem alright to me. Points antipodal to A or B such as the blue dot in very rough hand sketch: http://i18.tinypic.com/6kp5542.jpg subtending 90 degrees (instead of gamma = 60 degrees) between equator and north pole meridian BC, but is something left out here? === Subject: Re: Locus of point subtending an equal angle posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) >Given shortest length AB = c, find the locus of C when angle ACB >between variable straight lines AC and CB through C is constant = >gama. A,B and C are points on a sphere of radius R > c. TIA. > Not very well stated. > Given shortest length AB = c > Shortest? Shorter than what? Than AC and BC? But you haven't even mentioned C yet in the problem. > Also, you should state in _advance_ where the points live. > I would have assumed the points were all in the plane until you finally revealed that the points were on a sphere. > But if the points are on a sphere, you need to clarify the meaning of length. Length in R^3 or length based on distance on the sphere? > The meaning of angle also needs to be clarified. Is angle ACB an angle of triangle ABC regarded as a planar triangle or is it a spherical angle? > quasi > > Agreed,there is some ambiguity about 3-D distances,even when lengths > later are stated to be on 2-D. > > OK, it is the usual problem in spherical trigonometry of spherical > triangle ABC. AB,AC, and CB are geodesic/great circle arc segments on > the surface of a sphere radius R.(They are not directly connected > through the sphere by straight lines of 3-D). Angle at C (gama) > between tangents CA and CB is a given constant and geodesic side > length opposite to it is also given as constant c. > > In plane trigonometry when (R = Infinity,the locus is the circum- > circle of diameter c/sin(gama).In spherical trigonometry sin(c/R)/ > sin(gama) is a (geometrically obscure?) constant. > I'll write spherical coordinates as (phi,theta) where phi is latitude and theta longitude, defined as on Earth. > WLOG, let A = (0,t) and B = (0,-t). Then, according to my calculations, C = (phi,theta) satisfies > cos(gamma) = (Cos(2*t) - Cos(alpha) * Cos(beta))/(Sin(alpha) * Sin(beta)) > where > cos(alpha) = Cos(phi) * Cos(theta - t) cos(beta) = Cos(phi) * Cos(theta + t) > I drew some plots, and C traces out some interesting curves, but I don't see how to make any geometrical sense of them other than the sense the question already implies. They certainly aren't arcs of circles. > > Can you show some plots of representative (t-gamma)? > Here are some examples of what I got: > http://img402.imageshack.us/img402/6987/sphericaltrianglesfv1.gif > The red dots are the points A and B. The red line is the locus of C. The grey lines are the lines of latitude and longitude, for reference. This is the view looking directly down on one of the poles (it doesn't matter which because the two hemispheres are mirror images). > > BTW, which theorems of Euclid's Elements are known as generalized into > 3-D spherical trigonometry? (geodesic arcs taken for straight lines > &c.) > Not sure... The loci in the neighborhood of A and B seem alright to me. Points > antipodal to A or B such as the blue dot in very rough hand sketch: http://i18.tinypic.com/6kp5542.jpg subtending 90 degrees (instead of gamma = 60 degrees) between equator > and north pole meridian BC, but is something left out here? I don't really understand what you mean by is something left out?, but anyway... As I see it, the situation at the points antipodal to A and B (call them A' and B') is analogous to the situation at points A and B themselves. If C = A or C = B then gamma is undefined. Likewise, if C = A' or C = B' then gamma is undefined. The locus of C leaves A and B at an angle of 60 degrees to the equatorial plane. Likewise, the locus of C leaves A' and B' at an angle of 60 degrees to the equatorial plane (or 120 degrees, depending how you want to measure it). So, if you want to represent the situation where C is very close to B', then the plane of your blue line from B to C should be inclined to the equatorial plane by 60 degrees, not 90 degrees as you have it. === Subject: Does every obtuse triangle admit a periodic orbit for the path of a billiard ball? posting-account=mYmveAoAAAA6m8p7tyKTuI-_Mp56JWnf Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) We assume that the billiard ball bounces off each side so that the angle of incidence equals the angle of reflection. If it hits a vertex, it rebounds along the reflection of its entry path in the angle bisector of the angle at that vertex. The orbit (or trajectory) is periodic, if after a finite number of reflections, it returns to its starting point. How does one prove that? Any hints? Aktivated Aktivator === Subject: Re: Does every obtuse triangle admit a periodic orbit for the path of a > We assume that the billiard ball bounces off each side so that the > angle of incidence equals the angle of reflection. If it hits a > vertex, it rebounds along the reflection of its entry path in the > angle bisector of the angle at that vertex. The orbit (or trajectory) > is periodic, if after a finite number of reflections, it returns to > its starting point. How does one prove that? Any hints? > Aktivated Aktivator This is not the usual definition of periodic orbit, which would require returning to both the starting point and the starting direction. With your definition, you just need to hit a side at a 90 degree angle... -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Does every obtuse triangle admit a periodic orbit for the path of a billiard ball? posting-account=wigfZgkAAACDgITarXffzxJygX81YRSs 98),gzip(gfe),gzip(gfe) > We assume that the billiard ball bounces off each side so that the > angle of incidence equals the angle of reflection. If it hits a > vertex, it rebounds along the reflection of its entry path in the > angle bisector of the angle at that vertex. The orbit (or trajectory) > is periodic, if after a finite number of reflections, it returns to > its starting point. How does one prove that? Any hints? Buy your opponent a stiff drink and take a leasiurly visit to the dunny. When you return their might be enough impairment of aim that you can miss the shot without loosing the game. Next time, don't wager so much on the game, and you can enjoy playing instead of crunching numbers. P.S. Don't folks look at you a little funny bringing a laptop into a billard parlor? :o) http://en.wikipedia.org/wiki/Reflection_(physics)#Retroreflection Sue... > Aktivated Aktivator === Subject: Is there a closed curve that has two distinct equichordal points? posting-account=mYmveAoAAAA6m8p7tyKTuI-_Mp56JWnf Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) I would like to prove that a closed curve in the plane has more than one equichordal point. Any hints anyone?? Aktivated Aktivator === Subject: Re: Is there a closed curve that has two distinct equichordal points? posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > I would like to prove that a closed curve in the plane has more than > one equichordal point. > Any hints anyone?? > Aktivated Aktivator http://aimsciences.org/journals/pdfs.jsp?paperID=2473&mode=abstract If C is a Jordan curve on the plane and P;Q 2 C, then the segment PQ is called a chord of the curve C. A point inside the curve is called equichordal if every two chords through this point have the same length. Fujiwara in 1916 and independently Blaschke, Rothe and WeitzenbÂock in 1917 asked whether there exists a curve with two distinct equichordal points O1 and O2. This problem has been fully solved in the negative by the author of this announcement just recently. The proof (published elsewhere) reduces the question to that of existence of heteroclinic connections for multi-valued, algebraic mappings. In the current paper we outline the methods used in the course of the proof, discuss their further applications and formulate new problems. Tom Davidson Richmond, VA === Subject: Re: Is there a closed curve that has two distinct equichordal points? > I would like to prove that a closed curve in the plane has more than > one equichordal point. > Any hints anyone?? Try a Google search for two equichordal points. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Exponential Sums and best estimate Good morning, sums:http://en.wikipedia.org/wiki/Exponential_sum It's about estimating a sum S of N terms of the form S = e(x_1) + ... + e(x_N) where x_i are real numbers and e(x) := exp(2Pi i x). I understand that the trivial bound for S is obtained by using the triangle inequality, so we have |S| =< N. The best that is reasonable to hope for is an estimate of the form |S|= O(sqrt{N}) Why can't I take x_j = 0 or 1 for all j and get S = N exactly? Don't > we need to assume something about the x_j in order to know we can get > quantities substantially less than N? The quote didn't say, you're guaranteed to get O(sqrt N), it just said the best that it is reasonable to hope for... is O(sqrt N). In many situations where exponential sums arise naturally it is plausible that the x_i don't clump together too much -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Exponential Sums and best estimate > On 22 Nov, 05:01, Gerry Myerson I'll try. Suppose you flip a (fair) coin lots of times - N times, to be exact - and ask about the excess S of heads over tails. The trivial bound for S is |S| at most N. But in fact you expect the excess to be a standard deviation or two from 0, and in this experiment a standard deviation is O(sqrt N). Sorry, I'm not a native speaker in English: > What do you mean by excess S of heads over tails? (number of heads) minus (number of tails) -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: @quasi - inconsistency, J'accuse! >Off topic: >Quasi, how ya been? > I see you've been doing some math. Good for you. Your math postings show traits of honesty and humility which suggests > there's hope for you yet. But you're a kind of Jekyll & Hyde. Your personal vendettas with > various posters show a totally different side of your personality. > Even if the attacks are often witty, they make you look juvenile (and > perhaps you actually are?). As I see it, it's a waste of energy, and a > waste of your limited time on this planet to learn/do math. On the other hand, you may simply not want to lose the pleasures you > get from the flame wars. So most likely, you'll continue, fighting > meaningless battles. But there comes a point in those wars where you > become indistinguishable from one of the real cranks. >Get the guy off Ullrich, okay? >A fan >(and you know what that stands for, right?) Well, Ullrich doesn't need to be saved -- you do. Anyway, leave me out of it -- I tried my hand at negotiating a truce, > and it worked a little, but clearly, it's a very fragile truce. > Realistically, it's liable to break at any time. Anyway, I tried. quasi >You feel proud of yourself with your thoughts of negotiating truces, >yet won't address Tommy's behavior. >Understand, I was abandoning abusing Tommy before you requested a >truce. Thy pride is misplaced. >And did you see Tommy breaking your precious truce in my posts to >Bassam King Karzeddin? >I originally began abusing Tommy because I saw him lashing out and >denigrating others needlessly, including Ullrich, and no one was >addressing his behavior. >I started sublty, by telling Tommy to not be cranky (ha ha). But he >didn't listen to me. >Tommy posts multiple times, sometimes daily, over a range of topics, >and he can be abusive in a juvenile way as well. How is TOMMY >different from other cranks? >Just because Tommy and other cranks put out a little math, doesn't >justify their bad behavior, as well as their continuous misspellings, >bad English, and confusing thoughts. >Same with those cranks James Harris, Bassam King Karzeddin, and Bill >Newbold. I see a trend - I don't like cranks involving Fermat's Last >Theorem. Oh, my disgust at Marilyn Vos Ssvant is visceral! >But you seem to like Tommy, and others like other cranks. You have >your pals, or pets. Fine. >So you won't rein in or berate Tommy, but you berate _my_ behavior? >Inconsistent, thy name is quasi. >You call me juvenile. Well, when are you going to call Tommy and >others juvenile? Inconsistent, thy name is quasi. >And that Archimedes Plutonium. Ugh, what a waste of posting space. >There's so little math in his , it's pointless to even address >him. I was surprised, though, that he posted anti-Jewish thoughts, >and I addressed that briefly. Tsk tsk. >Oh, you want to keep out of it with Tommy and Ullrich and me? Fine. >Then don't single me out as juvenile. >Tommy criticizes me for telling someone to drop dead, yet he turns >around and says the same thing to me; that is, to hang myself. >And Tommy continues the Big Lie that I don't post math. You above >said I do. So are you going to correct Tommy? No? Inconsistent, thy >name is quasi. >Ooooo, if, with reference to the Big Lie, I start citing certain >German historical figures, would I offend some posters, such as the >Dutch (Dik Winter)? Will that Godwins' Law be evoked to shut me down? >Quasi, you call me Jekyll and Hyde, but alas YOU are inconsistent. >You have your buddy Tommy. You're happy? The company you keep >reflects on YOU, Quasi. Sure, tommy's behavior is sometimes equally juvenile. It's not my job to reign him in. Oops -- I meant rein. >But you queried to me (quasi, how ya been? ...), so I replied to >you. In any case, as I said before, I want out of this game. I stepped back only to correct the misspelling, but now I'm truly out. quasi === Subject: Primes & Non-Primes posting-account=JFkRmAoAAADFdq5qvYKYCJN39wasAloF SV1),gzip(gfe),gzip(gfe) Evraka, evraka, evraka === Subject: Re: an irrationality theorem > <13430240.1195658402954.JavaMail.jakarta@nitrogen.math > forum.org>, > > tetrational like irrationality theorem : > > notation: > > (0) no part of theorem > (1)=exp(x) > (2,3)=exp(exp(x))*exp(exp(exp(x))) > (-1,-2)=log(x)*log(log(x)) > > ... > > and inv means the inverse function. > > Int means the integral from 0 till oo. > > if for all () and all integers x_i in them [ > (x1,x2,...)] are the same mod 2. > > > ( so 1 or 0 ; odd or even ) > > let (+) denote a product of ( positive integers ) > > and (-) denote a product of > > ( negative integers )and/or inv(positive > integers) > > > then Int (+)/(-) = Irrational > > ( for complex -> abs and/or theta is irrational ) > > example > > Int log(x)/exp(x) = - eulers gamma ( assumed > irrational ) > > tommy1729 i hope the theorem is clear. Not really. But it is clear that it isn't a theorem, > as a theorem is something that has a proof. > Better to call it a feeling. -- > Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for > email) i call it conjecture :) (1) = exp(x) (2) = exp (exp (x)) etc (tetration) and (a,b) means (a)*(b) (product) hope that helps tommy1729 === Subject: Re: Integral equation posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) On Nov 21, 11:46 pm, Robert Israel On Nov 21, 5:56 am, Robert Israel > It may help to do the change of variables x = exp(t), F(x) = exp(t) y(t), > by which the differential equation becomes autonomous: > > y' + y'' = - y (y + y') > > You want F(x) = exp(t) y(t) -> 0 as t -> -infinity and > F'(x) = exp(t) (y(t) + y'(t)) -> 0 as t -> +infinity. > Should that be F'(x) = y(t) + y'(t)? No. x = exp(t), F = exp(t)*y(t) F'(x) = dF/dx = (dF/dt)/(dx/dt) = (exp(t)*y'(t) + exp(t)*y(t))/exp(t) = y'(t) + y(t) I don't see it. I think I'm having a blank moment. cross-sectional area dA, thus of volume dA dr and mass dm = rho(r) dA dr where > rho is the density. The gravitational force on it is > - G M(r) dm /r^2 = - G M(r) rho(r)/r^2 dA dr where > M(r) = 4 pi int_0^r rho(b) b^2 db is the mass within distance r of the origin. > This must be balanced by the difference in pressures: the pressure force on > the inside surface is p(r) dA and that on the outer surface is p(r+dr) dA, so > for the forces to balance we have > - G M(r) rho(r)/r^2 = dp/dr > Since p -> 0 as r -> infinity, we must have > p(r) = int_r^infty G M(a) rho(a)/a^2 da > i.e. if rho(a) = k p(a), > p(r) = k int_r^infty G M(a) p(a)/a^2 da > = C int_r^infty int_0^a b^2 p(b) p(a)/a^2 db da Now if F(r) = int_0^r p(b) b^2 db we have F'(r) = p(r) r^2 = C r^2 int_r^infty F(a) p(a)/a^2 da > = C r^2 int_r^infty F(a) F'(a)/a^4 da (F'/r^2)' = F/r^2 - 2 F'/r^3 = - C F(r) F'(r)/r^4 i.e. F'' = 2 F'/r - C F F'/r^2 > with F(r) -> 0 as r -> 0 and F'(r)/r^2 = p(r) -> 0 as r -> infty > and staying finite as r -> 0. Moreover, since we don't allow negative > pressures and densities, we need F > 0 and F' > 0 for r > 0. > Again, by scaling we can take C = 1. This time, if r = exp(t) and F(r) = exp(t) y(t), I get > y'' + y' = 2(y' + y) - y (y' + y) If z = y' + y, this says z' = 2 z - y z > y' = z - y and we want exp(t) y -> 0 as t -> -infinity, z exp(-2 t) -> 0 as > t -> infinity, y > 0 and z > 0. If we look at this in the phase plane, it > appears that the equilibrium y=z=2 is an attractor, attracting all solutions > in the region z > 0. The boundary condition as t -> infinity is automatically > satisfied. However, all trajectories except for one separatrix > coming out of the saddle point y=z=0 go into the region y < 0 as t - -infinity. That separatrix corresponds to the solutions you want. We can > write it as y = y_1(t - t_0), z = z_1(t - t_0), where t_0 is an arbitrary > constant; this corresponds to F(r) = r y_1(ln(r) - t_0) and > p(r) = z_1(ln(r)-t_0)/r^2. So you do get the > one arbitrary parameter you wanted. As t -> -infinity > this comes out of the saddle point along the eigenvector [1/3, 1], with > y_1(t) ~= 1/3 exp(2 t), z_1(t) ~= exp(2 t), and thus F(r) is approximately > a constant times r^3, and p(r) approaches a constant, as r -> 0. Ho-hum... so much for my physics then! Am I right in assuming there's no hope of a closed-form solution? OK, so I can solve F'' = 2 F'/r - F F'/r^2 numerically, provided I have some initial conditions. Based on your closing comment, I tried F(0) = u*r0^3, F'(0) = 3*u*r0^2, where r0 is a suitably small value of r to start at, and u is a constant that I can vary to get the various solutions for different total mass. Does that make sense? I seem to get plausible-looking pressure graphs out of this (and the discrete approximation of the force equation seems to come right too), but I'm not sure how conclusive that is. The other problem I'm having is determining the total mass. As r gets bigger and bigger, p gets smaller and smaller, and the volume of the discrete spherical shell that I'm adding (by moving from r to r + delta_r) gets bigger and bigger. This is all as expected, but I don't see any obvious convergence of the total mass. It just keeps on growing. I'm worried that at these higher values of r I'm just generating garbage numerical artefacts. Any ideas how I can pin down the total mass integral with confidence? === Subject: Re: Karzeddin's evolving conjectures ... Yes I made right this time, & I think I have the right to stay here with the generous offer by quasi You can't find a counter example to the following integer equation: Z^P = X^P + Y^P + 2*N*X*Y*Z Where: (X, Y, Z, N) are coprime positive integers pairwise Z is even positive integer P is odd prime number where P divides N*X*Y*Z, and P>3 Where also P=3, implies N=1, as was proved so easily in fermat's last theorem short proof Bassam Karzeddin === Subject: Re: Karzeddin's evolving conjectures ... >Yes I made right this time, & I think I have the right to stay here with the generous offer by quasi Of course you have the right to stay -- you don't need my permission. >You can't find a counter example to the following integer equation: Z^P = X^P + Y^P + 2*N*X*Y*Z Where: (X, Y, Z, N) are coprime positive integers pairwise >Z is even positive integer >P is odd prime number where P divides N*X*Y*Z, and P>3 But I already gave some counterexamples with P > 3. For example, for P = 5: p = 5, x = 1, y = 23, z = 5084, n = 14523267475345 >Where also P=3, implies N=1, as was proved so easily >in fermat's last theorem short proof But P = 3 doesn't imply N = 1. The counterexample I posted for P = 3 had N > 1: p = 3, x = 13, y = 67, z = 30296, n = 526893 Also, once you require N to to be relatively prime to X,Y,Z, the conjecture no longer generalizes FLT, since for FLT, you need N = 0. quasi === Subject: Re: Karzeddin's evolving conjectures ... > karzeddin Yes I made right this time, & I think I have the > right to stay here with the generous offer by quasi Of course you have the right to stay -- you don't > need my permission. > You can't find a counter example to the following > integer equation: Z^P = X^P + Y^P + 2*N*X*Y*Z Where: (X, Y, Z, N) are coprime positive integers pairwise Z is even positive integer P is odd prime number where P divides N*X*Y*Z, and > P>3 But I already gave some counterexamples with P > 3. For example, for P = 5: p = 5, x = 1, y = 23, z = 5084, n = > n = 14523267475345 > Where also P=3, implies N=1, as was proved so easily > in fermat's last theorem short proof But P = 3 doesn't imply N = 1. The counterexample I posted for P = 3 had N > 1: p = 3, x = 13, y = 67, z = 30296, n = 526893 Also, once you require N to to be relatively prime to > X,Y,Z, the > conjecture no longer generalizes FLT, since for FLT, > you need N = 0. quasi yes quasi I was trying to correct the special case (P=3), back in time I have stated the case where P=3, where also Dr.Gerry Myerson only gave a note, here is the link below http://mathforum.org/kb/message.jspa?messageID=5537524&tstart=0 I will study your counter examples more carefully about the generalisation of FLT, main point, I will explain it soon B.Karzeddin === Subject: midway between log(x) and x|->x exp ( log(x) ) = x, and exp(x) is exponential. Suppose f: R->R is increasing, and for sufficiently large x, f(f(x)) ~~= exp(x) . To try to bound f, we can try to bound log(f(.)). int_{1, x} ( dt/t ) = log(x) and (x>=1) int_{1, x} ( t^(epsilon-1) dt ) = ( x^(epsilon) - 1)/epsilon ( x>=1). [epsilon>0] As x -> oo, x^epsilon eventually surpasses any positive integer n, so x^(x^epsilon) will eventually dominate x^2. So we need to integrate something smaller than t^(epsilon-1), but larger than t^(-1). One idea is to have a positive, continuous g(t) such that lim_{t->oo} g(t) = 0. One could look at integrals int_{1, x} ( t^(g(t) - 1) dt that eventually dominate log(x) and are eventually dominated by b*x, for some b>0. An f(.) such that f(f(x)) is about e^x for large x might help with understanding extensions of tetration, i.e. 2 tetrated pi times. David Bernier === Subject: tanh(cosh^-1(a/x)) dilemma posting-account=ilwyGQoAAABKLf9bH9wj-v3w2LgKMJyt Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) I have been going insane for the last 5 hours trying to figure something out, and I thought maybe someone here would have the experience to figure it out. I have an equation [ a tanh( cosh^(-1) (a/ x) ) ] and I know that it is equal to [ sqrt( a^2 - x^2 ) ], but I can not figure out how to get it to this point. I have taken the fact that cosh^-1 (u) =ln [ u + sqrt(u^2 - 1 )] and subbed that into the tanh formula... but i can not seem to get it to work out. If anyone can help, Tim Worboys === Subject: Re: tanh(cosh^-1(a/x)) dilemma I have been going insane for the last 5 hours trying to figure > something out, and I thought maybe someone here would have the > experience to figure it out. I have an equation > [ a tanh( cosh^(-1) (a/x) ) ] (That's an expression, not an equation.) > and I know that it is equal to [ sqrt( a^2 - x^2 ) ], That's not true in general. But it is true if 0 <= x <= a. > but I can > not figure out how to get it to this point. I have taken the fact that > cosh^-1 (u) =ln [ u + sqrt(u^2 - 1 )] and subbed that into the tanh > formula... but i can not seem to get it to work out. If anyone can > help, The basic idea is to remember what you did in trigonometry, and then try to apply essentially the same ideas here with the hyperbolic functions... I would start with the identity tanh(u)^2 + sech(u)^2 = 1. Then substitute acosh(a/x) for u, giving tanh(acosh(a/x))^2 + sech(acosh(a/x))^2 = 1 The second term on the left side simplifies nicely: sech(acosh(a/x))^2 = (1/cosh(acosh(a/x)))^2 = (1/(a/x))^2 = (x/a)^2 and so we have tanh(acosh(a/x))^2 + (x/a)^2 = 1 tanh(acosh(a/x))^2 = 1 - (x/a)^2 tanh(acosh(a/x)) = sqrt(1 - (x/a)^2) Note that we chose the nonnegative square root since tanh(acosh(a/x)) must be nonnegative. Then multiplying by a on both sides, we get a tanh(acosh(a/x)) = a sqrt(1 - (x/a)^2) Finally, since a = sign(a) sqrt(a^2), we get a tanh(acosh(a/x)) = sign(a) sqrt(a^2 - x^2) which is almost what you wanted. David === Subject: Re: tanh(cosh^-1(a/x)) dilemma <20071122204805.281$H1@newsreader.com> posting-account=ilwyGQoAAABKLf9bH9wj-v3w2LgKMJyt Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) arccos?)? When I was first reading it I definitely thought it was the variable a. I am sure it is probably common knowledge, however, we have not been taught much about the hyperbolic functions in class. Tim === Subject: Re: tanh(cosh^-1(a/x)) dilemma > arccos?)? Exactly. I happen to prefer notations such as acosh to notations such as cosh^-1, although in the US, both types of notation are common. David > When I was first reading it I definitely thought it was the > variable a. I am sure it is probably common knowledge, however, we > have not been taught much about the hyperbolic functions in class. Tim === Subject: Re: tanh(cosh^-1(a/x)) dilemma > Exactly. I happen to prefer notations such as acosh to notations such as > cosh^-1, although in the US, both types of notation are common. As someone has pointed out, arccosh is incorrect, since it has nothing to do with arclength . You do sometimes see arcosh, standing for area cosh since it can be interpreted as an area. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: tanh(cosh^-1(a/x)) dilemma > Exactly. I happen to prefer notations such as acosh to notations such as cosh^-1, although in the US, both types of notation are common. As someone has pointed out, Tongue in cheek? I am certainly one person who has pointed that out in the past. Indeed, in replying to Rob Johnson on 2000 Feb. 15, I changed the name of a sci.math thread about hyperbolic functions to Arc{hyperbolic function} is a misnomer! But Google Groups seems to have no direct record of my reply and asserts that Pertti, may he rest in peace, made that name change; see My reply changing the thread's name is, however, archived by the MathForum: sometimes see arcosh, standing for area cosh since it can be > interpreted as an area. The OP might be amused or dismayed (or both) at the variety of different abbreviations. Statistics about them can be found in a post by Lee Rudolph and a reply by you in the previously mentioned thread. David === Subject: Re: How to calculate the proabability of a conditional probability? posting-account=zKSjoQoAAAC5wIsHKdIzIXzOHEFPgaXy Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > Hallo, I would like to know some opinion regarding a formula about the > probability on conditional probability that I've found but I can't > understand: if I toss a coin and on n=100 tosses I get #heads=70 heads I can > assert that my coin is biased at 20% and I have an empirical > probability of p_e=0.7 to obtain a head against the theoretical one > for an unbiased coin p=0.5: > definig X_e=(#heads-p*n)/sqrt(sigma), where sigma=n*p*(1-p)=n/4, I > obtain a normal standard variable that shows me how far I am from the > randomness condition calculating p(X >= X_e). Until here no problem easy probability theory. Now what I have some > difficulty to understand in a series of n tosses I count the different pairs outcomes: heads > (H) tails (T), HH, TH and TT, and I compute the empirical conditional > probabilities i.e. p(H|H)= #HH/#H =0.6 & p(T|H)= #HT/#H =0.4, p(T|T)= > #TT/#T =0.55 & p(H|T)= #TH/#T =0.45. It is not clear what you mean here. Say we observe the sequence HHTHTH (n = 6). The first H is a plain 'H' all by itself, as well as being the first 'H' in 'HH'; the second 'H' is a plain 'H' by itself, but is also the second H in 'HH' and the first 'H' in 'HT'. Is that what you want? In fact, please just tell us how (and why) you count the numbers of H, HH, HT, TH, TT and T for that sequence given above. R.G. Vickson Now I've found that the formula to see if the conditional probability > i.e p(H|H) is compatible with the condition of tosses indipendence, > the standard normal variable is given by Y=(#HH-n*p_e)/sqrt(sigma), where sigma=n*p_e*(1-p_e). Given that if the tosses were all > indipendent I should obtain #HH,TH,TT,HT=n/4, why in that formula the > nominator is not (#HH-(n/2)*p_e)? I would really appreciate an help to understand this problem. > Thx D. Tischler === Subject: Re: How to calculate the proabability of a conditional probability? posting-account=AAh79AoAAABl58J6xU87UYXR_C0-UL1L Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) Thx, for the reply. I'm using the coin example to speak about a test of randomness performed on a bit string. Then what I mean is the following: I have a biased coin which outcomes H with a probability p_e and T with probability p_T=(1-p_e). However, I have the suspect that the launches are not independent: an H tends to be followed by another H more often than T. I want to understand if this behavior depends only on the bias or really is a problem of lack of independence. Then I calculate the conditional probabilities p(H|H): H T H H T T T H H T H H H H H T T T H H I have n=20, #H=12, #T=8 --> p_e=(12/20) > p_T=(8/20). For XY I mean the transition X --> Y, that X at the toss i, and T at the toss i+1. In that sequence, I have #HH=7, #HT=4: then p(H|H)=#HH/(#HH+#HT). Now I need to see which is the probability of having p(H|H)=7/11 under the hypothesis that the launches are indipendent, say I have to calculate the p-value on p(H|H). The developer of the test I'm studying defined the standard normal variable Y=(#HH-n*p_e)/sqrt(sigma). where sigma=n*p_e*(1-p_e) and then the calculate the probability on it. I know quite well the theory of probability testing and, for example, the same standard normal variable for testing if p_e is acceptable under the hypotesis of fair coin, is Y=(#H-n*0.5)/sqrt(0.5*(1-0.5)): the #H follows a binomial distribution but for n big, Y follow the standard normal distribution. Same thing for #HH but I can't justify that formula. Please help. D. Tischler === Subject: Re: How to calculate the proabability of a conditional probability? posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Thx, for the reply. > I'm using the coin example to speak about a test of randomness > performed on a bit string. > Then what I mean is the following: > I have a biased coin which outcomes H with a probability p_e and T > with probability p_T=(1-p_e). However, I have the suspect that the > launches are not independent: an H tends to be followed by another H > more often than T. > I want to understand if this behavior depends only on the bias or > really is a problem of lack of independence. > Then I calculate the conditional probabilities p(H|H): H T H H T T T H H T H H H H H T T T H H I have n=20, #H=12, #T=8 --> p_e=(12/20) > p_T=(8/20). For XY I mean > the transition X --> Y, that X at the toss i, and T at the toss i+1. In that sequence, I have #HH=7, #HT=4: then p(H|H)=#HH/(#HH+#HT). Now > I need to see which is the probability of having p(H|H)=7/11 under the > hypothesis that the launches are indipendent, say I have to calculate > the p-value on p(H|H). The developer of the test I'm studying defined the standard normal > variable Y=(#HH-n*p_e)/sqrt(sigma). where sigma=n*p_e*(1-p_e) and then the calculate the probability on > it. I know quite well the theory of probability testing and, for > example, the same standard normal variable for testing if p_e is > acceptable under the hypotesis of fair coin, is > Y=(#H-n*0.5)/sqrt(0.5*(1-0.5)): the #H follows a binomial distribution > but for n big, Y follow the standard normal distribution. > Same thing for #HH but I can't justify that formula. Please help. D. Tischler Do you know anything at all about the coin beforehand, or are you inferring everything from the results you see? An observation, which probably doesn't by itself help much. Suppose Pr(H|H) = p Pr(T|H) = 1 - p Pr(H|T) = q Pr(T|T) = 1 - q and assume that the first toss follows the implied single-toss probability for Pr(H), namely Pr(H) = q/(1 - p + q). Then with n tosses and p = q I think we would expect #HH*n^2 = (#H)^2*(n - 1) The extent to which these two quantities are not equal, suitably scaled, is a measure of the likely extent to which p is not equal to q (i.e. the tosses are not independent), but I'm not sure how best to quantify this. I don't see how you can test the hypothesis that the tosses are independent; this is effectively indistinguishable from the case when p and q differ by some very tiny amount. Somehow you'd need to quantify the degree of dependence, and figure out a probability for the various degrees. Also, in this scenario, I don't think that either #H or #HH will have a binomial distribution, and the distributions won't be independent either, which could complicate matters... === Subject: Magnitude of a polynomial? posting-account=fE_VswoAAACI-_dtpz93YtnxfmeAS70T 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Suppose I have a t-degree polynomial p(x) defined over a finite field GF(p). If we define M as the maximum of the values of p(x) evaluated over all x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for such a value? 1) Can we relate M to the coefficients of p(x)? Say if we want M smaller than a certain value A, what are the constraints on the coefficients of p(x)? 2) How many polynomials with M greater than a certain value a? Does anyone have an idea about this problem? === Subject: Re: Magnitude of a polynomial? On 2007-11-22 20:49:34 -0500, brianjameskirby@yahoo.com.hk said: > Suppose I have a t-degree polynomial p(x) defined over a finite field > GF(p). > If we define M as the maximum of the values of p(x) evaluated over > all > x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for > such > a value? 1) Can we relate M to the coefficients of p(x)? Say if we want M > smaller > than a certain value A, what are the constraints on the coefficients > of p(x)? > 2) How many polynomials with M greater than a certain value a? Does anyone have an idea about this problem? How do you define an ordering on GF(p) that preserves arithmetic, i.e., x > y => x+z > y+z for any z? -- -kira === Subject: Re: Magnitude of a polynomial? <200711222100478930-kirakun@earthlinknet> posting-account=fE_VswoAAACI-_dtpz93YtnxfmeAS70T 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > On 2007-11-22 20:49:34 -0500, brianjameski...@yahoo.com.hk said: > Suppose I have a t-degree polynomial p(x) defined over a finite field GF(p). If we define M as the maximum of the values of p(x) evaluated over all x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for such a value? > 1) Can we relate M to the coefficients of p(x)? Say if we want M smaller than a certain value A, what are the constraints on the coefficients of p(x)? 2) How many polynomials with M greater than a certain value a? > Does anyone have an idea about this problem? How do you define an ordering on GF(p) that preserves arithmetic, i.e., > x > y => x+z > y+z > for any z? -- -kira Can we simply ignore such a preservation and assume p-1 > p-2 > .... > 2 > 1 >0? === Subject: Re: Magnitude of a polynomial? On 2007-11-22 22:51:02 -0500, brianjameskirby said: > On 2007-11-22 20:49:34 -0500, brianjameski...@yahoo.com.hk said: > Suppose I have a t-degree polynomial p(x) defined over a finite field > GF(p). > If we define M as the maximum of the values of p(x) evaluated over > all > x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for > such > a value? > 1) Can we relate M to the coefficients of p(x)? Say if we want M > smaller > than a certain value A, what are the constraints on the coefficients > of p(x)? > 2) How many polynomials with M greater than a certain value a? > Does anyone have an idea about this problem? How do you define an ordering on GF(p) that preserves arithmetic, i.e., > x > y => x+z > y+z > for any z? Can we simply ignore such a preservation and assume p-1 > p-2 > .... 2 > 1 >0? Without preservation of arithmetic, then your choice of ordering becomes quite arbitrary. Why not assume ... < 5 < 2 < 4 < 0 < 1 < 3 < 6 < ... or any other random ordering? A polynomial is about arithmetic on GF(p). Any question about GF(p) should say something about the question's relation to the field's arithmetic, or else the question is not about algebra anymore. -- -kira === Subject: Re: Magnitude of a polynomial? <2007112223182916807-kirakun@earthlinknet> posting-account=fE_VswoAAACI-_dtpz93YtnxfmeAS70T CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.6) > On 2007-11-22 22:51:02 -0500, brianjameskirby > said: On 2007-11-22 20:49:34 -0500, brianjameski...@yahoo.com.hk said: > Suppose I have a t-degree polynomial p(x) defined over a finite field > GF(p). > If we define M as the maximum of the values of p(x) evaluated over > all > x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for > such > a value? > 1) Can we relate M to the coefficients of p(x)? Say if we want M > smaller > than a certain value A, what are the constraints on the coefficients > of p(x)? > 2) How many polynomials with M greater than a certain value a? > Does anyone have an idea about this problem? How do you define an ordering on GF(p) that preserves arithmetic, i.e., > x > y => x+z > y+z > for any z? > Can we simply ignore such a preservation and assume p-1 > p-2 > .... > 2 > 1 >0? Without preservation of arithmetic, then your choice of ordering > becomes quite arbitrary. Why not assume > ... < 5 < 2 < 4 < 0 < 1 < 3 < 6 < ... > or any other random ordering? A polynomial is about arithmetic on GF(p). Any question about GF(p) > should say something about the question's relation to the field's > arithmetic, or else the question is not about algebra anymore. -- -kira- Hide quoted text - - Show quoted text - There is at least one reason why such an ordering is not arbitrary. If we consider continuouslly adding the multiplicative identity of GF(p) (which is 1) to itself, this is exactly the ordering, and the resulting additive group is exactly GF(p). This ordering results from generating GF(p) from a singler generator. Can your ordering be respresented by a concise generator? BTW, if you consider representing the elements of GF(p) on any computer, this is also the ordering of increasing bit size (if we neglect all leading zeros. === Subject: Re: Magnitude of a polynomial? >On 2007-11-22 22:51:02 -0500, brianjameskirby > said: On 2007-11-22 20:49:34 -0500, brianjameski...@yahoo.com.hk said: Suppose I have a t-degree polynomial p(x) defined over a finite field > GF(p). > If we define M as the maximum of the values of p(x) evaluated over > all > x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for > such > a value? 1) Can we relate M to the coefficients of p(x)? Say if we want M > smaller > than a certain value A, what are the constraints on the coefficients > of p(x)? > 2) How many polynomials with M greater than a certain value a? Does anyone have an idea about this problem? How do you define an ordering on GF(p) that preserves arithmetic, i.e., > x > y => x+z > y+z > for any z? Can we simply ignore such a preservation and assume p-1 > p-2 > .... > 2 > 1 >0? Without preservation of arithmetic, then your choice of ordering >becomes quite arbitrary. Why not assume > ... < 5 < 2 < 4 < 0 < 1 < 3 < 6 < ... >or any other random ordering? A polynomial is about arithmetic on GF(p). Any question about GF(p) >should say something about the question's relation to the field's >arithmetic, or else the question is not about algebra anymore. You might be overstating it. If the OP's question was just an idle question, then since the ordering is artificial, the question holds little interest, at least for me. But there might be some use for an ordering, perhaps for algorithmic purposes. Let's see what the OP has in mind. quasi === Subject: Re: Magnitude of a polynomial? > On 2007-11-22 20:49:34 -0500, brianjameski...@yahoo.com.hk said: > Suppose I have a t-degree polynomial p(x) defined over a finite field > GF(p). > If we define M as the maximum of the values of p(x) evaluated over > all > x in GF(p), i.e. M = max_{x in GP(p)}{p(x)}. Is there a name for > such > a value? > 1) Can we relate M to the coefficients of p(x)? Say if we want M > smaller > than a certain value A, what are the constraints on the coefficients > of p(x)? > 2) How many polynomials with M greater than a certain value a? > Does anyone have an idea about this problem? > How do you define an ordering on GF(p) that preserves arithmetic, i.e., > x > y => x+z > y+z > for any z? > -- > -kira Can we simply ignore such a preservation and assume p-1 > p-2 > .... 2 > 1 >0? Sure you can, but what significance do you think it has? quasi === Subject: Re: Magnitude of a polynomial? posting-account=fE_VswoAAACI-_dtpz93YtnxfmeAS70T CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.6) If you don't like this formulation, what about the following: If we are given with an ordering of elements in GF(p), we pick a subset X of it which contains a continuous block of elements in that ordering. If we take all t-degree polynomials over GF(p) be a family of functions, can we find a concise representation (in terms of realtionships on the coefficients) of a sub-family of functions whose range are subsets of X? Can we count the size of such a sub-family if given any X? If the above problem is too general to have a good looking answer, what about using the ordering I mentioned, i.e. 1<2< .... === Subject: Re: another question in topology I looked at it and the consequences of the theorem says that: no non-empty open subset of R^n can be homeomorphic to any open subset of R^m (m Is there a function h: [0,1]^n -> [0,1]^k > (Cartesian product and k injective? No. Use invariance of domain: http://en.wikipedia.org/wiki/Invariance_of_domain > Jose Carlos Santos === Subject: Re: another question in topology <9654499.1195782663013.JavaMail.jakarta@nitrogen.mathforum.org>, Yihong What about a closed subset of R^n which has no interior point (like Cantor > set)? Can it be homeomorphic to an subset of lower dimensional space? Yes, in fact every compact totally disconnected set in R^n is homeomorphic to the standard Cantor set in R. === === Subject: Study Engineering - Other Destinations posting-account=ROkrHAoAAADKmaK0nK8Y705ojLoUpamI CLR 2.0.50727),gzip(gfe),gzip(gfe) Statistics reveal that a big percentage of students go abroad to study in destinations other than U.S. Countries like UK, Canada, Australia and New Zealand are quite popular. But not many begin their efforts by choosing destinations other than U.S as their first choice. The main reason being lack of awareness about education in these countries. U.S is popular because every one knows about someone who studied there. U.S has been one of the more popular destinations for quite some time now. But this trend is changing. Students are becoming aware of the opportunities offered by other destinations. Most universities only require you to take the English language tests like TOEFL or IELTS. You do not need the GRE for most courses if you are applying to UK, Canada, Australia or New Zealand. There are some universities that may require you to take the GRE for some courses. Computer related courses in Canada for instance require you to take the GRE. ................... === Subject: Re: MathPuzzle 204: The fourth dimension > MathPuzzle 204: The fourth dimension > Good afternoon from sunny Ruuro, Today's puzzle is about the fourth dimension. Unfortunately, I was not > able to find the right words. It is your challenge to nevertheless find an > answer to the question. This should not be too difficult as soon as you > understand what the puzzle is all about. Puzzle 198, with the bridges, has been closed. Your solutions have been > added to my website. For puzzles 199 - 204 your answers and comments are > (still) more than welcome. Have fun with the new puzzle ! > Peter direct link: http://home.planet.nl/~p.j.hendriks/p204e.htm Please answer by email and not in this newsgroup. Question reguarding the stated problem: Quote: ... Imagine that you have an unlimited number of straight sticks, in three different lengths ... length of 3 m. ... second dimension ... area of 9 m2. ... third dimension ... 24 m3. Endquote If these sticks had a length of 1m each, then the third dimention I calcuate a volume of 27m3 for each cube, or 81m3 total. Where does 24 m3 come from? If it's from the three different lengths then the answer is arbitrarily any number, as so far you have shown use of two lengths of sticks, 1m and 2m. Is the third length 3m? 4m? 1035830m? === Subject: A best fit problem, only not. posting-account=-s6ALgoAAACjrfHlboZ_beKWmziVAaDU Gecko/20070508 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) Being the database guy at work apparently makes me the mathematician as well. Sometimes people throw me things that I just can't seem to get a start on. Here's one such example that I'd appreciate any help with. We have in inventory certain tonnages of various different qualities of wheat. We also have 2 contracts to which the wheat must be allocated. The contracts are bound in terms of weight allocation for the contract overall, but no minimum or maximum on any given quality. Each contract has a price for each different quality. The price of quality1 on contract1 is not related to the price of quality1 on contract2. (Prices depend on market prices at time of signing). What I've been asked to do is to figure out how best to allocate our inventory to the contracts in order to maximize return. My first thought went back to high school maths, where any maximize/ minimize was a turning point issue, find the zero gradient point, etc. But then I thought, no, this isn't a quadratic.... My limited mathematical intuition tells me this has a clearly defined optimum solution, without too complex an algorithm. I'm just struggling to express the problem. 10 years of database programming means I automatically begin assigning things to tables and relationships and dreaming up SQL, but that's not helping me here :) Help much appreciated. I don't even want to be given an answer, I'd rather get a pointer or two. I generally enjoy this kind of thing, but this one is making me feel downright ignorant due to its apparent simplicity. === Subject: Re: A best fit problem, only not. posting-account=zKSjoQoAAAC5wIsHKdIzIXzOHEFPgaXy Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > Being the database guy at work apparently makes me the mathematician > as well. Sometimes people throw me things that I just can't seem to > get a start on. Here's one such example that I'd appreciate any help > with. We have in inventory certain tonnages of various different qualities > of wheat. We also have 2 contracts to which the wheat must be allocated. The contracts are bound in terms of weight allocation for the contract > overall, but no minimum or maximum on any given quality. Each contract has a price for each different quality. The price of > quality1 on contract1 is not related to the price of quality1 on > contract2. (Prices depend on market prices at time of signing). What I've been asked to do is to figure out how best to allocate our > inventory to the contracts in order to maximize return. My first thought went back to high school maths, where any maximize/ > minimize was a turning point issue, find the zero gradient point, etc. > But then I thought, no, this isn't a quadratic.... My limited mathematical intuition tells me this has a clearly defined > optimum solution, without too complex an algorithm. I'm just > struggling to express the problem. 10 years of database programming > means I automatically begin assigning things to tables and > relationships and dreaming up SQL, but that's not helping me here :) Help much appreciated. I don't even want to be given an answer, I'd > rather get a pointer or two. I generally enjoy this kind of thing, but > this one is making me feel downright ignorant due to its apparent > simplicity. This looks like it might be a simple linear programming problem. To see how to deal with it, you can look at the on-line Operations Research notes of Beasley, at: http://people.brunel.ac.uk/~mastjjb/jeb/or/contents.html Of especial interest should be the sections entitled Basic OR concepts and Linear Programming Formulations. R.G. Vickson === Subject: Re: A best fit problem, only not. > We have in inventory certain tonnages of various different qualities > of wheat. We also have 2 contracts to which the wheat must be allocated. The contracts are bound in terms of weight allocation for the contract > overall, but no minimum or maximum on any given quality. Each contract has a price for each different quality. The price of > quality1 on contract1 is not related to the price of quality1 on > contract2. (Prices depend on market prices at time of signing). What is the value of inventory not allocated to a contract? Given a choice among varieties to be left over after fulfilling the contracts, what are our preferences? Without that, the problem seems underspecified. > What I've been asked to do is to figure out how best to allocate our > inventory to the contracts in order to maximize return. It's a linear programming problem, but a very simple one. However, without specifying values (and possibly other parameters, such as an imputed cost for inventory shortages of each quality), the optimal allocation between two contracts will probably not be optimal in the long run, over many contracts with terms arrived at at different times and with delivery made at different times. -- Randy Hudson === Subject: Re: A best fit problem, only not. >Being the database guy at work apparently makes me the mathematician >as well. Sometimes people throw me things that I just can't seem to >get a start on. Here's one such example that I'd appreciate any help >with. We have in inventory certain tonnages of various different qualities >of wheat. We also have 2 contracts to which the wheat must be allocated. The contracts are bound in terms of weight allocation for the contract >overall, but no minimum or maximum on any given quality. Each contract has a price for each different quality. The price of >quality1 on contract1 is not related to the price of quality1 on >contract2. (Prices depend on market prices at time of signing). What I've been asked to do is to figure out how best to allocate our >inventory to the contracts in order to maximize return. My first thought went back to high school maths, where any maximize/ >minimize was a turning point issue, find the zero gradient point, etc. >But then I thought, no, this isn't a quadratic.... My limited mathematical intuition tells me this has a clearly defined >optimum solution, without too complex an algorithm. I'm just >struggling to express the problem. 10 years of database programming >means I automatically begin assigning things to tables and >relationships and dreaming up SQL, but that's not helping me here :) Help much appreciated. I don't even want to be given an answer, I'd >rather get a pointer or two. I generally enjoy this kind of thing, but >this one is making me feel downright ignorant due to its apparent >simplicity. How about a prototype problem with some actual numbers? My gut feeling is the problem may be a linear programming type optimization problem, but without seeing some data, it's hard to be sure. In the prototype, without trying to optimize, give two different ways to satisfy the contracts, and show the return for each. I think that will make clear the essence of the problem. quasi === Subject: Re: A best fit problem, only not. posting-account=-s6ALgoAAACjrfHlboZ_beKWmziVAaDU Gecko/20070508 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) Being the database guy at work apparently makes me the mathematician as well. Sometimes people throw me things that I just can't seem to get a start on. Here's one such example that I'd appreciate any help with. > We have in inventory certain tonnages of various different qualities of wheat. > We also have 2 contracts to which the wheat must be allocated. > The contracts are bound in terms of weight allocation for the contract overall, but no minimum or maximum on any given quality. > Each contract has a price for each different quality. The price of quality1 on contract1 is not related to the price of quality1 on contract2. (Prices depend on market prices at time of signing). > What I've been asked to do is to figure out how best to allocate our inventory to the contracts in order to maximize return. > My first thought went back to high school maths, where any maximize/ minimize was a turning point issue, find the zero gradient point, etc. But then I thought, no, this isn't a quadratic.... > My limited mathematical intuition tells me this has a clearly defined optimum solution, without too complex an algorithm. I'm just struggling to express the problem. 10 years of database programming means I automatically begin assigning things to tables and relationships and dreaming up SQL, but that's not helping me here :) > Help much appreciated. I don't even want to be given an answer, I'd rather get a pointer or two. I generally enjoy this kind of thing, but this one is making me feel downright ignorant due to its apparent simplicity. How about a prototype problem with some actual numbers? My gut feeling is the problem may be a linear programming type > optimization problem, but without seeing some data, it's hard to be > sure. In the prototype, without trying to optimize, give two different ways > to satisfy the contracts, and show the return for each. I think that > will make clear the essence of the problem. quasi How about this. Fixed width font will be helpful... Quality Stock(tons) Contract1Price Contract2Price Q1 30 60 40 Q2 10 30 25 Contract1 max = 15 tons Contract2 max = 25 tons Simple solution 1: Fill ordering by quality, price, contract $60 * 15 + $40 * 15 + $30 * 10 = $1800 Simple solution 2: Fill ordering by available quantity, price $40 * 25 + $60 * 5 + $30 * 10 = $1600 Obviously which allocation actually works out best in the general case depends on the ratios involving price, tonnage in stock, and tonnage available on contract, which neither of these algorithms take into account. === Subject: Re: A best fit problem, only not. >Being the database guy at work apparently makes me the mathematician >as well. Sometimes people throw me things that I just can't seem to >get a start on. Here's one such example that I'd appreciate any help >with. > We have in inventory certain tonnages of various different qualities >of wheat. > We also have 2 contracts to which the wheat must be allocated. > The contracts are bound in terms of weight allocation for the contract >overall, but no minimum or maximum on any given quality. > Each contract has a price for each different quality. The price of >quality1 on contract1 is not related to the price of quality1 on >contract2. (Prices depend on market prices at time of signing). > What I've been asked to do is to figure out how best to allocate our >inventory to the contracts in order to maximize return. > My first thought went back to high school maths, where any maximize/ >minimize was a turning point issue, find the zero gradient point, etc. >But then I thought, no, this isn't a quadratic.... > My limited mathematical intuition tells me this has a clearly defined >optimum solution, without too complex an algorithm. I'm just >struggling to express the problem. 10 years of database programming >means I automatically begin assigning things to tables and >relationships and dreaming up SQL, but that's not helping me here :) > Help much appreciated. I don't even want to be given an answer, I'd >rather get a pointer or two. I generally enjoy this kind of thing, but >this one is making me feel downright ignorant due to its apparent >simplicity. > How about a prototype problem with some actual numbers? > My gut feeling is the problem may be a linear programming type > optimization problem, but without seeing some data, it's hard to be > sure. > In the prototype, without trying to optimize, give two different ways > to satisfy the contracts, and show the return for each. I think that > will make clear the essence of the problem. > quasi >How about this. Fixed width font will be helpful... Quality Stock(tons) Contract1Price Contract2Price >Q1 30 60 40 >Q2 10 30 25 Contract1 max = 15 tons >Contract2 max = 25 tons Simple solution 1: Fill ordering by quality, price, contract $60 * 15 + $40 * 15 + $30 * 10 = $1800 The above solution is invalid -- it exceeds Contract1 max. >Simple solution 2: Fill ordering by available quantity, price $40 * 25 + $60 * 5 + $30 * 10 = $1600 Obviously which allocation actually works out best in the general case >depends on the ratios involving price, tonnage in stock, and tonnage >available on contract, which neither of these algorithms take into >account. For this data, the problem can be modeled as a linear programming problem. Define variable x11, x12, x21, x22 by x11 = the amount of Q1 to contract 1 x12 = the amount of Q1 to contract 2 x21 = the amount of Q2 to contract 1 x22 = the amount of Q2 to contract 2 The constraints: x11, x12, x21, x22 are all >= 0 x11 + x12 <= 30 x21 + x22 <= 10 x11 + x21 <= 15 x12 + x22 <= 25 objective: maximize 60x11 + 40x12 + 30x21 + 25x22 As I expected, this type of optimization is what's called a linear program. There are lots of books that discuss this, and many software packages have built-in routines for solving such problems. I use Maple (a symbolic math program). With that data, using Maple's built-in linear programming routines, I get the following optimal solution: x11 = 15, x12 = 15, x21 = 0, x22 = 10 which gives a maximum return of $1750. quasi === Subject: Question about Contiunuity Definition I'm using the definition of continuity that says: let f be a mapping from R into R. f is continuous at c if: for every .83Ì>0 there exists a .83å>0 s.t. |f(x)-f(c)| <.83Ì whenever |x-c|<.83å and x is in R. Alright, so my question is, are .83Ì and .83å, specifically .83å, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .83å that exists is in R, or do I have to show that it is/can be? === Subject: Re: Question about Contiunuity Definition === Subject: Re: Question about Contiunuity Definition The epsilon-delta definition of continuity of a function f: I -> D makes perfectly good sense even if I and D are merely metric spaces, not necessarily subsets of R. The epsilon and delta that appear in the definition are still positive real numbers. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === Subject: Re: Question about Contiunuity Definition I'm using the definition of continuity that says: let f be a mapping from R into R. f is continuous at c if: for every ?>0 there exists a ?>0 s.t. |f(x)-f(c)| Alright, so my question is, are ? and ?, specifically ?, in R as well, Yes. > or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the ? that exists is in R, or do I have to show that it is/can be? ************************ David C. Ullrich === Subject: Re: Question about Contiunuity Definition I'm using the definition of continuity that says: let f be a mapping from R into R. f is continuous at c if: for every ?>0 there exists a ?>0 s.t. |f(x)-f(c)| Alright, so my question is, are ? and ?, specifically ?, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the ? that exists is in R, or do I have to show that it is/can be? If f is a function from R to R, then by default, all variables mentioned are automatically regarded as real. Moreover, the inequalities ?>0 and |x-c|0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? **************************************************************************** ********* Not only it is clear, imho, that epsilon and delta are reals... where else could they be? I'm talking of real analysis, of course. Now, in order to show f is continuous in c you have to prove the existence of such a delta for any epsilon > 0 whatsoever, but the search is done within R. In this respect you don't know for a fact that such a delta exists, but you rather prove its existence. Tonio === Subject: Re: Question about Contiunuity Definition posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) I'm using the definition of continuity that says: > let f be a mapping from R into R. > f is continuous at c if: > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? ***************************************************************************- * ********* > Not only it is clear, imho, that epsilon and delta are reals... where > else could they be? I'm talking of real analysis, of course. Now, in order to show f is continuous in c you have to prove the > existence of such a delta for any epsilon > 0 whatsoever, but the > search is done within R. In this respect you don't know for a fact > that such a delta exists, but you rather prove its existence. Disclaimer: If you just want to get some answer for your assignment so that you can get good grades, ignore the following. But if you want to really think about this, read on. Nope. those epsilon and delta do not exist in R. When you try to verify them by thought process, they practically become infinitesimals which are excluded from R. But you might reason that the specified condition ensures that all points between c and x are covered. This is only a belief based on the unknown properties of the infinite. So, except by assuming that continuity is built by points, you can't prove continuity using the standard R. - venkat === Subject: Re: Question about Contiunuity Definition posting-account=KMurQQkAAACkDDGELZpG-7yQAg7fSfzi Gecko/20061201 Firefox/2.0.0.6 (Ubuntu-feisty),gzip(gfe),gzip(gfe) > > I'm using the definition of continuity that says: > > let f be a mapping from R into R. > > f is continuous at c if: > > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? > ***************************************************************************- * ********* Not only it is clear, imho, that epsilon and delta are reals... where else could they be? I'm talking of real analysis, of course. > Now, in order to show f is continuous in c you have to prove the existence of such a delta for any epsilon > 0 whatsoever, but the search is done within R. In this respect you don't know for a fact that such a delta exists, but you rather prove its existence. Disclaimer: If you just want to get some answer for your assignment so > that you can get good grades, ignore the following. But if you want to > really think about this, read on. Nope. those epsilon and delta do not exist in R. When you try to > verify them by thought process, they practically become infinitesimals > which are excluded from R. But you might reason that the specified > condition ensures that all points between c and x are covered. This is > only a belief based on the unknown properties of the infinite. So, > except by assuming that continuity is built by points, you can't prove > continuity using the standard R. - venkat Are you insane or just an intellectual vandal? I fear it is the latter. === Subject: Re: Question about Contiunuity Definition > I'm using the definition of continuity that says: > let f be a mapping from R into R. > f is continuous at c if: > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? > ***************************************************************************- * ********* > Not only it is clear, imho, that epsilon and delta are reals... where > else could they be? I'm talking of real analysis, of course. > Now, in order to show f is continuous in c you have to prove the > existence of such a delta for any epsilon > 0 whatsoever, but the > search is done within R. In this respect you don't know for a fact > that such a delta exists, but you rather prove its existence. Disclaimer: If you just want to get some answer for your assignment so >that you can get good grades, ignore the following. But if you want to >really think about this, read on. If you're including disclaimers you should begin by specifying that you're very confused about all this. >Nope. those epsilon and delta do not exist in R. When you try to >verify them by thought process, they practically become infinitesimals >which are excluded from R. This is simply nonsense. To take a very simple example, say f(x) = x. Say we want to verify that f is continuous at 0. We'd say this: Suppose epsilon > 0. Let delta = epsilon. Now if |x - 0| < delta it follows that |f(x) - f(0)| < epsilon. QED. Nothing became infinitesmal there. epsilon is _not_ infinitesmal, it is simply an ordinary positive real number. >But you might reason that the specified >condition ensures that all points between c and x are covered. _You_ might reason this, but not the rest of us. We have no idea what it even _means_ to say that all points between x and c are covered. > This is >only a belief based on the unknown properties of the infinite. So, >except by assuming that continuity is built by points, you can't prove >continuity using the standard R. Possibly a few centuries ago there might have been an excuse for this sort of mysticism and confusion. But mathematics has made a lot of progress in the last few centuries. That definition of continuous being a big example of the sort of progress I'm talking about - clear and simple, not involving anything infinitesmal, just simple statements about ordinary real numbers. >- venkat ************************ David C. Ullrich === Subject: Re: Question about Contiunuity Definition <6hhdk3pcv0lbsdha857qfj12jc8g4qpkdq@4ax.com> posting-account=i1MELAoAAADwo_-GGwN3NKKSXm8aSdBN SV1),gzip(gfe),gzip(gfe) > I'm using the definition of continuity that says: > let f be a mapping from R into R. > f is continuous at c if: > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? ***************************************************************************- - ********** > Not only it is clear, imho, that epsilon and delta are reals... where > else could they be? I'm talking of real analysis, of course. Now, in order to show f is continuous in c you have to prove the > existence of such a delta for any epsilon > 0 whatsoever, but the > search is done within R. In this respect you don't know for a fact > that such a delta exists, but you rather prove its existence. > Disclaimer: If you just want to get some answer for your assignment so that you can get good grades, ignore the following. But if you want to really think about this, read on. If you're including disclaimers you should begin by specifying > that you're very confused about all this. > Nope. those epsilon and delta do not exist in R. When you try to verify them by thought process, they practically become infinitesimals which are excluded from R. This is simply nonsense. To take a very simple example, say f(x) = x. Say we want to > verify that f is continuous at 0. We'd say this: Suppose epsilon > 0. Let delta = epsilon. Now if |x - 0| < delta > it follows that |f(x) - f(0)| < epsilon. QED. That's right but I think Venkat Reddie means that you need a delta for any possible epsilon, no matter how small the latter is. So, the existence of the corresponding delta must hold for any term of an infinite sequence of epsilons with limit 0. Isn't this the gist of the question? Of course, none of the epsilons is neither 0 nor infinitesimal; this is what Venkat should consider here. === Subject: Re: Question about Contiunuity Definition > I'm using the definition of continuity that says: > let f be a mapping from R into R. > f is continuous at c if: > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? > ***************************************************************************- - ********** > Not only it is clear, imho, that epsilon and delta are reals... where > else could they be? I'm talking of real analysis, of course. > Now, in order to show f is continuous in c you have to prove the > existence of such a delta for any epsilon > 0 whatsoever, but the > search is done within R. In this respect you don't know for a fact > that such a delta exists, but you rather prove its existence. > Disclaimer: If you just want to get some answer for your assignment so >that you can get good grades, ignore the following. But if you want to >really think about this, read on. > If you're including disclaimers you should begin by specifying > that you're very confused about all this. > Nope. those epsilon and delta do not exist in R. When you try to >verify them by thought process, they practically become infinitesimals >which are excluded from R. > This is simply nonsense. > To take a very simple example, say f(x) = x. Say we want to > verify that f is continuous at 0. We'd say this: > Suppose epsilon > 0. Let delta = epsilon. Now if |x - 0| < delta > it follows that |f(x) - f(0)| < epsilon. QED. > That's right but I think Venkat Reddie means that you need a delta for > any possible epsilon, no matter how small the latter is. What do you think Suppose epsilon > 0 means, exactly? Did you think it really meant Suppose epsilon > 0, but don't let epsilon get really small? This may surprise you, but in mathematical arguments we really do say precisely what we mean. Suppose epsilon > 0 really does mean absolutely nothing more nor less than suppose epsilon > 0. > So, the existence of the corresponding delta must hold for any term of > an infinite sequence of epsilons with limit 0. Isn't this the gist of > the question? If you prove something for one epsilon > 0, and your proof makes no use of any properties of epsilon other than the stated fact that epsilon > 0, then that same proof holds for *every* epsilon > 0. > Of course, none of the epsilons is neither 0 nor infinitesimal; this > is what Venkat should consider here. Correct. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === Subject: Re: Question about Contiunuity Definition > I'm using the definition of continuity that says: > let f be a mapping from R into R. > f is continuous at c if: > for every .8c>0 there exists a .8a>0 s.t. |f(x)-f(c)| <.8c whenever |x-c|<.8a and x is in R. > Alright, so my question is, are .8c and .8a, specifically .8a, in R as well, or do we not know. I figure it would be stupid if they aren't in R, but do I know for a fact that the .8a that exists is in R, or do I have to show that it is/can be? > ***************************************************************************- * ********* > Not only it is clear, imho, that epsilon and delta are reals... where > else could they be? I'm talking of real analysis, of course. > Now, in order to show f is continuous in c you have to prove the > existence of such a delta for any epsilon > 0 whatsoever, but the > search is done within R. In this respect you don't know for a fact > that such a delta exists, but you rather prove its existence. Disclaimer: If you just want to get some answer for your assignment so >that you can get good grades, ignore the following. And if you want to retain your sanity, also ignore it. >But if you want to really think about this, read on. Nope. those epsilon and delta do not exist in R. Nonsense. They are variables representing positive real numbers. >When you try to verify them by thought process, they practically >become infinitesimals Practically become? A vague statement. Infinitesimals? Those aren't part of standard modern math. The reason we don't have them is simple -- trying to define them, though technically possible, invites all kinds of crank interpretations (as we've seen from you, for example). The concept of limit is sufficient -- no need for infinitesimals. Especially not if we have to suffer half-brained, non-rigorous misinterpretations of the concept (such as yours). >which are excluded from R. But you might reason that the specified >condition ensures that all points between c and x are covered. This is >only a belief based on the unknown properties of the infinite. So, >except by assuming that continuity is built by points, you can't prove >continuity using the standard R. Like many of the other foundation-rejecting cranks, you show no knowledge of what the standard foundation actually is. I'm not saying alternative foundations aren't worth pursuing, but only after you truly understand the standard foundation, as forged from the debates and eventual consensus of many great mathematicians over the last few hundred years. quasi === Subject: Re: Algebra with english question. > Hello sir~ Consider the prime field Z_p of characteristic p =/= 0. Show that, for p =/= 2, > not every element in Z_p is a square of an element of Z_p. ------------------------------------------------- > I can't interpret last sentence. > not every element in Z_p is a square of an element of Z_p. > What's this mean ? There exists y in Z_p such that x^2 = y has no solution in Z_p. For example in Z_3, 0^2 = 0, and 1^2 = 1 and 2^2 = 1, so that x^2 = 2 has no solution in Z_3. === Subject: Re: Algebra with english question. On 2007-11-22 08:11:35 -0500, mina_world said: > Yes, you are right. quasi, too. not every element in Z_p is a square of an element of Z_p. > = ~[every element in Z_p is a square of an element of Z_p.] > = ~[For any b in Z_p, there is c in Z_p such that b = c^2.] > = There is a b in Z_p such that for any c in Z_p, b =/= c^2. I have a question. ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e.] This is not right. The negation of p->q is not p->~q. By definition, p -> q = ~p v q. So, ~(p -> q) = ~(~p v q) = p ^ ~q. Therefore, the correct derivation should be ~(for each e>0, exists d>0, for each x, |x-c| |f(x)-f(c)|0, exists d>0, for each x, not |x-c|0, for each d>0, exists x, |x-c|=e). This is the equivalent definition for discontinuity of f at x=c. To see how (1) differs from your conclusion: (2) There exists e>0, for each d>0, |x-c| |f(x)-f(c)|>=e, use the following example: Let f(x) = { 1/x sin(1/x) if x <> 0, = { 0 if x = 0. This function will fail (2), since f crosses zeros infinitely many times near x=0. Hence you cannot pick any e>0 such that |x-c| |f(x)-f(c)|>=e. Hence according to (2) f is not discontinuous. But f is discontinuous, which agrees with (1) as you can verify. ~[For any e >0 , there is d >0 such that for all x, |x-c| < d == |f(x)-f(c)| < e.] This is correct. > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e for > some x.] This is not. See my comment above. > = There is a x, e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] no problem ?? -- -kira === Subject: Re: Algebra with english question. > On 2007-11-22 08:11:35 -0500, mina_world said: > Yes, you are right. quasi, too. > not every element in Z_p is a square of an element of Z_p. > = ~[every element in Z_p is a square of an element of Z_p.] > = ~[For any b in Z_p, there is c in Z_p such that b = c^2.] > = There is a b in Z_p such that for any c in Z_p, b =/= c^2. > I have a question. > ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] This is not right. The negation of p->q is not p->~q. By definition, > p -> q = ~p v q. > So, > ~(p -> q) = ~(~p v q) = p ^ ~q. Therefore, the correct derivation should be > ~(for each e>0, exists d>0, for each x, |x-c| |f(x)-f(c)| = ~(for each e>0, exists d>0, for each x, not |x-c| (1) = there exists e>0, for each d>0, exists x, |x-c| |f(x)-f(c)|>=e). > This is the equivalent definition for discontinuity of f at x=c. To see how (1) differs from your conclusion: > (2) There exists e>0, for each d>0, |x-c| |f(x)-f(c)|>=e, > use the following example: Let > f(x) = { 1/x sin(1/x) if x <> 0, > = { 0 if x = 0. > This function will fail (2), since f crosses zeros infinitely many times > near x=0. Hence you cannot pick any e>0 such that |x-c|=e. Hence according to (2) f is not discontinuous. But f is discontinuous, which agrees with (1) as you can verify. > ~[For any e >0 , there is d >0 such that for all x, |x-c| < d == > |f(x)-f(c)| < e.] This is correct. > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e > for > some x.] This is not. See my comment above. > = There is a x, e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] > no problem ?? Oh, sorry. I'm under the illusion about uniformly continuous. In fact, my original quesion is... 1) ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e.] 2) ~[For any e >0, there is d >0 such that for all x, y, |x-y| |f(x)-f(y)|< e.] = There is a e >0 such that for any d >0, there is x,y such that |x-y| |f(x)-f(y)| >= e. = There is a e >0 such that for any d >0, |x-y| |f(x)-f(y)| >= e for some x, y. = There is a e>0, x, y such that for any d >0, |x-y| |f(x)-f(y)| >= e. is this no problem ? === Subject: Re: Algebra with english question. On 2007-11-22 23:38:31 -0500, mina_world said: On 2007-11-22 08:11:35 -0500, mina_world said: > Yes, you are right. quasi, too. not every element in Z_p is a square of an element of Z_p. > = ~[every element in Z_p is a square of an element of Z_p.] > = ~[For any b in Z_p, there is c in Z_p such that b = c^2.] > = There is a b in Z_p such that for any c in Z_p, b =/= c^2. I have a question. ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] This is not right. The negation of p->q is not p->~q. By definition, > p -> q = ~p v q. > So, > ~(p -> q) = ~(~p v q) = p ^ ~q. Therefore, the correct derivation should be > ~(for each e>0, exists d>0, for each x, |x-c| |f(x)-f(c)| = ~(for each e>0, exists d>0, for each x, not |x-c| (1) = there exists e>0, for each d>0, exists x, |x-c| |f(x)-f(c)|>=e). > This is the equivalent definition for discontinuity of f at x=c. To see how (1) differs from your conclusion: > (2) There exists e>0, for each d>0, |x-c| |f(x)-f(c)|>=e, > use the following example: Let > f(x) = { 1/x sin(1/x) if x <> 0, > = { 0 if x = 0. > This function will fail (2), since f crosses zeros infinitely many times > near x=0. Hence you cannot pick any e>0 such that |x-c| |f(x)-f(c)|>=e. Hence according to (2) f is not discontinuous. But f is discontinuous, which agrees with (1) as you can verify. ~[For any e >0 , there is d >0 such that for all x, |x-c| < d == |f(x)-f(c)| < e.] This is correct. > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e > for > some x.] This is not. See my comment above. > = There is a x, e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] no problem ?? Oh, sorry. > I'm under the illusion about uniformly continuous. Hmm... I just realized that I mistakenly called your statement the continuity statement when it was really the uniform continuity statement. The general continuity statement reads for each e>0, for each x, there exists d>0 such that |x-c|0, there exists d>0, for each x, we have |x-c| 1) > ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= e.] This is incorrect. I've given the reason and correction in a prior post in this thread. 2) > ~[For any e >0, there is d >0 such that for all x, y, |x-y| = There is a e >0 such that > for any d >0, there is x,y such that |x-y| |f(x)-f(y)| >= e. Same mistake as above. > = There is a e >0 such that for any d >0, |x-y| |f(x)-f(y)| >= e for > some x, y. > = There is a e>0, x, y such that for any d >0, |x-y| |f(x)-f(y)| >= > e. You dropped the qualifer for some x, y here. Without it, you're implying for all x, y. is this no problem ? Please refer to a prior post for the correction. -- -kira === Subject: Re: Algebra with english question. > In fact, my original quesion is... > 1) > ~[For any e >0 , there is d >0 such that |x-c| < d ==> |f(x)-f(c)| < e.] > = There is a e >0 such that for any d >0, |x-c| < d ==> |f(x)-f(c)| >= > e.] This is incorrect. I've given the reason and correction in a prior post > in this thread. Yes, you're right. ~[For any e >0 , there is d >0 such that for all x,y, |x-c| < d ==> |f(x)-f(c)| < e.] = There is a e >0 such that for any d >0, for some x, y, |x-c| < d ==> |f(x)-f(c)| >= e.] ~(for each e>0, exists d>0, for each x, |x-c| |f(x)-f(c)|0, exists d>0, for each x, not |x-c|0, for each d>0, exists x, |x-c|=e). > 2) > ~[For any e >0, there is d >0 such that for all x, y, |x-y| |f(x)-f(y)|< e.] > = There is a e >0 such that > for any d >0, there is x,y such that |x-y| |f(x)-f(y)| >= e. Same mistake as above. Yes, you're right. There is a e >0 such that for any d >0 such that for some x,y with |x-y| |f(x)-f(y)| >= e. > = There is a e >0 such that for any d >0, |x-y| |f(x)-f(y)| >= e > for > some x, y. > = There is a e>0, x, y such that for any d >0, |x-y| |f(x)-f(y)| > >= > e. You dropped the qualifer for some x, y here. Without it, you're > implying for all x, y. Yes, you're right. = There is a e >0 such that for any d >0, |x-y| |f(x)-f(y)| >= e for some x, y. = for any d >0, |x-y| |f(x)-f(y)| >= e for some e>0, x, y. NOW, no problem ? === Subject: Re: Algebra with english question. <5t2ak3tuvvvj4nip56kjde0f88fa45vmfl@4ax.com> <4c7ak3lgbi68jq8kdm8ounuolt8a071egg@4ax.com> <57dbk3d94hnegj1sveesbbpktpd32g49eq@4ax.com> posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Your error, in a nutshell, is that you changed the order of the > variables which then, as you now see, changed the meaning. In other words, quantifier dyslexia -- which is one of the most common complaints on this newsgroup, especially in the Cantor threads. === Subject: Checkout SmartBookFinder.com posting-account=bS6ekQoAAAAhghfGNh_IPxQlZCCeG77U Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) Check SmartBookFinder.com, http://www.smartbookfinder.com. We search all major on-line bookstores (Amazon, Half, B & N, Alibris, AbeBooks, etc.) and find you there lowest price. We also offer the first even book rental comparison search engine. Check us out if you want to save some money on books. Let us know what you think! We take criticism very well ;). Your Friends at SmartBookFinder.com === === === Subject: Re: The infintely small number b > b is the number that represents smallest extent. That makes no sense whatsoever. What do you mean by number in the first place? Usually a number means an element of some set with arithmetic operations. For example an element of a ring might be considered a number. An element of a group might also qualify as a number. What ring (or group) is b supposed to be a number in? The word extent has no meaning in mathematics. You need to define what you mean by the word before you use it to define something else. === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) On Nov 23, 11:50 am, rem6...@yahoo.com (Robert Maas, see http://tinyurl.com/uh3t) b is the number that represents smallest extent. That makes no sense whatsoever. What do you mean by number in the > first place? Usually a number means an element of some set with > arithmetic operations. For example an element of a ring might be > considered a number. An element of a group might also qualify as > a number. What ring (or group) is b supposed to be a number in? The word extent has no meaning in mathematics. You need to define > what you mean by the word before you use it to define something else. For me, a number means the measure of a quantity, such as 2 in 2 apples or 2 miles. If it now means something else, does it still have a purpose in understanding the properties of the physical world? The word extent is from English language and does not require mathematicians to redefine it. If the English language meaning of it is not enough for you to understand this discussion, then I can't help it. - venkat === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > ends. It does not mean it is not finite. Why should it have to > contain the points at it's ends? Suppose you pluck them off. > What are you left with? If I can imagine something like wire (since you meant it is possible to pluck), I can still touch it's new inclusive endpoints after you pluck the existing end points. - venkat === Subject: Re: The infintely small number b posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; .NET CLR 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) > So, you imagination allows you to imagine a finite segment without > endpoints? This contradicts the finiteness of the line segment, or > those endpoints live in some other imaginary space, and still giving > the finite extent to the line segment which lives in this world? > No, it simply means that the segnment does not _contain_ it's ends. It does not mean it is not finite. Why should it have to contain the points at it's ends? Suppose you pluck them off. What are you left with? If I can imagine something like wire (since you meant it is possible > to pluck), I can still touch it's new inclusive endpoints after you > pluck the existing end points. > I can't believe you actually said what you said. Pluck them off, as in remove them, as in plucking grapes off of a vine. The length of the line does not change, since the points have zero size (zero measure, to be exact, at least with the common Lebesgue measure that is used in this case), so the measure of the set as a whole is unchanged: x - 0 = x. Nor does removing the endpoints from the line suddenly make it explode to infinite size. But it seems you want something else. You want the points to have measure b (which means you have to modify the original definition of measure itself somewhat so it's a function into your extended number system instead of into the closed affinely-extended real right half-line [0, inf]), so that when you pluck them off, the length of the remaining segment is no longer y - x, but y - x - 2b, where b is the infinitesimal unit, equivalent to the size of a single point. BTW: what then is infinity * b? 1? Indeterminate? (like 0*infinity? Hey, then why CAN'T points have 0 size? Why even BOTHER with b?) You therefore seem to be wanting to discretize the real numbers, to turn the continuum into a discretuum. But you can't do that. Also, in your system, is b/2 undefined (hence it's not a field anymore algebraically, but a ring like Z)? === Subject: Re: The infintely small number b posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > So, you imagination allows you to imagine a finite segment without > endpoints? This contradicts the finiteness of the line segment, or > those endpoints live in some other imaginary space, and still giving > the finite extent to the line segment which lives in this world? > No, it simply means that the segnment does not _contain_ it's ends. It does not mean it is not finite. Why should it have to contain the points at it's ends? Suppose you pluck them off. What are you left with? If I can imagine something like wire (since you meant it is possible > to pluck), I can still touch it's new inclusive endpoints after you > pluck the existing end points. It appears that you think that talking about the properties of something made of a finite number of discrete pieces of finite size is relevant. You are wrong. - William Hughes - venkat === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > So, you imagination allows you to imagine a finite segment without endpoints? This contradicts the finiteness of the line segment, or those endpoints live in some other imaginary space, and still giving the finite extent to the line segment which lives in this world? > > No, it simply means that the segnment does not _contain_ it's > ends. It does not mean it is not finite. Why should it have to > contain the points at it's ends? Suppose you pluck them off. > What are you left with? > If I can imagine something like wire (since you meant it is possible to pluck), I can still touch it's new inclusive endpoints after you pluck the existing end points. It appears that you think that talking about the properties of > something > made of a finite number of discrete pieces of finite size is relevant. > You are wrong. Not to mention the fact that he thinks it's valid to reason about abstractions from properties of physical objects. I went through this on another newsgroup with a crank who denied the possibility that the empty set was unique, because if he had two burlap sacks with different things in them and he took all the things out, he still had two distinct sacks. Marshall === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > > No. A finite segment must have bounds. It need not > contain these bounds. There is nothing contradictory > about a bounded set without largest or smallest element. > Yes I understand that. But we are trying to find the inclusive bounds for that open set D, and they are not in R according to you. I would like to correct you here. They are still in R but we just can't know them. As we knew, it boils down to the fact of not being able to navigate from a point to next one. Let's take a simple, *discrete* example, and see if it's illustrative > of anything. Suppose we have a set R = {a b c d}. Suppose the elements > of R are in the following partial order: b < a > c < a > d < b > d < c Or diagrammatically: a > / > b c > / > d Consider the set D = {a, b, c} What is the lower bound of the set D? If I understand > you correctly, it must exist and it must be in the set. That misses the point that all numbers in R or ordered. So in your example b and c should be ordered. If you provide me the ordering among b and c then I can tell. - venkat === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) No. A finite segment must have bounds. It need not contain these bounds. There is nothing contradictory about a bounded set without largest or smallest element. > > Yes I understand that. But we are trying to find the inclusive bounds > for that open set D, and they are not in R according to you. I would > like to correct you here. They are still in R but we just can't know > them. As we knew, it boils down to the fact of not being able to > navigate from a point to next one. > Let's take a simple, *discrete* example, and see if it's illustrative of anything. > Suppose we have a set R = {a b c d}. Suppose the elements of R are in the following partial order: > b < a c < a d < b d < c > Or diagrammatically: > a / b c / d > Consider the set D = {a, b, c} > What is the lower bound of the set D? If I understand you correctly, it must exist and it must be in the set. That misses the point that all numbers in R or ordered. So in your > example b and c should be ordered. If you provide me the ordering > among b and c then I can tell. Okay. So your claim that an ordered set must contain its bounds is only true for sets whose order is total. What is your response to my other post, in which I show that this is not true for the total order on the real numbers either? Marshall === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > > No. A finite segment must have bounds. It need not > contain these bounds. There is nothing contradictory > about a bounded set without largest or smallest element. > Yes I understand that. But we are trying to find the inclusive bounds for that open set D, and they are not in R according to you. I would like to correct you here. They are still in R but we just can't know them. As we knew, it boils down to the fact of not being able to navigate from a point to next one. > > Let's take a simple, *discrete* example, and see if it's illustrative > of anything. > > Suppose we have a set R = {a b c d}. Suppose the elements > of R are in the following partial order: > > b < a > c < a > d < b > d < c > > Or diagrammatically: > > a > / > b c > / > d > > Consider the set D = {a, b, c} > > What is the lower bound of the set D? If I understand > you correctly, it must exist and it must be in the set. > That misses the point that all numbers in R or ordered. So in your example b and c should be ordered. If you provide me the ordering among b and c then I can tell. Okay. So your claim that an ordered set must contain > its bounds is only true for sets whose order is total. What is your response to my other post, in which > I show that this is not true for the total order on the > real numbers either? I'm not denying the fact that an open interval, defined by a set of numbers in R doesn't have bounds. I hardly care whether it is doesn't have, or can't have or don't know. I'm not interseted in fixing your model. I'm only asserting that a finite interval in a continuum should always have bounds, irrespective of how you look at it. Your ways of looking at it should not lead to a conclusion that an interval (not set) does not have bounds. This might suggest that you are using an incorrect model. - venkat === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) No. A finite segment must have bounds. It need not contain these bounds. There is nothing contradictory about a bounded set without largest or smallest element. > > Yes I understand that. But we are trying to find the inclusive bounds > for that open set D, and they are not in R according to you. I would > like to correct you here. They are still in R but we just can't know > them. As we knew, it boils down to the fact of not being able to > navigate from a point to next one. > Let's take a simple, *discrete* example, and see if it's illustrative of anything. > Suppose we have a set R = {a b c d}. Suppose the elements of R are in the following partial order: > b < a c < a d < b d < c > Or diagrammatically: > a / b c / d > Consider the set D = {a, b, c} > What is the lower bound of the set D? If I understand you correctly, it must exist and it must be in the set. > > That misses the point that all numbers in R or ordered. So in your > example b and c should be ordered. If you provide me the ordering > among b and c then I can tell. > Okay. So your claim that an ordered set must contain its bounds is only true for sets whose order is total. > What is your response to my other post, in which I show that this is not true for the total order on the real numbers either? I'm not denying the fact that an open interval, defined by a set of > numbers in R doesn't have bounds. I hardly care whether it is > doesn't have, or can't have or don't know. I'm not interseted in > fixing your model. I'm only asserting that a finite interval in a continuum should always > have bounds, irrespective of how you look at it. Your ways of > looking at it should not lead to a conclusion that an interval (not > set) does not have bounds. This might suggest that you are using an > incorrect model. To clarify further, inclusive bounds and exclusive bounds do not makes sense for a finite interval in continuum. There are only one kind of bounds - that which define the interval itself. Anny other extra kind of bounds are superfluous or redundant. For you to understand all this, as I've told before on these threads, you need to thiink of continuum just as it is, not a set or collection of single kind of things. Because your model of collection of single kind of things confuses things with their bounds. Got it? - venkat === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > > No. A finite segment must have bounds. It need not > contain these bounds. There is nothing contradictory > about a bounded set without largest or smallest element. > Yes I understand that. But we are trying to find the inclusive bounds for that open set D, and they are not in R according to you. I would like to correct you here. They are still in R but we just can't know them. As we knew, it boils down to the fact of not being able to navigate from a point to next one. > > Let's take a simple, *discrete* example, and see if it's illustrative > of anything. > > Suppose we have a set R = {a b c d}. Suppose the elements > of R are in the following partial order: > > b < a > c < a > d < b > d < c > > Or diagrammatically: > > a > / > b c > / > d > > Consider the set D = {a, b, c} > > What is the lower bound of the set D? If I understand > you correctly, it must exist and it must be in the set. > That misses the point that all numbers in R or ordered. So in your example b and c should be ordered. If you provide me the ordering among b and c then I can tell. > > Okay. So your claim that an ordered set must contain > its bounds is only true for sets whose order is total. > > What is your response to my other post, in which > I show that this is not true for the total order on the > real numbers either? > I'm not denying the fact that an open interval, defined by a set of numbers in R doesn't have bounds. Um, the rest of us are all saying that it *does* have bounds. I hardly care whether it is doesn't have, or can't have or don't know. I'm not interseted in fixing your model. I presented a simple proof that some properties of real numbers don't have bounds that also have those properties. So if you'd been paying attention you'd know now that it was can't. I'm only asserting that a finite interval in a continuum should always have bounds, irrespective of how you look at it. Right, and everyone agrees with that. Your ways of looking at it should not lead to a conclusion that an interval (not set) does not have bounds. This might suggest that you are using an incorrect model. It might suggest that you're not reading the posts, given that you're apparently responding to something that no one said. > To clarify further, inclusive bounds and exclusive bounds do not > makes sense for a finite interval in continuum. Actually, I' > There are only one > kind of bounds - that which define the interval itself. Anny other > extra kind of bounds are superfluous or redundant. For you to understand all this, as I've told before on these threads, > you need to thiink of continuum just as it is, not a set or collection > of single kind of things. Because your model of collection of single > kind of things confuses things with their bounds. Got it? - venkat === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > To clarify further, inclusive bounds and exclusive bounds do not makes sense for a finite interval in continuum. Actually, I' Ahem. Actually, I've proven that they do make sense. You need to respond to that proof. (Well, actually, you'll need to read it and understand it first. Let me know if you have any questions.) There are only one kind of bounds - that which define the interval itself. Anny other extra kind of bounds are superfluous or redundant. Again: I've proven this false. For you to understand all this, as I've told before on these threads, you need to thiink of continuum just as it is, not a set or collection of single kind of things. Just as it is is exactly and precisely what we can prove about it. Since I've proven, without reference to any theory of sets or collections, using only simple properties of the real numbers, that your claim that bounds are necessarily inclusive is false, just as it is means that some bounds are exclusive. You've said that you're only interested in using high school math. So, using only high school math, I showed how your claims do not apply to the real numbers. Please, using only high school math, respond to the proof. Complete failure to respond suggests either an inability to comprehend or a recognition that the proof destroys your argument. Marshall === Subject: Re: The infintely small number b posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) works for infinite size? Many basic operations, including comparison, > that work for finite numbers do not work for the infinite, isn't it? > But *mapping* can work between infinite *sets*. What about all those functions of real numbers that you've doubtlessly heard about? ADDITION: a + b. That is a mapping between infinite sets. One set is the Cartesian product of two real lines, the other is the real line itself. Why does it not work? === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) Yes I understand that. But we are trying to find the inclusive bounds > for that open set D, and they are not in R according to you. I would > like to correct you here. They are still in R but we just can't know > them. As we knew, it boils down to the fact of not being able to > navigate from a point to next one. Let P(x) mean that x is a real number greater than 0: 1) for all x, P(x) if and only if (x > 0 and x is a real number) We call some l a lower bound of some P if for every x that satisfies P(x), l <= x. We call some lower bound l of P an inclusive lower bound if P(l). Assumption A) the inclusive lower bound l of P exists: A1) exists l, P(l). A2) for all x, P(x) means l <= x. Let m = l/2 Since P(l), l > 0. Division of nonzero numbers is closed over the reals, so m is real. For all x, x > 0 means (x/2) > 0, so m > 0. m is real and m > 0, so P(m) from 1). However, m < l, which contradicts 2). Since we have reached a contradiction starting from our assumption, our assumption must be false. Therefore l does not exist. This proves that there exists a quality of the real numbers, namely P, for which there is no smallest number exhibiting that quality. It does so without recourse to any geometry or set theory. Just high school math. Note that this doesn't prove that we can't know l; it actually proves that there is no l. Your comments? Marshall === Subject: Re: The infintely small number b posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > Yes I understand that. But we are trying to find the inclusive bounds for that open set D, and they are not in R according to you. I would like to correct you here. They are still in R but we just can't know them. As we knew, it boils down to the fact of not being able to navigate from a point to next one. Let P(x) mean that x is a real number greater than 0: 1) for all x, P(x) if and only if (x > 0 and > x is a real number) We call some l a lower bound of some P > if for every x that satisfies P(x), l <= x. > We call some lower bound l of P an > inclusive lower bound if P(l). Assumption A) the inclusive lower bound l of P exists: A1) exists l, P(l). > A2) for all x, P(x) means l <= x. Let m = l/2 Since P(l), l > 0. Division of nonzero numbers is closed > over the reals, so m is real. For all x, x > 0 means > (x/2) > 0, so m > 0. m is real and m > 0, so P(m) > from 1). However, m < l, which contradicts 2). Since we have > reached a contradiction starting from our assumption, > our assumption must be false. Therefore l does not > exist. This proves that there exists a quality of the real > numbers, namely P, for which there is no smallest > number exhibiting that quality. So, P is a quality where P(x) means x is a real number greater than 0. And you have proved that there is no smallest number exhibiting that quality. If we remove the redundant words from the above, you mean to say there is no smallest number greater than 0. This could have been much simpler to proove. So you mean this proof contradicts my saying that smallest number exists in R. Fine. Thats not my core argument, anyway. My argument was - every finite interval in continuum (not modeled with single kind of points or numbers yet) always has its bounds just like any other finite interval. There are no multiple types of bounds. It doesn't matter whether your next points exist or not, or whether your smallest number exists or not. - venkat > It does so without recourse > to any geometry or set theory. Just high school math. > Note that this doesn't prove that we can't know l; > it actually proves that there is no l. Your comments? Marshall === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) My argument was - every finite interval in continuum (not modeled with > single kind of points or numbers yet) always has its bounds just like > any other finite interval. There are no multiple types of bounds. Let's see: you're not talking about points, and you're not talking about numbers. So what *are* you talking about? I know, a continuum, but apparently not one that we can describe with real numbers. Since continuum and real numbers generally go hand-in-hand, you must be speaking about something of your own creation. Good luck with that. Marshall === Subject: Re: The infintely small number b posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Gecko/20060418 Firefox/1.0.8 (Ubuntu package 1.0.8),gzip(gfe),gzip(gfe) > Yes I understand that. But we are trying to find the inclusive bounds > for that open set D, and they are not in R according to you. I would > like to correct you here. They are still in R but we just can't know > them. As we knew, it boils down to the fact of not being able to > navigate from a point to next one. > Let P(x) mean that x is a real number greater than 0: > 1) for all x, P(x) if and only if (x > 0 and x is a real number) > We call some l a lower bound of some P if for every x that satisfies P(x), l <= x. We call some lower bound l of P an inclusive lower bound if P(l). > Assumption A) the inclusive lower bound l of P exists: > A1) exists l, P(l). A2) for all x, P(x) means l <= x. > Let m = l/2 > Since P(l), l > 0. Division of nonzero numbers is closed over the reals, so m is real. For all x, x > 0 means (x/2) > 0, so m > 0. m is real and m > 0, so P(m) from 1). > However, m < l, which contradicts 2). Since we have reached a contradiction starting from our assumption, our assumption must be false. Therefore l does not exist. > This proves that there exists a quality of the real numbers, namely P, for which there is no smallest number exhibiting that quality. So, P is a quality where P(x) means x is a real number greater than 0. > And you have proved that there is no smallest number exhibiting that > quality. If we remove the redundant words from the above, you mean to say there > is no smallest number greater than 0. This could have been much > simpler to proove. So you mean this proof contradicts my saying that > smallest number exists in R. Fine. Thats not my core argument, anyway. My argument was - every finite interval in continuum (not modeled with > single kind of points or numbers yet) always has its bounds just like > any other finite interval. 1. This is ex cathedra. You give no reason that an interval should have its bounds (whatever that means) (You had a confused argument having to do with cutting and hence duplicating points, but you backed off that when it was pointed out that saying y was a bound for more than one segment, did not mean y had to be duplicated) 2 You do not say what you mean by have its bounds. You do not mean have bounds because you agree that the open set (a,b) has bounds even though it does not contain them. You don't mean that the bounds are elements of the interval because you have been explicit in saying that an interval is not made up of bounds. - William Hughes === Subject: Re: The infintely small number b posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > My argument was - every finite interval in continuum (not modeled with single kind of points or numbers yet) always has its bounds just like any other finite interval. 1. This is ex cathedra. You give no reason that an interval > should have its bounds (whatever that means) (You had a confused > argument having to do with cutting and hence duplicating points, > but you backed off that when it was pointed out that saying > y was a bound for more than one segment, did not mean y had > to be duplicated) 2 You do not say what you mean by have its bounds. You do > not mean have bounds because you agree that the open set > (a,b) has bounds even though it does not contain them. > You don't mean that the bounds are elements of the interval because > you have been explicit in saying that an interval is not > made up of bounds. > - William Hughes Dude's just not used to thinking clearly. Marshall === Subject: Re: Another one posting-account=9F70KwkAAADloWPH_Z0lOPxF98dtfKh6 Gecko/20060508 Firefox/1.5.0.4,gzip(gfe),gzip(gfe) > Is -1 another one? And the Internet Oracle responded: > No. You owe the Internet Oracle some context. === Subject: Re: Another one Is -1 another one? And the Internet Oracle responded: > No. You owe the Internet Oracle some context. > Robber Johnson told me negative for which I owe him a chuckle . === Subject: Re: Another one > Is -1 another one? And the Internet Oracle responded: > No. > You owe the Internet Oracle some context. > Robber Johnson told me > negative for which I owe him a chuckle . > Dave Seaman answered absolutely which, with a chuckle for Dave, be reason to toss Internet Oracle overboard. === Subject: Re: Another one > Is -1 another one? Absolutely. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit === Subject: Re: Another one <20071122.031040@whim.org> posting-account=u8_ddgoAAADEnjcEJ4lflyn5ygFN0Cdb SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.590),gzip(gfe),gzip(gfe) > Is -1 another one? negative. Rob Johnson Is -1 another one? What does that even mean? === Subject: Re: Another one Is -1 another one? What does that even mean? > That even is a strange question. Since one is some one, then minus one is another one, just to get even. Look, 1 + -1 = 0 evens the score. === Subject: Re: Another one posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/20061201 Firefox/2.0.0.8 (Ubuntu-feisty),gzip(gfe),gzip(gfe) > Look, 1 + -1 = 0 evens the score. As it is written, another one bites the dust. --c === Subject: Re: 2000 availables Solutions manual posting-account=8KXSmAoAAABB-3Gy_9rlKg2w1HuNsjpv .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > My List of Solutions Manual > contact me to : newbergh123yahoo.com > newbergh123(at)yahoo.com ot to : mattos...@gmail.com > mattosbw1(at)gmail.com If your wanted solutions manual ins't on this list, also can ask me if > is available . These are some only. This same list of tites (not links) is available from : http://rapidshare.com/files/64945514/List of solutions manual.txt - Mechanics, Mechanical Engineering & Aerospace Engineering: > Classical mechanics (2nd Ed., Goldstein) > Classical Mechanics (Douglas Gregory) + original Ebook > Advanced Dynamics (Greenwood) + original Ebook > Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) + Ebook > Classical Dynamics (Jorge V. Jos¬.a6) + Ebook > Impact Mechanics (W.J. Stronge) > Introduction to Mechanical Engineering (Rizza) > Mechanical Engineering Principles (Bird & Ross) + original Ebook > Engineering Fluid Mechanics (William Graebel) > Advanced Fluid Mechanics (William Graebel) + original Ebook > Mechanics of Fluids (8th Ed., Massey) + original Ebook > Fluid Mechanics (5th Ed., White) + Ebook > Fluid Mechanics (6th Ed., White) > Viscous Fluid Flow (3rd Ed., White) + Ebook > Fundamentals of Thermal-Fluid Sciences (1st Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences (2nd Ed., Cengel) + original > Ebook > Fundamentals of Thermal-Fluid Sciences with Student Resource CD (3rd > Ed., Cengel & Turner) > Thermodynamics: An Engineering Approach (5th Ed., Cengel) + original > Ebook > Thermodynamics: An Engineering Approach (6th Ed., Cengel) + original > Ebook > Essentials of Fluid Mechanics: Fundamentals and Applications (1st Ed., > Cengel) + original > Fluid Mechanics (1st Ed., Cengel) + original Ebook > Heat Tranfer (2nd Ed., Cengel) + original Ebook > Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel) + > original Ebook > Design and Simulation of Thermal Systems (Suryanarayana & Arici) > Introduction to Fluid Mechanics (6th Ed., Robert Fox, Alan McDonald & > Philip Pritchard) > Fluid Mechanics (5th Ed., Douglas) > Fluid Mechanics (3rd Ed., Kundu) > Fluid Mechanics with Engineering Applications (Finnemore) > Fundamentals of Fluid Mechanics, 4th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) + original ebook > Fundamentals of Fluid Mechanics, 5th Ed (Bruce R. Munson, Donald F. > Young, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 3rd Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi) > A Brief Introduction to Fluid Mechanics, 4th Ed (Donald F. Young, > Bruce R. Munson, Theodore H. Okiishi, Wade W.) > Engineering Fluid Mechanics, 7th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Engineering Fluid Mechanics, 8th Ed (Clayton T. Crowe, Donald F. > Elger, John A. Roberson) > Mechanics of Fluids (3rd Ed., Potter) > Mechanics of Fluids (4th Ed., Shames) > Extended Irreversible Thermodynamics (3rd Ed., D. Jou, J. Casas- > Vazquez & G. Lebon) > Thermodynamics: An Integrated Learning System (Schmidt, Ezekoye, > Howell & Baker) > Introduction to Thermal and Fluids Engineering (Kaminski & Jensen) > Heating, Ventilating and Air Conditioning Analysis and Design (6th > Ed., McQuiston) > An Introduction to Fluid Dynamics: Principles of Analysis and Design > (Middleman) > Introduction to Mass and Heat Transfer: Principles of Analysis and > Design (Middleman) > Heat Transfer (2nd Ed., Mills) > Convective Heat and Mass Transfer (4th Ed., Kays & Crawford) > Advanced Engineering Thermodynamics (3rd Ed., Bejan) > Convection Heat Transfer (2nd Ed., Bejan) > Convection Heat Transfer (3rd Ed., Bejan) > Thermal Design and Optimization (Bejan) > Shape and Structure, from Engineering to Nature (Bejan) > An Introduction to Combustion: Concepts and Applications (2nd Ed., > Turns) > Thermodynamics: Concepts and Applications (Stephen Turns) > Thermal-Fluid Sciences: An Integrated Approach (Stephen Turns) > Principles of Heat Transfer (Kaviany) > Heat Convection (Latif M. Jiji) + original Ebook > Heat Transfer (9th Ed., Holman) > Fundamentals of Momentum, Heat and Mass Transfer (4th Ed., Welty) > Fundamentals of Momentum, Heat and Mass Transfer (5th Ed., Welty) > Momentum, Heat, and Mass Transfer Fundamentals (Kessler) + original > Ebook > Analytical Methods for Heat Transfer and Fluid Flow Problems (Bernhard > Weigand) > Heat Tranfer (Rao) > Heat Conduction (kakac) > Heat Exchanges (Kakac) > Convective Heat Transfer (kakac) > Heat Exchangers: Selection, Rating and Thermal Design (2nd Ed. Sadik > Kakac & Hongtan Liu) > Fundamentals of Engineering Thermodynamics, 5th Ed (Michael J. Moran, > Howard N. Shapiro) + original Ebook > Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, > Howard N. Shapiro) > Fundamentals of Heat and Mass Transfer (5th Ed., Incropera, DeWitt) > Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (4th Ed., Incropera, DeWitt) > Introduction to Heat Transfer (5th Ed., Incropera, DeWitt) > Radiation Detection and Measurement (3rd Ed., Glenn Knoll) > Radiative Heat Transfer (2nd Ed., Michael Modest) > Engineering Heat Transfer (2nd Ed., Janna) > Engineering Thermodynamics: Work and Heat Transfer (4th Ed., G.F.C. > Rogers & Y.R. Mayhew) > Elements of Heat Transfer (Yildiz Bayazitoglu and M. Necati Ozisik) > Inverse Heat Transfer: Fundamentals and Applications (M.N. Ozisik & > Helcio R.B. Orlande) > Thermal Radiation Heat Transfer (4th Ed.,Robert Siegel & John R. > Howell) > Computational Heat Transfer (2nd Ed., Jaluria) > Principles of Combustion (2nd Ed., Kenneth Kuan-yun Kuo) > Incompressible Flow (3rd Ed., Panton) > Modern Compressible Flow: With Historical Perspective (3rd Ed., John > D. Anderson) > Non-Newtonian Flow : Fundamentals and Engineering Applications (R P > Chhabra & J F Richardson) + original Ebook > Computational Techniques for Fluid Dynamics (Srinivas, K., Fletcher, > C.A.J.) > Ebook > Theory of Applied Robotics: Kinematics, Dynamics and Control (Reza N. > Jazar) > Kinematic Chains and Machine Components Design (Dan B. Marghitu) + > original Ebook > Kinematics and Dynamics of Machinery (3rd Ed., Wilson & Sadler) > Kinematics, Dynamics, and Design of Machinery (2nd Ed., Waldron & > Kinzel) > Mechanism Design: Analysis and Synthesis-Volume 1 (4th Ed., Erdman & > Sandor) > Machines and Mechanisms: Applied Kinematic Analysis (3rd Ed., > Myszka) > Mechanical Design: A Components Approach (Peter Childs) > Mechanical Design of Machine Elements and Machines: A Failure > Prevention Perspective (Collins) > Fundamentals of Machine Component Design (3rd Ed., Juvinall) > Fundamentals of Machine Component Design (4th Ed., Juvinall) > Design of Machine Elements (8th Ed., Spotts) > Machine Design (Wentzell) > Solutions Manual to the text : Problems on the Design of Machine > Elements (Faires) > Machine Elements in Mechanical Design (4th Ed., Mott) > Mechanical Design: An Integrated Approach (1st Ed., Ugural) > Design of Machinery (3rd Ed., Norton) > Design of Machinery (4th Ed., Norton) > Machine Design (2nd Ed., Norton) > Machine Design : An Integrated Approach (3rd Ed., Norton) > Mechanical Engineering Design (6th Ed., Shigley) > Mechanical Engineering Design (7th Ed., Shigley) > Shigley's Mechanical Engineering Design (8th Ed., Budynas) > Fundamentals of Machine Elements (1st Ed., Hamrock) > Fundamentals of Machine Elements (2nd Ed., Hamrock) > Mechanics of Materials: A Modern Integration of Mechanics and > Materials in Structural Design (Christopher Jenkins & Sanjeev Khanna) > Mechanics of Materials (3th Ed., Beer) > Mechanics of Materials (5th Ed., Gere) > Mechanics of Materials (6th Ed., Gere) > Mechanics of Materials (Ugural) > Simplified Mechanics and Strength of Materials (6th Ed., James > Ambrose) > Engineering Mechanics, Statics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics, Dynamics, 2nd Ed (William F. Riley, Leroy D. > Sturges) > Engineering Mechanics - Statics, 5th Ed (J. L. Meriam, L. G. Kraige) + > Ebook > Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige) > Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige) > Vector Mechanics for Engineers: Statics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Statics (8th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (7th Ed., Ferdinand P. Beer) > Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) > Statics: Analysis and Design of Systems in Equilibrium (Sheppard & > Tongue) > Dynamics: Analysis and Design of Systems in Motion (Sheppard & Tongue) > Statics and Mechanics of Materials: An Integrated Approach (2nd Ed., > Riley, Sturges & Morris) > Mechanics of Materials (6th Ed., Riley, Sturges & Morris) > Deformable Bodies and Their Material Behavior (Haslach & Armstrong) > Strength of Materials - Volume 1 : Elementary Theory and Problems > (Timoshenko) > Intermediate Mechanics of Materials, (1st Ed., Barber) > Elasticity (2nd Ed., J.R. Barber) + original Ebook > Elasticity: Theory, Applications, and Numerics (Martin Sadd) + > original Ebook > Elasticity in Engineering Mechanics (2nd Ed., Boresi) > Advanced Mechanics of Materials (6th Ed., Boresi) + Ebook > Engineering Mechanics: Dynamics (Boresi) > Metal Fatigue in Engineering (2nd Ed., Stephens, Fatemi & Fuchs) > Applied Mechanics for Engineering Technology (8th Ed., Keith M. > Walker) > Applied Fluid Mechanics (6th Ed., Mott) > Applied Strength of Materials (4th Ed., Mott) > Applied Strength of Materials (5th Ed., Mott) > Intermediate Dynamics for Engineers (Marcelo R.M & Crespo da Silva) > Engineering Mechanics - Statics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Statics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (4th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics - Dynamics (5th Ed., Anthony Bedford & Wallace > Fowler) > Engineering Mechanics: Statics (2nd Ed., Pytel) > Engineering Mechanics: Dynamics (2nd Ed., Pytel) > Engineering Mechanics: Statics (2nd Ed., Shames) > Engineering Mechanics: Statics (4th Ed., Shames) > Engineering £À£Àü.9f[Para gr aph].88 >... hello, i'm interested in Solutions Manual of Unit Operations of Chemical Engineering (7th Ed., McCabe & Smith) thank you very much. my email: semith8@hotmail.com === Subject: Algebra with root and Z_2[x]. Hello sir~ Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] has a root in Z_2[x] / . --------------------------------------------- x^4 + x + 1 is irreducible over Z_2. By Kronecker, x^4 + x + 1 has a root in Z_2[x] / . Anyway, this is not useful in my problem. Let f(x) = x + a in Z_2[x]. a is 0 or 1. so, f(x) has a root in Z_2. Let f(x) = x^2 + a.x + b in Z_2[x]. Sorry. I can't progress any more. so, I need your advice. === Subject: Re: Algebra with root and Z_2[x]. > Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] > has a root in Z_2[x] / . > If P(x) has degree 1, then P(x) = x + a, which has root. If P(x) has degree 2, then P(x) = x^2 + ax + b. Case x^2 + ax + 1 subcase x^2 + 1 = (x + 1)^2, has root. subcase x^2 + x + 1, has root x^2 + x + 1 x^4 + x^2 + 1 + x^2 + x + 1 + 1 If P(x) has degree 4, then P(x) = x^4 + ax^3 + bx^2 + cx + d. Case x^4 + ax^3 + bx^2 + cx + 1 subcase a = c = 0. Use previous results and (x^2 + bx + 1)^2 = x^4 + bx^2 + 1 ???? === Subject: Re: Algebra with root and Z_2[x]. > Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] > has a root in Z_2[x] / . > If P(x) has degree 1, then P(x) = x + a, which has root. > If P(x) has degree 2, then P(x) = x^2 + ax + b. > Case x^2 + ax + 1 > subcase x^2 + 1 = (x + 1)^2, has root. > subcase x^2 + x + 1, has root x^2 + x + 1 x^4 + x^2 + 1 + x^2 + x + 1 + 1 If P(x) has degree 4, then P(x) = x^4 + ax^3 + bx^2 + cx + d. > Case x^4 + ax^3 + bx^2 + cx + 1 > subcase a = c = 0. Use previous results and > (x^2 + bx + 1)^2 = x^4 + bx^2 + 1 ???? If f(x) = x^4 + x^2 + 1. a = x^2 + x + 1 + is a root of f(x). Because, f(a) = x^8 + x^2 + 1 + . Since (x^4 + x + 1)^2 = x^8 + x^2 + 1, f(a) = 0 + . so, a is a root of f(x) in Z_2[x] / . If f(x) = x^4 + x^3 + 1... If f(x) = x^4 + x^3 + x^2 + x + 1... complex... === Subject: Re: Algebra with root and Z_2[x]. has a root in Z_2[x] / . > If P(x) has degree 1, then P(x) = x + a, which has root. If P(x) has degree 2, then P(x) = x^2 + ax + b. Case x^2 + ax + 1 subcase x^2 + 1 = (x + 1)^2, has root. subcase x^2 + x + 1, has root x^2 + x + 1 x^4 + x^2 + 1 + x^2 + x + 1 + 1 If P(x) has degree 4, then P(x) = x^4 + ax^3 + bx^2 + cx + d. Case x^4 + ax^3 + bx^2 + cx + 1 subcase a = c = 0. Use previous results and (x^2 + bx + 1)^2 = x^4 + bx^2 + 1 ???? > (x^2 + rx + 1)(x^2 + sx + 1) = x^4 + rx^3 + x^2 + sx^3 + rsx^2 + sx + x^2 + sx + 1 = x^4 + (r + s)x^3 + rs.x^2 + (r + s)x + 1 Thus when a = c, use the results for degree 2. Cases left: x^4 + x^3 + bx^2 + 1 x^4 + bx^2 + x + 1 which upon examination, leaves x^4 + x^3 + 1 x^4 + x + 1 a = x^2 + 1; a^2 = x^4 + 1 = x; a^3 = x^3 + x; a^4 = x^2 a^4 + a + 1 = 0 > If f(x) = x^4 + x^2 + 1. > a = x^2 + x + 1 + is a root of f(x). > Because, f(a) = x^8 + x^2 + 1 + . Since (x^4 + x + 1)^2 = x^8 + x^2 + 1, > f(a) = 0 + . so, a is a root of f(x) in Z_2[x] / . > If f(x) = x^4 + x^3 + 1... > If f(x) = x^4 + x^3 + x^2 + x + 1... > complex... > === Subject: Re: Algebra with root and Z_2[x]. > Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] > has a root in Z_2[x] / . --------------------------------------------- > x^4 + x + 1 is irreducible over Z_2. > By Kronecker, x^4 + x + 1 has a root in Z_2[x] / . > Anyway, this is not useful in my problem. Let f(x) = x + a in Z_2[x]. > a is 0 or 1. > so, f(x) has a root in Z_2. Let f(x) = x^2 + a.x + b in Z_2[x]. > Sorry. I can't progress any more. > so, I need your advice. You have four possibilities: f(x) = x^2, f(x) = x^2 + x, f(x) = x^2 + 1, and f(x) = x^2 + x + 1. The first three have a root in Z_2 already. Now, take a = [x] in Z_2[x]/. Then a^2 + a + 1 = [x^2 + x + 1] and therefore (a^2 + a + 1)^2 = [x^4 + x^2 + 1] = [x^2 + x] = (a^2 + a + 1) + 1. So, a^2 + a + 1 is a root of x^2 + x + 1 in Z_2[x]/. Now, try the same approach with fourth degree polynomials. Jose Carlos Santos === Subject: Re: Algebra with root and Z_2[x]. > Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] > has a root in Z_2[x] / . > --------------------------------------------- > x^4 + x + 1 is irreducible over Z_2. > By Kronecker, x^4 + x + 1 has a root in Z_2[x] / . > Anyway, this is not useful in my problem. > Let f(x) = x + a in Z_2[x]. > a is 0 or 1. > so, f(x) has a root in Z_2. > Let f(x) = x^2 + a.x + b in Z_2[x]. > Sorry. I can't progress any more. > so, I need your advice. You have four possibilities: f(x) = x^2, f(x) = x^2 + x, f(x) = x^2 + 1, > and f(x) = x^2 + x + 1. The first three have a root in Z_2 already. Now, > take a = [x] in Z_2[x]/. Then a^2 + a + 1 = [x^2 + x + 1] and therefore (a^2 + a + 1)^2 = [x^4 + x^2 + 1] = [x^2 + x] = (a^2 + a + 1) + 1. So, a^2 + a + 1 is a root of x^2 + x + 1 in Z_2[x]/. Now, try the same approach with fourth degree polynomials. Oh, good idea. With fourth degree... I have 16 possibilities. I must examine 4 cases among 16 possibiliteis. Namely, f(x) = x^4 + x^3 + 1, x^4 + x^2 + 1, x^4 + x + 1, x^4 + x^3 + x^2 + x + 1. If f(x) = x^4 + x + 1, f(x) has a root in Z_2[x] / by Kronecker. so, I must examine 3 cases. Anyway, If f(x) = x^4 + x^3 + 1, Let a = 1 + . f(a) not in . then a is not root of f(x). Let a = x + . f(a) not in . then a is not root of f(x). Let a = (x + 1) + . f(a) not in . then a is not root of f(x). Let a = x^2 + . f(a) not in . then a is not root of f(x). ...... Maybe, this is drudgery. === Subject: Re: Algebra with root and Z_2[x]. > Prove that every polynomial of degree 1, 2, or 4 in Z_2[x] > has a root in Z_2[x] / . --------------------------------------------- > x^4 + x + 1 is irreducible over Z_2. > By Kronecker, x^4 + x + 1 has a root in Z_2[x] / . > Anyway, this is not useful in my problem. Let f(x) = x + a in Z_2[x]. > a is 0 or 1. > so, f(x) has a root in Z_2. Let f(x) = x^2 + a.x + b in Z_2[x]. > Sorry. I can't progress any more. > so, I need your advice. > You have four possibilities: f(x) = x^2, f(x) = x^2 + x, f(x) = x^2 + 1, > and f(x) = x^2 + x + 1. The first three have a root in Z_2 already. Now, > take a = [x] in Z_2[x]/. Then > a^2 + a + 1 = [x^2 + x + 1] > and therefore > (a^2 + a + 1)^2 = [x^4 + x^2 + 1] = [x^2 + x] = (a^2 + a + 1) + 1. > So, a^2 + a + 1 is a root of x^2 + x + 1 in Z_2[x]/. > Now, try the same approach with fourth degree polynomials. Oh, good idea. > With fourth degree... > I have 16 possibilities. > I must examine 4 cases among 16 possibiliteis. > Namely, f(x) = x^4 + x^3 + 1, x^4 + x^2 + 1, x^4 + x + 1, > x^4 + x^3 + x^2 + x + 1. Indeed. > If f(x) = x^4 + x + 1, f(x) has a root in Z_2[x] / by > Kronecker. > so, I must examine 3 cases. Anyway, > If f(x) = x^4 + x^3 + 1, > Let a = 1 + . f(a) not in . then a is not root of > f(x). > Let a = x + . f(a) not in . then a is not root of > f(x). > Let a = (x + 1) + . f(a) not in . then a is not > root of f(x). > Let a = x^2 + . f(a) not in . then a is not root > of f(x). Let a = x + . Then a^4 + a + 1 = 0, and, since _a_ is not 0, a^4(1 + 1/a^3 + 1/a^4) = 0 <=> 1 + 1/a^3 + 1/a^4 <=> (1/a)^4 + (1/a)^3 + 1 = 0. So, 1/a is a root of x^4 + x^3 + 1 = 0. Jose Carlos Santos === Subject: Re: Algebra with root and Z_2[x]. posting-account=-PngCgkAAAD2yUjosqWv1Nf1lkqWP4lp Gecko/20020408,gzip(gfe),gzip(gfe) > Prove that every polynomial of degree 1, 2, or 4 in Z 2[x] > has a root in Z 2[x] / . --------------------------------------------- > x^4 + x + 1 is irreducible over Z 2. > By Kronecker, x^4 + x + 1 has a root in Z 2[x] / . > Anyway, this is not useful in my problem. Let f(x) = x + a in Z 2[x]. > a is 0 or 1. > so, f(x) has a root in Z 2. Let f(x) = x^2 + a.x + b in Z 2[x]. > Sorry. I can't progress any more. > so, I need your advice. You have four possibilities: f(x) = x^2, f(x) = x^2 + x, f(x) = x^2 + 1, and f(x) = x^2 + x + 1. The first three have a root in Z 2 already. Now, take a = [x] in Z 2[x]/. Then a^2 + a + 1 = [x^2 + x + 1] and therefore (a^2 + a + 1)^2 = [x^4 + x^2 + 1] = [x^2 + x] = (a^2 + a + 1) + 1. So, a^2 + a + 1 is a root of x^2 + x + 1 in Z 2[x]/. Now, try the same approach with fourth degree polynomials. Oh, good idea. > With fourth degree... > I have 16 possibilities. > I must examine 4 cases among 16 possibiliteis. > Namely, f(x) = x^4 + x^3 + 1, x^4 + x^2 + 1, x^4 + x + 1, > x^4 + x^3 + x^2 + x + 1. If f(x) = x^4 + x + 1, f(x) has a root in Z 2[x] / by > Kronecker. > so, I must examine 3 cases. Anyway, > If f(x) = x^4 + x^3 + 1, > Let a = 1 + . f(a) not in . then a is not root of > f(x). > Let a = x + . f(a) not in . then a is not root of > f(x). > Let a = (x + 1) + . f(a) not in . then a is not > root of f(x). > Let a = x^2 + . f(a) not in . then a is not root > of f(x). > ...... > Maybe, this is drudgery. If f is reducible, then f = f 1 f 2, where f 1, f 2 have degrees 1,3 or 2,2. In the first case you are done, and in the second case you are also done because you have dealt with degree 2 already. So you can assume that f is irreducible. The best way to do this is to use the fact that there is only one isomorphism class of fields of order p^n for any prime p and any n>=1. Now Z 2[x] / and Z 2[x]/ are both fields of order 16, and hence isomorphic, from which you should be able to deduce the result. Derek Holt. === Subject: Re: 1^2 =3, Discovered > I am trying to make you understand that the traditional notion > that 1^2= 1, is not a reflection of the true nature of the number > one. What's the point of trying to make somebody understand something that is not true? The true nature of 1 is the multiplicative identity. The true nature of the ^ operator with integer on right side is product of left side that many times. Thus 1^2 means 1*1 (multiplying 1, 2 times). Since 1 is the multiplicative identity, 1*1 = 1. Thus a reflection of the true nature of 1 and the true nature of ^ is that 1^2=1. To say otherwise is to say a lie. Why do you want to convince people of lies?? Are you a lonely liar? You seek to recruit others to join you in your lying ways? Pehaps you should join Jehovahs Witness. They are full of liars!! You would have lots of company there. === Subject: Re: 1^2 =3, Discovered Quantum Geometry. The length or perimeter, of every possible natural number isosceles triple, is invariably and infinitely rational. -Aiya-Oba. === Subject: Re: 1^2 =3, Discovered <28382633.1195776047074.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=FH_Q0goAAAAJ5KtCX_meKSiqoRvUgwne SV1),gzip(gfe),gzip(gfe) On Nov 22, 7:00 pm, Anthony A. Aiya-Oba Hi mathematician, > > I have a problem and I can not solve it. I have the equation p (t) (t > is the time), and we know that p (t) = 0 for t = 0 and for t = Tp > p(T) = P. In every moment I can calculate for t p (t). > Then I got a quadratic function y = a * X ^ 2 + b + c * x, and for > this function, we know that for t = 0 , > the function is in point (X1, Y1), and for t = T in point (X2, Y2). > The question: > If the time changes for dt For example, if the time changes for 5 msec, how much will change X > and Y? > Anybody knows how the quadratic function y = a * X ^ 2 + b + c * x is > writing in parameterized representation? >Leo > I would like once again to make a description: We have a Parabole in 2D and we must follow these Parabole (between points (X1, Y1) And (X2, Y2), but the change of route, the function p (t) is known. It is also known that in t = T we reach the point (X2, Y2) And that we are in t = 0 at the point (X1, Y1) .Ich hope that the problem is now clear. Not very clear. I think what you're asking for is a parametric curve > x = x(t), y = y(t), such that y(t) = a x(t)^2 + b + c x(t), with > x(0) = X1 and x(T) = X2. There are lots of possible solutions, but > the simplest is > x(t) = X1 + (X2-X1) t/T > y(t) = a (X1 + (X2-X1) t/T)^2 + b + c (X1 + (X2-X1) t/T) > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada- Zitierten Text ausblenden - - Zitierten Text anzeigen - Hello Mr Israel A blend is used to smoothly connect two trajectory polynomials x1(t) and x2(t). It is assumed that x1(t) and x2(t) are also smooth functions. Let the blend start at point p1a and end at point p1b (Figure 4.1). These points have corresponding velocities v1a and v1b. The blend between the two polynomials x1(t) and x2(t) is designed in parametrized space with a new nondimensional time coordinate, .83[CapitalEth]=(t-ts+TAU)/(2*TAU) such that the blend occurs in the interval .83[CapitalEth] .81ü [0,1]. In Eq. 4.1 t is the time parameter, ts is the time at which the trajectories intersect and .83.84 is half the time allowed for switching between the two paths (Figure 4.1). Lloyd and Hayward approximate the two polynomials by linear paths during the transition interval, such that : x1(.83[CapitalEth] ) = b1 + m1*.83[CapitalEth] x2(.83[CapitalEth] ) = b2 + m2*.83[CapitalEth] A quintic polynomial could be used to generate a blend satisfying the above conditions. However, the quintic does not control the shape of the blend (that is, the path that it follows). To address this problem, Lloyd and Hayward blend x1(t) and x2(t) together using a convex average of the two polynomials. In addition, the average acceleration is minimized by adding a damping function, .83Ë(.83[CapitalEth]), that does not affect the end conditions of the blend. The blend function is defined as : x(.83[CapitalEth]) = x1(.83[CapitalEth]) +.83À(.83[CapitalEth])*(x2(.83[CapitalEth]) - x1(.83[CapitalEth])) -k*.83Ë(.83[CapitalEth])*vd(.83[CapitalEth]) where .83À(.83[CapitalEth] )= 6.83[CapitalEth]^5 -15.83[CapitalEth]^4 +10.83[CapitalEth]^3 .83Ë(.83[CapitalEth] )=.83[CapitalEth]^6 - 3*.83[CapitalEth]^5 + 3.83[CapitalEth]^4 -.83[CapitalEth]^3 v = m2 -m1 and k is the parameter that controls the amount of acceleration compensation to apply (constant=15/2). The resulting blend function is a sixth-order polynomial, if x1(t) and x2(t) are first-order polynomials. So, it means I have function of trajectory (X(.83[CapitalEth]), but I need this function between points p1a and p1b in Cartesian coordinate system. I send you picture. Leo === Subject: Re: HELP!!! for your answer! > and if it is possible can you tell me something about the Bases for > topology?for example;for 2 topology(T2 is finer than T1) what can i > say about the bases B1 and B2 ? > Having very limited time is also why your punctuation is extremely bad? Accordingly your post is hard to read. In addition your question seems ill stated. Please do better. === Subject: Introduction to Logic Solutios Manual I need a complete electronic solutions manual to Introduction to Logic by Irving M. Copi and Carl Cohen === Subject: Hilbert's Hotel Hilbert's Hotel is now always empty. Due to complaints from guests, that every time a new guest arrived, everybody and to wake up and go to another room, new room assignements are being made. After check out time, if there wasn't already infinitely many rooms available, then each guest would be asked to move from room n to room 2n. This way no matter how many guests arrived, they're still be room for more. === Subject: Re: Hilbert's Hotel posting-account=I_skQAoAAAC9gDWTfV0rKgAhSCFRNVYw Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > Hilbert's Hotel is now always empty. Due to complaints from guests, that every time a new guest arrived, > everybody and to wake up and go to another room, new room assignements > are being made. After check out time, if there wasn't already infinitely many rooms > available, then each guest would be asked to move from room n to room 2n. This way no matter how many guests arrived, they're still be room for > more. How about this strategy: On day 1, only place new guests in odd numbered rooms i.e. those whose numbers are equal to 1 mod 2. On day 2, only use rooms whose numbers are equal to 2 mod 4. On day 3, use rooms equal to 4 mod 8. On day n, use rooms equal to 2 ^ (n - 1) mod 2 ^ n. On any day, there is a (countable) infinity of rooms free and no one has to move ever. A lot of rooms will be wasted if guests don't typically stay for ever but does that matter? It would save on cleaning costs if the rooms were not reused. Se.87n .94 Leathl.97bhair === Subject: Re: Hilbert's Hotel > Hilbert's Hotel is now always empty. Due to complaints from guests, that every time a new guest arrived, > everybody and to wake up and go to another room, new room assignements > are being made. After check out time, if there wasn't already infinitely many rooms > available, then each guest would be asked to move from room n to room 2n. This way no matter how many guests arrived, they're still be room for > more. Do they take Visa, or only American Express? === Subject: Solution manuals impair the growth of math. Hello sir~ My professor says before that solution manuals impair the growth of math. Are you agree ? Most math book does not include solution of exercise. What do you think the reason about it ? 1) Author is lazy. 2) For the growth of math for students. 3) Tacit consent in math world. 4) Vogue in math world. 5) Book become bulky book. etc... === Subject: Re: Solution manuals impair the growth of math. posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; .NET CLR 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) > Hello sir~ My professor says before that > solution manuals impair the growth of math. Are you agree ? > I agree that they deprive the student of vital practice if they are used to obtain the answers to exercises before working the exercises out oneself. === === Subject: #350 did Mueckenheim et al furnish an analogy? the set of all Primes is infinite because it contains Infinite Integers such as ....1110987654321 ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) > This is a _very_ common idea. Wolfgang Mueckenheim suggested it, as well as several others. I wonder if Mueckenheim furnished some analogy or plain talk to convince others. I hate to chase down an analogy only to find others have found one better. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #352 here are two analogies; did Mueckenheim et al furnish an analogy? the set of all Primes is infinite because it contains Infinite Integers such as ....1110987654321 ; new textbook: Mathematical Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years onward posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd Gecko/20021120 Netscape/7.01,gzip(gfe),gzip(gfe) > > This is a _very_ common idea. Wolfgang Mueckenheim suggested > it, as well as several others. > I wonder if Mueckenheim furnished some analogy or plain talk to > convince others. I hate to chase > down an analogy only to find others have found one better. > It is doubtful that Mueckenheim or others furnished any analogy to ease the mind into the thought that in order for a set to be an infinite set is that it must contain infinite numbers. So I make the analogy to Parallelism of straight lines in Euclidean geometry. If we find a truth in numbers, there should be the similar truth in geometry. So we have a straight line in Euclid geometry which goes to infinity and we have a point not on the straight line and we have line segments. And the first such line segment has length of the first prime of 2 and the second line segment is of length 3 and the third line segment is of length 5 and the fourth is of length 7 etc etc. Now are these ever increasing line segments parallel to the infinite line? Where Parallelism is switched for Being Prime, can we thus say the set of primes is infinite if they are all finite numbers? So in this analogy we instantly appreciate and see that every prime number was a Infinite Integer in that every prime number such as 2 was really 00000.....000002 and that the Primes also include 9999.....22212019181716151413121110987654321 and include 733333.....3333337 and include 9555555.....5555559 and include 311111.....111113. Because is Primes were only Finite Integers then your Euclidean axiom no longer holds since a line and a point not on that line has no parallel line since the primes can not produce a infinite line but only a finite line segment and we can never know if a finite line segment is really parallel unless it stretches all the way to infinity. So this Analogy of comparing Parallelism to Primeness tells us that the set of all Primes has to have Infinite Integers. Here is a Second Analogy, but it comes from physics so will not convince mathematicians but will perk the minds of physicists and mathematicians. The Atom Totality Theory posits that the entire Cosmos is just one big atom of plutonium where dots of the electron-dot-cloud are galaxies and where the Nucleus is located nearby the Great Attractor and Great Wall and Sloan Great Wall of galaxies. Now within an individual atom plucked out at random in the Cosmos that individual atom has a geometry of infinity in that the Electric Potential of Maxwell's theory goes to infinity. It does not terminate but reaches to infinity. So each atom of the Cosmos goes to infinity and has a characteristic of infinity. So, the logical question is can you have a Universe or Cosmos that does not go to infinity, whilst elements of that Cosmos go to infinity? Obviously the answer is no. That you cannot have a part of the Cosmos that is infinite in reach and not have the Cosmos itself infinite. This argument is also a good argument that the Universe is an atom since atoms stretch to infinity. So above I have given two logical analogies that simply say that a set that is an infinite reaching set, must have elements which are infinite elements. So the old foggy and fogy and fogey math of finite integers died in the 1990s and either went to heaven or went to hell depending on how long that corrupt and fake concept remains in science and math. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === === Subject: Could a tetration function exist? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; .NET CLR 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) Hi. I was wondering about this method of approach to the problem of tetration. Could a function for tetrating to real towers actually exist? The method I had was to dream up a list of properties that would seem intuitively reasonable until one has a set of such properties that only one function satisfies it, and that would be the extension of tetration. I'd start off with working on ^x b where x and b are real numbers greater than or equal to one. Things get tricky with b (base) values that are less than one. Then, a function f(b, x) generalizes tetration if it satisfies these properties: 1. f(b, x) satisfies the recurrence relation f(b, x+1) = f(b, x). 2. f(b, 1) = b. 3. f(b, x) is infinitely differentiable everywhere (perfectly smooth) in both x and b. 4. f(b, x) increases strictly monotonically with respect to x, as do all it's derivatives with respect to x. 5. For every x, there exists a T such that f(f(b, T), x) = b. (ie. the tetraroot of b exists and can be extracted via tetration.) So now, the question is, does a function of real x and b, both greater than or equal to one, satisfying the above 5 properties exist? If so, what is it, and is it unique? === Subject: Re: Could a tetration function exist? > Hi. I was wondering about this method of approach to the problem of > tetration. Could > a function for tetrating to real towers actually exist? The method I > had was to dream > up a list of properties that would seem intuitively reasonable until > one has a set > of such properties that only one function satisfies it, and that would > be the extension > of tetration. I'd start off with working on ^x b where x and b are real numbers > greater than or > equal to one. Things get tricky with b (base) values that are less > than one. Then, > a function f(b, x) generalizes tetration if it satisfies these > properties: 1. f(b, x) satisfies the recurrence relation f(b, x+1) = f(b, x). > I guess you mean: f(b,x+1) = b^f(b,x) > 2. f(b, 1) = b. 3. f(b, x) is infinitely differentiable everywhere (perfectly smooth) > in both x and b. Everywhere may be too much. How about b>1 for starters? And for b too large, you end up with negative, then imaginary when x gets too negative, which you probably don't want. 4. f(b, x) increases strictly monotonically with respect to x, as do > all it's derivatives > with respect to x. at least for x large enough, say x>1 or something. Or maybe the start of monotonicity varies depending on which derivative. 5. For every x, there exists a T such that f(f(b, T), x) = b. (ie. the > tetraroot of b > exists and can be extracted via tetration.) > and this requirement is crazy! > So now, the question is, does a function of real x and b, both greater > than or > equal to one, satisfying the above 5 properties exist? If so, what is > it, and is it > unique? Find a lot more by searching this group (for example at > Marek Kuczma: Functional Equations in a Single Variable > Monografie Matematyczne 46, Warsaw 1968 > æFor the equation > (*) æ æ æ æ æ æ æf^2(x) = e^x, > a real analytic solution has been found by H. Kneser. > This solution, however, is not single-valued (Baker) > and, as pointed out by G. Szekeres, there is no > uniqueness attached to the solution. It seems reasonable > to admit f(x)=F^(1/2)(x), where F^u is the regular > iteration group of æg(x)=e^x, as the best solution of > the equation (*) (best behaved at infinity). However, > we do not know whether this solution is analytic for > x>0. > [Kuczma defines and discusses regular iterations at > infinity in Chapter IX, Sec 5.] > Baker, I.N.: The iteration of entire transcendental > æfunctions and the solution of the functional equation > æf(f(z))=F(z), Math. Ann. 120(1955), pp. 174-180 > Kneser, H.: Reele analytische Loesungen der Gleichung > æf(f(x))=e^x und verwandten Funktionalgleichungen, > æJ. reine angew. Math. 187(1950), pp. 56-67 > Szekeres, G.: Fractional iterations of exponentially > growing functions, > æJ. Australian Math. Soc. 2(1961/62), pp. 301-320 -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Could a tetration function exist? 1. f(b, x) satisfies the recurrence relation > f(b, x+1) = f(b, x). > that's a periodic function ? why do you use that ? seems more like sin(x/2pi)^b then tetration ... since when do we associate periodic functions with tetration ? tommy1729 === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad posting-account=obCvlwoAAACRa2lwY9-1fJv7UyLLPmAH InfoPath.2),gzip(gfe),gzip(gfe) > Making the assumption that the key is uniform and C is fixed is equivalent to making the assumption that the plaintext is uniform. > -----yes,but it is useless to slove any problem. > > You claim that > > when only considering key is uniform and c is fixed > > you can show that the plaintext is uniform. > > However, we note from above that this is equivalent to > > when considering that the plaintext is uniform > > you can show that the plaintext is uniform. > > - William Hughes > the results are the same ,but consequence is not the same.cause and effect change. Your claim is that the two assumptions are equivalent > but the consequence of making one assumption is not the > same as the consequence of making the other assumption? - William Hughes- ñ[Thorn].b2¯±È[Ca pitalOGrave][YAcute]îÌë[CapitalA DoubleDot][Times].85 - - ìïæ.beñ[YAcute] îÌ[Micro]Äë[C apitalADoubleDot][Times].85 - in one assumption,the plaintext is uniform is cause, and in another the plaintext is uniform is effect === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Making the assumption that the key > is uniform and C is fixed is equivalent to > making the assumption that the plaintext is > uniform. > > -----yes,but it is useless to slove any problem. > You claim that > when only considering key is uniform and c is fixed > you can show that the plaintext is uniform. > However, we note from above that this is equivalent to > when considering that the plaintext is uniform > you can show that the plaintext is uniform. > - William Hughes > > the results are the same ,but consequence is not the same.cause and > effect change. > Your claim is that the two assumptions are equivalent but the consequence of making one assumption is not the same as the consequence of making the other assumption? > - William Hughes- ñ[Thorn].b2¯±È[Ca pitalOGrave][YAcute]îÌë[CapitalA DoubleDot][Times].85 - > - ìïæ.beñ[YAcute] îÌ[Micro]Äë[C apitalADoubleDot][Times].85 - in one assumption,the plaintext is uniform is cause, and in another > the plaintext is uniform is effect I see. If you have the equation y = x + 5 you draw a distinction between making the assumption that x = 2, in which case x=2 is a cause and y=7 is an effect, and making the assumption y=7. in which case y=7 is a cause and x=2 is an effect. I would claim that the assumptions x=2 and y=7 are equivalent. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/20070725 Firefox/2.0.0.6,gzip(gfe),gzip(gfe) > Making the assumption that the key > is uniform and C is fixed is equivalent to > making the assumption that the plaintext is > uniform. > > -----yes,but it is useless to slove any problem. > You claim that > when only considering key is uniform and c is fixed > you can show that the plaintext is uniform. > However, we note from above that this is equivalent to > when considering that the plaintext is uniform > you can show that the plaintext is uniform. > - William Hughes > > the results are the same ,but consequence is not the same.cause and > effect change. > Your claim is that the two assumptions are equivalent but the consequence of making one assumption is not the same as the consequence of making the other assumption? > - William Hughes- ñ[Thorn].b2¯±È[Ca pitalOGrave][YAcute]îÌë[CapitalA DoubleDot][Times].85 - > - ìïæ.beñ[YAcute] îÌ[Micro]Äë[C apitalADoubleDot][Times].85 - in one assumption,the plaintext is uniform is cause, and in another > the plaintext is uniform is effect Sorry to jump back into this discussion I wanted to have left long ago, but -- can you please define the notion of cause and effect in this context? === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad posting-account=obCvlwoAAACRa2lwY9-1fJv7UyLLPmAH InfoPath.2),gzip(gfe),gzip(gfe) > Making the assumption that the key is uniform and C is fixed is equivalent to making the assumption that the plaintext is uniform. > -----yes,but it is useless to slove any problem. > > You claim that > > when only considering key is uniform and c is fixed > > you can show that the plaintext is uniform. > > However, we note from above that this is equivalent to > > when considering that the plaintext is uniform > > you can show that the plaintext is uniform. > > - William Hughes > the results are the same ,but consequence is not the same.cause and effect change. Your claim is that the two assumptions are equivalent > but the consequence of making one assumption is not the > same as the consequence of making the other assumption? - William Hughes- ñ[Thorn].b2¯±È[Ca pitalOGrave][YAcute]îÌë[CapitalA DoubleDot][Times].85 - - ìïæ.beñ[YAcute] îÌ[Micro]Äë[C apitalADoubleDot][Times].85 - result is the same, you use equivalent, the word is not proper. === Subject: Re: Multilateration with 3 receivers posting-account=qlb0CwoAAADCEuLqa5o9vjtvqi7-FncY Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > cannot get the maths to work. I know that normally multilateration uses 4 receivers, but when you know one of the lenghts, usually depth or hieght, you can use 3. The only real resource I have found is in wikipedia, but they just say solve for the unknown target location. Ive been trying to solve it, but cannot. Does anyone know of any better resources I can get my teeth into? > Phil Winder Bump! For all those people searching in the future, I never did find an answer to the analytical solution mainly because it has lots of nasty square roots (which the solution could have errors anyway) so I went for a numerical method. Using matlabs FMINSEARCH function, i created the two TDOA equations in a seperate function that both square and add as an error. Pass the error variable back to the fminsearch function and it will find a solution. Phil Winder === Subject: Locally Lipschitz at boundary posting-account=KMurQQkAAACkDDGELZpG-7yQAg7fSfzi Gecko/20061201 Firefox/2.0.0.6 (Ubuntu-feisty),gzip(gfe),gzip(gfe) Let's say I have an ODE which I can prove is locally Lipschitz on (0, infty) giving local existence and uniqueness on (0, infty). What I actually want to prove is local existence and uniqueness on [0, infty), but it makes no sense to speak of being locally Lipschitz on an interval which is not open (because 0 has no neighbourhood in [0, infty)). One example might be the following system (so now we mean (0, infty)^2 of course as our locally Lipschitz domain): da/dt = -a / (a + b) + b / (a + b); db/dt = a / (a + b) - b / (a + b); where the fractions are taken to be 0 where they would otherwise be undefined. What is the usual way of dealing with such situations? Richard. === Subject: Re: How to calculate factorial of fractions? posting-account=7reEUQoAAADPec9tkt-M5k8UrEn3Uifh CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I have seen several posts as to how to calculate factorial of > fractions like using gamma method. Can any one explain it using any > approximation such as sterling's?. I am able to calculate half > fractions using gamma but not the other fractions. > For example (3.142)! Have a look at Peter Luschny's page Approximation Formulas for the Factorial Function n! http://www.luschny.de/math/factorial/approx/SimpleCases.html All formulas given there are also valid for non-integer arguments n. Hugo Pfoertner === Subject: Re: How to calculate factorial of fractions? posting-account=5X7MGQoAAABRnasWHDVTU338LKjZEH5J InfoPath.2; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I have seen several posts as to how to calculate factorial of > fractions like using gamma method. Can any one explain it using any > approximation such as sterling's?. I am able to calculate half > fractions using gamma but not the other fractions. For example (3.142)! My PASCAL program to calculate 1/Gamma, Gamma, Beta, Factorial and Binom type float=extended; function ammag(x:float):float; const g:array [0..26] of float=(0,1, 0.57721566490153286060651209, -6.5587807152025388e-1,-4.200263503409524e-2, 1.6653861138229149e-1,-4.219773455554434e-2, -9.62197152787697e-3,7.21894324666310e-3, -1.16516759185906e-3,-2.1524167411495e-4, 1.2805028238812e-4,-2.013485478079e-5, -1.25049348214e-6,1.13302723198e-6, -2.0563384170e-7,6.11609510e-9,5.00200764e-9, -1.18127457e-9,1.0434267e-10,7.78226e-12, -3.69680e-12,5.1004e-13,-2.058e-14, -5.35e-15,1.23e-15,-1.2e-16); var p,q,r:float; i:integer; begin p:=1; q:=1; r:=1; while x>=2 do begin x:=x-1; q:=q*x; end; while x<1 do begin r:=r*x; x:=x+1; end; if x>1 then begin p:=0; for i:=26 downto 0 do p:=p*x+g[i]; end; result:=p/q*r; end; function gamma(x:float):float; begin gamma:=1/ammag(x); end; function beta(x,y:float):float; begin beta:=ammag(x+y)/ammag(x)/ammag(y); end; function fact(x:float):float; begin fact:=gamma(x+1); end; function binom(x,y:float):float; begin result:=ammag(x-y+1)*ammag(y+1)/ammag(x+1); end; === Subject: R^R = aleph_1 N = aleph_0 R = aleph_1 R ^ N = aleph_1 the above is well known R ^ R = aleph_1 proof or disproof this is intresting to both cantorians and anticantorians so everyone intrested into set theory should consider this. and since ^ stands for dimension , people intrested in dimension should consider this too. note that R ^ R = aleph_2 is insufficient to disproof R ^ R = aleph_1 unless you can also prove aleph_2 =/= aleph_1 if both cantorians and anticantorians agree on R ^ R then we might evolve to a meaningfull debate about modern set theory, since we can both refer to something we both accept. it might lead to constructive conversations. if you ignore this thread or post off topic stuff like insults only , you should be ashamed of yourself and you do not deserve to call yourself a cantorian nor anticantorian ... since you have nothing meaningfull to say to defend your vision(s). (no offense to people into more exotic set theories) tommy1729 === Subject: Re: R^R = aleph_1 <7661144.1195820353559.JavaMail.jakarta@nitrogen.mathforum.org>, > N = aleph_0 > R = aleph_1 assuming the Continuum Hypothesis > R ^ N = aleph_1 the above is well known R ^ R = aleph_1 proof or disproof In standard set theory, R ^ R >= 2 ^ R > R, so the answer is no. I have nothing to say about the anticantorian case. this is intresting to both cantorians and anticantorians so everyone intrested into set theory should consider this. > === Subject: Re: R^R = aleph_1 A N Niel a .8ecrit : > <7661144.1195820353559.JavaMail.jakarta@nitrogen.mathforum.org>, N = aleph_0 > R = aleph_1 assuming the Continuum Hypothesis R ^ N = aleph_1 > the above is well known > R ^ R = aleph_1 > proof or disproof In standard set theory, R ^ R >= 2 ^ R > R, > so the answer is no. I have nothing to say about the > anticantorian case. It is unbelievable some people still answer to this crank/troll/moron (pick your choice) this is intresting to both cantorians and anticantorians > so everyone intrested into set theory should consider this. > === Subject: Re: x^x is not an integer for x not integer > I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? > Xan. Really, suppose that x > 0. >That is: x^x is not an integer if x > 0 is not an integer People have given hints, and (curiously) given decimal _approximations_ to counterexamples, but I don't see any clear proof of why this is simply wrong. Here it is: Let f(x) = x^x for x > 0. Then f is continuous, f(1) = 1 and f(2) = 4. Hence there exists x between 1 and 2 such that x^x = 2. ************************ David C. Ullrich === Subject: Re: x^x is not an integer for x not integer > I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? Xan. > Really, suppose that x > 0. > That is: x^x is not an integer if x > 0 is not an integer People have given hints, and (curiously) given decimal > _approximations_ to counterexamples, but I don't see any > clear proof of why this is simply wrong. Here it is: Let f(x) = x^x for x > 0. Then f is continuous, f(1) = 1 > and f(2) = 4. Hence there exists x between 1 and 2 such > that x^x = 2. Virgil had already posted this proof. Jose Carlos Santos === Subject: Re: x^x is not an integer for x not integer posting-account=rltBVQkAAABzJdnKp0dFuDqa5xCvlbif Gecko/20061201 Firefox/2.0.0.8 (Ubuntu-feisty),gzip(gfe),gzip(gfe) > I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? Xan. > Really, suppose that x > 0. That is: x^x is not an integer if x > 0 is not an integer People have given hints, and (curiously) given decimal > _approximations_ to counterexamples, but I don't see any > clear proof of why this is simply wrong. Here it is: Let f(x) = x^x for x > 0. Then f is continuous, f(1) = 1 > and f(2) = 4. Hence there exists x between 1 and 2 such > that x^x = 2. ************************ David C. Ullrich For the Mean Value Theorem and other reasoning, yes, we have that it's false. And really, we have that there are infinitely many (irrational) x such that x^x is an integer! Sorry: I could not see it Xan. === Subject: Re: x^x is not an integer for x not integer mike3 a .8ecrit : > I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? > Xan. > Really, suppose that x > 0. > That is: x^x is not an integer if x > 0 is not an integer > That's obviously false. > For example, x^x = 2 has the real solution x = 1.55961044... > David This makes me wonder about a different hypothesis. > x^x is not an integer for any non-integer, *rational* x > 0. True. If (p/q)^(p/q)=n, we have p/q= n^(q/p). If p/q is irreducible, this implies n must be a perfect p-power (n =m^p) and th equality becomes p/q=m^q, so q=1... === Subject: Re: x^x is not an integer for x not integer posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; .NET CLR 2.0.50727; CNPVersion2 - Congoo NetPass),gzip(gfe),gzip(gfe) On Nov 22, 10:56 pm, Denis Feldmann mike3 a .8ecrit : I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? > Xan. > Really, suppose that x > 0. > That is: x^x is not an integer if x > 0 is not an integer > That's obviously false. > For example, x^x = 2 has the real solution x = 1.55961044... David > This makes me wonder about a different hypothesis. x^x is not an integer for any non-integer, *rational* x > 0. True. If (p/q)^(p/q)=n, we have p/q= n^(q/p). If p/q is irreducible, > this implies n must be a perfect p-power (n =m^p) and th equality > becomes p/q=m^q, so q=1... === Subject: Re: x^x is not an integer for x not integer >mike3 a .8ecrit : > I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? > Xan. > Really, suppose that x > 0. > That is: x^x is not an integer if x > 0 is not an integer > That's obviously false. > For example, x^x = 2 has the real solution x = 1.55961044... David This makes me wonder about a different hypothesis. > x^x is not an integer for any non-integer, *rational* x > 0. True. If (p/q)^(p/q)=n, we have p/q= n^(q/p). If p/q is irreducible, >this implies n must be a perfect p-power (n =m^p) and th equality >becomes p/q=m^q, so q=1... An alternative proof: Assume (p/q)^(p/q) = n where p,q, n are positive integers and p,q are relatively prime. (p/q)^(p/q) = n => p^p = (n^q) (q^p) => q divides p^p => q = 1 quasi === Subject: Re: x^x is not an integer for x not integer posting-account=mYmveAoAAAA6m8p7tyKTuI-_Mp56JWnf Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) I want to prove that x^x is not an integer if x is not an integer, > but I don't know how > Any hint? Xan. And I would like to prove that every even integer larger than 2 is the sum of two primes, but I don't know how Any hint? Aktivated Aktivator === Subject: Re: x^x is not an integer for x not integer I want to prove that x^x is not an integer if x is not an integer, but I don't know how Any hint? Xan. > Really, suppose that x > 0. > That is: x^x is not an integer if x > 0 is not an integer That's obviously false. For example, x^x = 2 has the real solution x = 1.55961044... David This makes me wonder about a different hypothesis. > x^x is not an integer for any non-integer, *rational* x > 0. Yes, of course. Moreover, by Gelfond-Schneider, it is not an integer for any irrational algebraic x. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: x^x is not an integer for x not integer This makes me wonder about a different hypothesis. > x^x is not an integer for any non-integer, *rational* x > 0. See if you can prove it... write x = p/q in lowest terms, expand, use unique factorization, get contradiction. === Subject: a rabbits problem fibonacci like m(0) = 17 f(0) = 23 m(i) = 5 m(i-1) + 4 m(i-2) - m(i-3) + 3 f(i) + 2 f(i-1) + 7 f(i-2) f(i) = 7 f(i-1) + 5 f(i-2) - f(i-3) + 8 m(i) + 3 m(i-1) + m(i-2) tommy1729 ps m = male and f = female :) === Subject: Re: a rabbits problem posting-account=8gN6GAoAAADodAxKy9eNVOdtaDtGQLgv Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > fibonacci like m(0) = 17 > f(0) = 23 m(i) = 5 m(i-1) + 4 m(i-2) - m(i-3) + 3 f(i) + 2 f(i-1) + 7 f(i-2) f(i) = 7 f(i-1) + 5 f(i-2) - f(i-3) + 8 m(i) + 3 m(i-1) + m(i-2) tommy1729 ps m = male and f = female :) so, what is the problem === Subject: Re: a rabbits problem posting-account=iBgNeAoAAADRhzuSC4Ai7MUeMmxtwlM7 Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > fibonacci like > m(0) = 17 f(0) = 23 > m(i) = 5 m(i-1) + 4 m(i-2) - m(i-3) + 3 f(i) + 2 f(i-1) + 7 f(i-2) > f(i) = 7 f(i-1) + 5 f(i-2) - f(i-3) + 8 m(i) + 3 m(i-1) + m(i-2) > tommy1729 > ps m = male and f = female :) so, what is the problem You know what the problem is, kundan. === Subject: Re: Prove: Quadratic Non-Residue! Any ideas??? === Subject: Re: Prove: Quadratic Non-Residue! posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/20070725 Firefox/2.0.0.6,gzip(gfe),gzip(gfe) > Any ideas??? QED!!! === Subject: Find the equivalent intersection point of multi lines in 3D space Find the equivalent intersection point of multi lines in 3D space. HI everyone, I'm not a native english speaker, so I wonder you could understand my question very well. This question originates from my physics experiments. When I catch several lights from my equipment, the light source is far away, so I should caculate the position of the equivalent light source. This comes the post title. Normally, all these light lines were skew each other. For two lines, this is very simple to get the answer, because we can easily define the equivalent point as the mid-point of the shortest distance of the two lines. Several algorthms can be found by Google. For more then two lines, How can I do? I have dig into some math stuff about linear algebra or algebra geometry. Each lines can be constrined by two equations of plans.like Ax+By+Cz=D. so, as n lines, we can get 2*n equations. Now, I wonder the best root of these equations. Normally, the least square method could be used, but I don't think this could applied to my case. The criterion is different, maybe, I want to find the point that the sum of distance to those lines are minimun. But this make the prolems get more complex to solve. Does anybody coulde give me some ideas to solve this? All what I want to is to get the equivalent point. I'd appreciate your reply! THANKS! === === Subject: hi posting-account=xDIs1QoAAAAcRMKbET2kH1Wu6K8x7ecX 2.0.50727; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) I really need The Science and Engineering of materials solution manual by askeland please send me manual. === Subject: Re: tommy's division...a halting problem <23907329.1195665746581.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.11~pre071022-0etch1),gzip(gfe),gzip(gfe) with * i meant ordinary multiplication > and with '*' i meant tommy devision. Learn to spell, you moron. > sorry if its confusing. Learn to use contractions properly, you moron. > but its what you hoped for :) Learn to use contractions properly, you moron. > sorry for the misunderstanding. Not sorry enough to learn from your multiple mistakes, you moron. ( all in the frame of solving equations and galois theory ) > galois theory is used to decide if e.g. a real part of an equation can be given in root form. Capitalize the proper name Galois, you moron. properly, or don't use them at all, you moron. > log(a/b) gives problems too. > and log(a/b) = log(a) - log(b) > log(a/b) = A ; log(a) = B ; - log(b) = C > and A = B + C has zerodivisor problems. > i have given more details of this in the past. Capitalize i, you moron. > but dont worry about it now. > ill get back to it later ; its not so important ( at the moment ) Learn to use contractions properly, you moron. > it is no weakness of polysigned ; rather of all dimensional numbers ; it cannot be fixed or avoided... You're education in English was pathetic. Or were you just a poor > student? After all these years, you're still a moron. I don't recall many interactions with nihilist but this is a fine instance of an American debate; no content. Sorry Tommy to go so tangential but I'm going to. After going to all of the trouble of reading the post zero informational input has been introduced. We are creating enemies faster than we can destroy them Is the text of a bumper sticker that I used to wear stuck to the back of one of my shirts. This is somewhat like the media conversation after 9/11/2001. No content was provided as to why these people would do what they did. Merely label them enemies and attack them back and then some. We already won the arms race yet now the race continues in a David and Goliath sort of battle. Even now six years later no such conversation has taken place as to the material motivations of 9/11/2001. Fortunately on the topic of Iran such a debate is happening and the powers that be have decided to allow this level of truth, though I can say that only CSPAN seems to carry this signal. They still dodge the hostage crisis when Iran held spies prisoner. These stories bleed into each other since that crisis gave Carter his bad name and hoisted Reagan even while the Iran/Contra coverup was such an obvious system of lies. Iran's relations with the United States became deeply antagonistic during the revolution. On November 4, 1979, Iranian students seized US embassy personnel, labeling the embassy a den of spies.[61] They accused its personnel of being CIA agents plotting to overthrow the revolutionary government, as the CIA had done to Mohammad Mossadegh in 1953. - http://en.wikipedia.org/wiki/Iran Tens of thousands of Iranian civilians and military personnel were killed when Iraq used chemical weapons in its warfare. Iraq was financially backed by Egypt, the Arab countries of the Persian Gulf, the Soviet Union and the Warsaw Pact states, the United States (beginning in 1983), France, the United Kingdom, Germany, Brazil, and the People's Republic of China (which also sold weapons to Iran). - http://en.wikipedia.org/wiki/Iran How do we come to destroy the people we once supported e.g. the Taliban and Iraq's Baathist regime? These are instances of the ambiguity that the USFG (or should I say the USSA?) faces. These problems are larger than the Bush administration by many decades so both parties have to answer why to a trail of injustice that stretches back to the second world war. The simple solution to discovering the next step is simply for the US to step down from its hyper-active position in the world and engage the UN as much as possible, but when we consider that US actions beyond its now Sovietized border are largely covert then we have an answer to why the US cannot recognize the ICC which is a creation of the UN; when these unknown deeds come to light then I predict that the US will fall even more deeply than it has already fallen. Such information is valuable and likely in use behind the curtain which helps explain some of the wriggling which is going on right now. Noone wants to see chaos within a superpower with 10,000 nuclear warheads and countless systems of destruction funded by half of the countries exorbitant revenues. So the tidbits that lead in trails back in time have more than one meaning. If the full truth is exposed then the US will be exposed as acting in the world not on behalf of its citizens, but instead it will be shown that the US has acted badly in the world in the interest of a few powerful organizers. Can it be called organized crime if it is endemic to the system such that the system's own laws are flexed? Certainly it cannot be called a true democracy if this is the case. So we need to push for open government. They want our phone records and email and we want their backroom deals. Fine. Open up Uncle Sam, here comes a big bat. Uranium tipped for your pleaure... -Tim === Subject: Re: Characterising subrings of the complex numbers <473A22A1.600@math.uni-muenster.de> posting-account=GblQ2AoAAACb2_WQuHLJg33R6cM5WGVE Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) On 13 Nov, 22:18, linus kramer Is there a straightforward algebraic characterisation of thesubrings of thecomplexnumbers? Any such subring must be commutative, of characteristic 0, have 0=/=1, and be without zero divisors (so ab=0 implies a=0 or b=0). These are precisely the integral domains of characteristic 0 whose > cardinality is at most card(C). for a proof of this in the literature? === Subject: can anyone help out with this number quiz??? posting-account=UP86AwoAAAAzAmr5OcYaQpGi-dI5juTD .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) The question is as follows: Add the numbers seven plus twelve= 25+3x8= 14+2+21+7= :) === Subject: Re: can anyone help out with this number quiz??? > The question is as follows: Add the numbers seven plus > twelve= 25+3x8= 14+2+21+7= :) 19, 49 and 44. and their sum is 112. i used a calculator so its definitely correct. === Subject: f_x,f_y non-measurable , but f(x,y) measurable Suppose f(x,y) is a function, such that the x-sections and the y-sections of f: f_{x} and f_{y} are measurable what's a counterexample that f(x,y) is not a measurable function ? === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable The example in your subject is easy: Let v(t) be the indicator function on a nonmeasurable set on the real line. Then, define f(x,y) as followed: f(x, y) = { v(y) if x = 0, { v(x) if y = 0, { 0 otherwise. On 2007-11-23 04:08:42 -0500, jane said: > Suppose f(x,y) is a function, such that the x-sections and the > y-sections of f: f_{x} and f_{y} are measurable what's a counterexample that f(x,y) is not a measurable function ? This example is much harder. In the book Counterexamples in Analysis by Gelbaum & Olmsted, there is an example of a nonmeasurable plane set having at most two points in common with any line. Take the indicator function on this set. Perhaps someone else will have a much simpler example. -- -kira === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable > The example in your subject is easy: Let v(t) be the indicator function > on a nonmeasurable set on the real line. Then, define f(x,y) as followed: > f(x, y) = { v(y) if x = 0, > { v(x) if y = 0, > { 0 otherwise. Your function is measurable. And a suggestion: do not toppost. If you want to know what's that and why you shouldn't do it, read http://www.caliburn.nl/topposting.html or http://www.html-faq.com/etiquette/?toppost Jose Carlos Santos === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable On 2007-11-23 11:52:24 -0500, Jos.8e Carlos Santos said: The example in your subject is easy: Let v(t) be the indicator > function on a nonmeasurable set on the real line. Then, define f(x,y) > as followed: > f(x, y) = { v(y) if x = 0, > { v(x) if y = 0, > { 0 otherwise. Your function is measurable. Yea, I know. I was referring to the subject line: f_x,f_y non-measurable , but f(x,y) measurable And a suggestion: do not toppost. Well I was responding to her subject line and not to her body of the message. So, I thought it might be ok to put my response right below the subject line. > If you want to know what's that and > why you shouldn't do it, read http://www.caliburn.nl/topposting.html or http://www.html-faq.com/etiquette/?toppost > -- -kira === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable > The example in your subject is easy: Let v(t) be the indicator > function on a nonmeasurable set on the real line. Then, define > f(x,y) as followed: > f(x, y) = { v(y) if x = 0, > { v(x) if y = 0, > { 0 otherwise. > Your function is measurable. Yea, I know. I was referring to the subject line: f_x,f_y > non-measurable , but f(x,y) measurable OK. I had not noticed that the question from the subject line was a sort of the opposite of what the OP wanted. > And a suggestion: do not toppost. Well I was responding to her subject line and not to her body of the > message. So, I thought it might be ok to put my response right below > the subject line. I guess it makes sense. :-) Jose Carlos Santos === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable <29455905.1195826953390.JavaMail.jakarta@nitrogen.mathforum.org>, jane > Suppose f(x,y) is a function, such that the x-sections and the y-sections of > f: f_{x} and f_{y} are measurable what's a counterexample that f(x,y) is not a measurable function ? Here's a nice one (I think due to Sierpinski ?) assuming the continuum hypothesis. Let # be an ordering of R with order type of the first uncountable ordinal. Let f be the characteristic function of the set E = {(x,y) : x # y}. Then each cross-section in one direction is countable, but in the other direction each cross-section is cocountable. By Fubini, the set is not measurable. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable > <29455905.1195826953390.JavaMail.jakarta@nitrogen.math > forum.org>, jane > Suppose f(x,y) is a function, such that the > x-sections and the y-sections of f: f_{x} and f_{y} are measurable what's a counterexample that f(x,y) is not a > measurable function ? Here's a nice one (I think due to Sierpinski ?) > assuming the continuum > hypothesis. Let # be an ordering of R with order > type of the first > uncountable ordinal. Let f be the characteristic > function of the > set E = {(x,y) : x # y}. Then each cross-section in > one direction > is countable, but in the other direction each > cross-section is > cocountable. By Fubini, the set is not measurable. > -- > G. A. Edgar > http://www.math.ohio-state.edu/~edgar/ === Subject: Re: f_x,f_y non-measurable , but f(x,y) measurable > Suppose f(x,y) is a function, such that the x-sections and the > y-sections of f: f_{x} and f_{y} are measurable what's a counterexample that f(x,y) is not a measurable function ? Find a non-measurable subset A of the plane such that its intersection with every horizontal line and every vertical line is measurable and define _f_ as the characteristic function of A. Sierpinski found such a set; in fact, he constructed a non-measurable subset of R^2 that intersects each line in at most two points. A proof of the existence of a set with the property described at the previous paragraph is given in Section 16.5.1 of the book Set functions, by Hans Hahn and Arthur Rosenthal. Jose Carlos Santos === Subject: Re: Triangle with more than 180 degrees- Nntp-Posting-Host: hera.cwi.nl > That i tried to explain in my last letter. > Just practical, given two points their distance is taken between the > tips of a circle. Now let a line connect these two points. If the > middle between these two points does not lie on this line, the line > is not straight. > . It is less straight-forward then you think. To get the middle between two points, you need a straight line, so you can not define straight lines using the middle between two points. Or tell me how to get the middle of a point without using the concept of straight lines? > . > This is a nice problem. > Just for the definition of straight this would do already: No, it will not. > Given two points, draw a circle around one of them, which is cutting > through the other point. Without changing the circle, draw around the > other point intersecting the first circle, from this intersection > again without changing the circle draw a circle intersecting the first > circle, and one more time. Now this point and the given two points are > three points and one of them is in the middle between two of them. > That is doubling the distance, You say. Okay, but proceed a few steps > further on and one can find the middle between the first two points as > well, just using a circle. Perhaps it can be done, but I still do not see the definition of a straight line. If I want to distill a definition for that, I get: a line between two points is straight if its midpoint is on the line, and the two halves of the line are also straight. A recursive definition. But this all is a bit moot. Consider the following: take a function f: [0,1) -> [0,oo) that is monotonously increasing (x > y -> f(x) > f(y)), has f(0) = 0 and when x goes to 1, f(x) grows without bound. Now consider the inside of the unit circle in Euclidean 2D space. Define on it a distance as follows (using polar coordinates): given x = (r_x, phi_x) and y = (r_y, phi_i), d(x, y) = sqrt(f(r_x)^2 + f(r_y)^2 - 2.f(r_x).f(r_y).cos(phi_x - phi_y)). Define the straight lines as: a.f(r).cos(phi) + b.f(r).sin(phi) = c with any real a, b and c. You may check that this defines an Euclidean geometry on the inside of that circle. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: I think I have found it - two kinds of points that make up space posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.11~pre071022-0etch1),gzip(gfe),gzip(gfe) >[...] > > Math is not physics. > > How 'big' are your points? > >I guess you are asking me. They are as small as one can imagine, just >like an infinity is as large as one can imagine. Is it fine to talk >about infinity in Math? > Yes, that's fine. _if_ you know the math. The definition of infinity is _not_ as large as you can imagine. That may have something to do with the intuitive idea that developed into precise mathematical infinities, but as large as you can imagine is much too fuzzy to be a _mathematical_ notion. > There are in fact various notions of infinity in mathematics. For example, a set S is infinite, by definition, if it can be put into 1-1 correspondence with a proper subset of S. > Note that there's nothing about what we can or cannot imagine in the definition of S is infinite. It's certainly _not_ ok in math to define infinity to be as large as you can imagine. I agree, but I've used the term as large as you can imagine only to > make my point clear with brief talk, not really to define it. Also, > for the purpose of the topic under discussion, I think it is enough to > stick to the plain infinity that was imagined before the set theory > and Cantor. I have no calibre to doubt the great value of set theory > and Cantor's concepts. It is just that I thought we are applying them > even when we don't need them in this topic. - venkat Your concept of a point which does carry a minimal magnitude is alright. Rather than attempt to reconstruct the real line from it this principle should be followed out on its own behaviors. There is a natural form of exclusion here which can be induced by allowing such a singularities you already have coherence at a physical level. This is somewhat the exclusion principle. Reliance upon the real line may not be necessary to extend your crux. The issue of adjacency can allow you to extend immediately to a Planck sort of distance whether that distance be instantiated or not. Regardless of that distance's instantiation it will always be scalable based on the choice of what a unit distance is and so a specific number h can be taken as meaningless from the mathematicians perspective. If there is physical congruence with such a theory and it would seem that the physicist's usage of Planck's constant h is such a congruence, then all the better. In effect the declaration of this exclusive point on a continuum does suggest a smallest distance without the need for a lattice theory; the continuum can extend upward from such a magnitude. The invalidity is in a declaration of a zero magnitude for two adjacent points. This serves as a redefinition of space with a subtle modification and so to attempt to recover the real line is not desirable. Your construction in its native form without the second type of traditional point may be more productive than you realize. By taking this leap I think you introduce a new concept of adjacency which may then be investigated in higher dimensions. I don't see the way forward there directly but there may be some specific choices to make along the way and this will then structure higher dimension spaces under the choice to maximize a quantity of adjacent points or whatever structure is chosen. These constructions are not exactly lattice theories though they seem akin. -Tim === Subject: Re: I think I have found it - two kinds of points that make up space posting-account=bSICGQkAAADSbkxAJ5uMxFegr4rp0Qig rv:1.8.1.9) Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) >[...] > > Math is not physics. > > How 'big' are your points? > >I guess you are asking me. They are as small as one can imagine, just >like an infinity is as large as one can imagine. Is it fine to talk >about infinity in Math? > Yes, that's fine. _if_ you know the math. The definition of infinity is _not_ as large as you can imagine. That may have something to do with the intuitive idea that developed into precise mathematical infinities, but as large as you can imagine is much too fuzzy to be a _mathematical_ notion. > There are in fact various notions of infinity in mathematics. For example, a set S is infinite, by definition, if it can be put into 1-1 correspondence with a proper subset of S. > Note that there's nothing about what we can or cannot imagine in the definition of S is infinite. It's certainly _not_ ok in math to define infinity to be as large as you can imagine. I agree, but I've used the term as large as you can imagine only to > make my point clear with brief talk, not really to define it. Also, > for the purpose of the topic under discussion, I think it is enough to > stick to the plain infinity that was imagined before the set theory > and Cantor. You think it's better to go back to before anyone had established rigorous axioms which allowed reasoning about infinite things. You think that having something undefined is better. You think that what you want to say about points is better served by going back to a state before infinite was subject to reasoning also. Well, then as I've said, reasoning and mathematics are clearly not what you're interested in, and you're in the wrong forum. This is a forum for people interested in mathematics, and what we are interested in involves reasoning. If you want to make vague pronouncements of the type that are typically fueled by a couple of beers, there are many more of that sort of forum on Usenet than there are of this type of forum. - Randy === Subject: Re: I think I have found it - two kinds of points that make up space posting-account=YRJk-woAAABDjOj1Gx4VUCNw52xBfDaL IE 6.0 Build 20060616; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > >[...] > > Math is not physics. > > How 'big' are your points? > I guess you are asking me. They are as small as one can imagine, just like an infinity is as large as one can imagine. Is it fine to talk about infinity in Math? > > Yes, that's fine. _if_ you know the math. The definition of infinity > is _not_ as large as you can imagine. That may have something to > do with the intuitive idea that developed into precise mathematical > infinities, but as large as you can imagine is much too fuzzy to > be a _mathematical_ notion. > > There are in fact various notions of infinity in mathematics. > For example, a set S is infinite, by definition, if it can be > put into 1-1 correspondence with a proper subset of S. > > Note that there's nothing about what we can or cannot imagine > in the definition of S is infinite. It's certainly _not_ > ok in math to define infinity to be as large as you can > imagine. > I agree, but I've used the term as large as you can imagine only to make my point clear with brief talk, not really to define it. Also, for the purpose of the topic under discussion, I think it is enough to stick to the plain infinity that was imagined before the set theory and Cantor. You think it's better to go back to before anyone had > established rigorous axioms which allowed reasoning about > infinite things. You think that having something undefined > is better. You think that what you want to say about > points is better served by going back to a state before > infinite was subject to reasoning also. It is not to avoid the advances that are made over the time, or not to tell which is better. We just need to cut down the complexities that we don't really need in the specific context. The differences in infinities and choosing one or the other of them for this discussion is not really going change anything with the questions or answers. If you think otherwise, can you tell me how does it matter here? Even better, you choose own your infinity and I'll accept it and can still show my arguments mean the same with your infinity. - venkat === Subject: Re: I think I have found it - two kinds of points that make up space >[...] > Math is not physics. > How 'big' are your points? > I guess you are asking me. They are as small as one can imagine, just >like an infinity is as large as one can imagine. Is it fine to talk >about infinity in Math? > Yes, that's fine. _if_ you know the math. The definition of infinity > is _not_ as large as you can imagine. That may have something to > do with the intuitive idea that developed into precise mathematical > infinities, but as large as you can imagine is much too fuzzy to > be a _mathematical_ notion. > There are in fact various notions of infinity in mathematics. > For example, a set S is infinite, by definition, if it can be > put into 1-1 correspondence with a proper subset of S. > Note that there's nothing about what we can or cannot imagine > in the definition of S is infinite. It's certainly _not_ > ok in math to define infinity to be as large as you can > imagine. I agree, but I've used the term as large as you can imagine only to >make my point clear with brief talk, not really to define it. We need to speak more precisely in order to see why the point you were trying to make is simply invalid. Someone asked how big your points are. You said as small as you can imagine. _If_ we're trying to talk about _mathematics_ here, which evidently we are, then that's a totally useless answer. And you realized that it was not going to be accepted as a meaningful answer, so you tried to defend it by analogy with infinity. If in fact mathematical infinity _were_ defined to be as large as you can imagine then you'd have a valid analogy. But it's not. So you don't. _If_ you want people to react with anything other than laughter you _need_ to define things precisely. >Also, >for the purpose of the topic under discussion, I think it is enough to >stick to the plain infinity that was imagined before the set theory >and Cantor. I have no calibre to doubt the great value of set theory >and Cantor's concepts. It is just that I thought we are applying them >even when we don't need them in this topic. - venkat ************************ David C. Ullrich === Subject: Re: I think I have found it - two kinds of points that make up space > Reddy > On Nov 22, 8:32 pm, David C. Ullrich > Reddy > On Nov 21, 7:55 pm, malibu > On Nov 21, 8:45 am, David C. Ullrich >[...] Math is not physics. How 'big' are your points? > I guess you are asking me. They are as small as > one can imagine, just like an infinity is as large as one can imagine. > Is it fine to talk about infinity in Math? Yes, that's fine. _if_ you know the math. The > definition of infinity > is _not_ as large as you can imagine. That may > have something to > do with the intuitive idea that developed into > precise mathematical > infinities, but as large as you can imagine is > much too fuzzy to > be a _mathematical_ notion. There are in fact various notions of infinity in > mathematics. > For example, a set S is infinite, by definition, > if it can be > put into 1-1 correspondence with a proper subset > of S. Note that there's nothing about what we can or > cannot imagine > in the definition of S is infinite. It's > certainly _not_ > ok in math to define infinity to be as large as > you can > imagine. I agree, but I've used the term as large as you can > imagine only to make my point clear with brief talk, not really to > define it. We need to speak more precisely in order to see why > the point > you were trying to make is simply invalid. Someone > asked > how big your points are. You said as small as you > can imagine. > _If_ we're trying to talk about _mathematics_ here, > which > evidently we are, then that's a totally useless > answer. And you realized that it was not going to be accepted > as a > meaningful answer, so you tried to defend it by > analogy with > infinity. If in fact mathematical infinity _were_ > defined > to be as large as you can imagine then you'd have a > valid > analogy. But it's not. So you don't. _If_ you want people to react with anything other > than > laughter you _need_ to define things precisely. it seems you posted this thread already 3 times now !!! without answers apart from me or yourself seems people laugh or ignore you too ... somewhat pathetic ; your cry for attention, and not getting it. > Also, for the purpose of the topic under discussion, I > think it is enough to stick to the plain infinity that was imagined > before the set theory and Cantor. I have no calibre to doubt the great > value of set theory and Cantor's concepts. It is just that I thought we > are applying them even when we don't need them in this topic. - venkat > ************************ David C. Ullrich === Subject: Re: Number_Theory_Problem > border1.nntp.dca.giganews.com!border2.nntp.dca.giganews.com!nntp.giganews.co m !out02b.usenetserver.com!news.usenetserver.com!in01.usenetserver.com!news.us e netserver.com!spln!extra.newsguy.com!newsp.newsguy.com!news2 === > Subject: Re: Number_Theory_Problem > <5ISdnWkAJqo5-9nanZ2dnUVZ_qmlnZ2d@giganews.com pa4d2bfbfff000000ba09f95eb0b7339a45f8e100f78839be.newsdawg.com 9nanZ2dnUVZ_qmlnZ2d@giganews.com: > sorry: Find all positive number such that n^3 - 14n^2 + 64n - 93 is prime. Hint: What if n=3?. B. -- > Cheerfully resisting change since 1959. ------------ Braver ------------ === Subject: Re: Number_Theory_Problem > border1.nntp.dca.giganews.com!nntp.giganews.com!local01.nntp.dca.giganews.co m !news.giganews.com.POSTED!not-for-mail === > Subject: Re: Number_Theory_Problem > <5ISdnWkAJqo5-9nanZ2dnUVZ_qmlnZ2d@giganews.com X-Usenet-Provider: http://www.giganews.com > sv3-IH497wiW/hrk5qCbBYWqMoP4Jkxp41UxADnZ5A2Q68dSP9UIcKRmFD7C3nZKZd+XC+t+wNiw a PEtL/0!nQFfqTztwn5wgcz7Y4T1kL/FRnhpPs5ggB7gYTKBgLVLpQqRjdpsY8RBR18eqdeW3KjV8 e xM > complaint properly sorry: Find all positive number such that n^3 - 14n^2 + 64n - 93 is prime. I assume you mean n is a positive _integer_. Hint: Factor the polynomial n^3 - 14n^2 + 64n - 93 and then look at it again. quasi -------------- Braver ------------- === Subject: Re: Number_Theory_Problem === > Subject: Re: Number_Theory_Problem > <5ISdnWkAJqo5-9nanZ2dnUVZ_qmlnZ2d@giganews.com > posting-account=n7oCtQoAAACNS6CgW2a2eDoP2d9IRGfY > X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1; > .NET > CLR 1.1.4322),gzip(gfe),gzip(gfe) > Find all positive number such that n^3 - 14n^2 + 64n - 93 is prime. n^3 - 14n^2 + 64n - 93 = (n - 3)*(n^2 - 11n + 31) For the product to be prime, it is necessary - > but not sufficient - that one factor should > be +1 or -1. End of hint. > -- Sorry for bad statement. n = positive interger ----------- Braver ---------- === Subject: Vector subspaces exercise posting-account=13KbngoAAABfTatbRX9gGDZXi3iESPtC AppleWebKit/419.3 (KHTML, like Gecko) Safari/419.3,gzip(gfe),gzip(gfe) Hi all! Can you please check this exercise? Text: In R^4 you have this vectors: v1=(-1,2,0,-1) v2=(0,-1,3,3) v3=(1/2, -1/2, 1, 2) Find U and T: R=V+U R=V+T direct sum My solution: I created a matrix with v1,v2,v3,(1,0,0,0),(0,1,0,0),(0,0,1,0), (0,0,0,1) as column vectors in order to complete the basis of V=Span(v1,v2,v3) to the basis of R^4. I got these bases: v1,v2,v3, (1,0,0,0) So, T=Span{(1,0,0,0)} U=Span{(1,0,0,0), (-1,2,0,-1)} === Subject: www.200836.com---Beijing 2008 olympic pin official licensed product posting-account=wMezJwoAAABG1HLbZmi9Tnff7PulgCvJ TencentTraveler ; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) The website www.200836.com was aimed at that all the people in the world can buy Olympic souvenirs anywhere anytime The website www.200836.com was exclusively authorized by BOCOG to sell licensed products of the Beijing Olympics if you want to know any information about 2008 beijing Olympic games ,please contact me or visit : my website--www.200836.com MSN:feiallen@hotmail.com e-mail:sales@200836.com yahooID:feiallen@yahoo.com.cn QQ:846233546 Skype:a200836 ICQ:391836515 or leave your e-mail or msn-number or other contact methods we can e-mail our souvenirs-list to you === Subject: Re: zeno paradox. posting-account=i1MELAoAAADwo_-GGwN3NKKSXm8aSdBN SV1),gzip(gfe),gzip(gfe) > Now, if you stipulate that the fly needs > some fixed time to turn around, the question of the direction *can* be > answered (maybe it is just turning around at the time of collision). > In the latter case it is clear that in the original formulation there > are some things that are impossible in the real world (a fly turning > around in zero time). But certainly the time the fly takes to bounce on each locomotive can be made less than any given number; not an instant, however; that is, not a point-like time extension. So, an ideal fly that takes only an instant to rebound is logically impossible. I'd say this suggests that point-like extensions (whether spatial or temporal) must be banned. Then the matematical model seems to require, besides points and instants representing locations and not extensions, non point-like minimal extensions of time and space. For how long does a stone thrown upwards remain at the top of its trajectory? If point-like extensions are no longer available, it seems the new model requires infinitesimal (or non archimedean) quantities. === Subject: Re: second edition published >I heard today from Springer (New York) that the Second Edition of my >book, entitled Measure, Topology, and Fractal Geometry, in the Springer >Undergraduate Texts in Mathematics series, has now been published. The >U.S. list price is $49.95, European price 39.95 Euros. > Dr. Edgar, The first edition is my continuing reference. ( at half that price with shipping, ha, ha... ) My hope it that you go to seven editions. For me it is already a classic... Roger Bagula === Subject: Re: Riddle of the day > How long does it take to close an open set? There is no concept of time in mathematics. Things either are, or they are not, and they stay that way for all time. For example, if x=4, it will never happen that later on x=5! Now ... I have considered the possibility of adding time into mathematics. One of the advantages of this is that mathematics can sustain paradoxes. You could have two statements that contradict each other, but because they are superficially sufficiently different it takes a while for the contradiction to propogate. And by the time this does happen, one of the statements will have changed. In particular, all published papers should come with expiry dates. Stephen === Subject: Re: Riddle of the day posting-account=xU7PxwoAAAAIO2TPTOLSo9k8ZCVsMVSh Gecko/20071025 Firefox/2.0.0.9,gzip(gfe),gzip(gfe) > How long? How much time (temporal) implies increments of change on the object, not on the abstract building of the object-ie. algorithm? > does it take? What if it an infinite amount of time? > to close an open set? Is this a view of the object(read set), or is it a model representation? If it is an open set and it is a model representation then the openness property of the set is limited by the static state and the axiom building blocks. But if we look at the set as a view, then we see it outside the axiomatic description and are able to apply non-axiomatic viewpoints. But are we not then developing a new set then? Conclusion: The time it takes to close an open set is the amount of time it takes to realize that we are really only creating a new set through our point of view (whatever that is). === Subject: Re: Riddle of the day <18237296.1195741281782.JavaMail.jakarta@nitrogen.mathforum.org> Please cross post to alt.math.recreational as this post is. I read this thread there and usually not here. Had the thread not been short last night, I would have missed your post. Tonigh the thread was long and I would have missed your post except by good chance, I took note of your participation last night and though to look for you here (sci.math) before deleating the thread whole sale. How long does it take to close an open set? > For the empty set, zero seconds. > That's because it clopen and all clopen set close and open instantously. Yes, that is very intuitive. Let ( X, T ) be a topological space. Let us consider a map: t : T -> IR^+ We say that t ( A ) is the time we take to close the > open set A if and only if ... It would be interesting for t to have at least the following > properties: 1.- t ( A ) = 0 iff A is clopen 2.- t does not depends on people mathematical skills. > Generalizing t to all of P(S) for the space (S,tau) t(A) = 0 iff A closed In another post I've gone much farther with details. The upshot of it is to find some sort of measure for P(S). ---- === Subject: Re: Riddle of the day <87ve7u77v1.fsf@nonospaz.fatphil.org> Please don't keep us in suspense too long. > If I'm not mistaken, there's no such thing as retorically riddle. A consortium of elves with the assistance of a few hobbits have brough froth the riddle unto sci.math for consulation and insight. Apparently, some sets close quickly and some take longer. A fear that lurks is some may never close, ie take infinitely long to close. An example of this is the set { x in R : P(x) } where P(x) is an undeciable proposition about real numbers. Here's the most recent results of our efforts. Let (S,tau) be a topological space and for A subset S, let t(A) >= 0, be the time it takes to close A. Clearly when A is closed, t(A) = 0. We propose t(A) = 0 iff A closed. Thus when A isn't closed, t(A) > 0. We are considing whether t(A / B) <= t(A) + t(B). To help us in this effort, we are willing to entertain t(A) = |cl A - A|, which we'd like to normalize to R. Availing ourselves of the common consenses that Aleph_omega0 is large enough for all except transfinite mathematicians, we'll set t(A) = n + 1 when |cl A - A| = Aleph_n t(A) = 1 - 1/(|cl A - A| + 1) when 0 < |cl A - A| < Aleph_0 t(A) = 0 when |cl A - A| = 0. (I think this could be pushed upto Aleph_xi, for any xi < omega_1, as countable ordinals embed in R.) Does this establish t(A / B) <= t(A) + t(B) ? Let us ponder. cl A/B - (A / B) = (cl A / cl B) / SA / SB = (cl A / SA / SB) / (cl B / SA / SB) subset (cl A - A) / (cl B - B) Thus indeed, the first result of this thread. t(A / B) <= t(A) + t(B). Is t a metric or measure thing? What are measures for P(S)? ---- === Subject: Re: Riddle of the day posting-account=9F70KwkAAADloWPH_Z0lOPxF98dtfKh6 Gecko/20060508 Firefox/1.5.0.4,gzip(gfe),gzip(gfe) > How long does it take to close an open set? > It depends on what shape (topos) you're in. Oh now now, since when do topological spaces need to get into shape? That's close to the joke, but you're still missing it. --- Christopher Heckman . . S P O I L E R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The joke was a combination of it depends on what shape you're in, i.e., how strong you are, and it depends on what topology you're in, since in the discrete topology, every open set is also closed, so closing it requires no work at all. === Subject: Re: Riddle of the day <87ve7u77v1.fsf@nonospaz.fatphil.org> How long does it take to close an open set? Why should I answer that - I just don't see the point? > No problem, use pointless topology. > Will this nonsense ever end? > Will the circle remain unbroken? Upon the categorically theory of abstract nonsense, there sprouted forth pointless topology, which was of course pointless, unless your space wasn't sober. Thus pointless spaces were required to be sober and when they were, points in them could be defined. Consequently, to not have points in a pointless topology required an unsobering up. This paradox can be resolved by using illogical morphisms in the category of nonsense. ---- === Subject: Re: Riddle of the day <5016870.1195728085556.JavaMail.jakarta@nitrogen.mathforum.org> > Give R the cocountable topology. The first time I saw this sentence I read coconutable. Oh my gibbers, you've been taken by a course in creative reading. ;-) === Subject: Re: Riddle of the day > How long does it take to close an open set? If you manage to close it... it was never really open in the first place. There are topologies in which every open set is also closed, and vice versa. E.g., a topology with only two open sets. === Subject: Re: Riddle of the day <3r5ak314eqn9ptg78dm8v35tbpf82eh5o5@4ax.com> How long does it take to close an open set? If you manage to close it... it was never really open in the first place. There are topologies in which every open set is also closed, and vice > versa. E.g., a topology with only two open sets. > Every set is clopen? Hm... If it's T1, then it's discrete. Assume T0, a in cl {x}, a /= x. some open U with a in U, x not in U or a not in U, x in U. a not in U, x in U U closed; a in cl {x} subset cl U = U, no! Thus cl {x} = {x} and space is discrete. If not T0, then some x with open cl {x}, 1 < |cl {x}|. How long does it take to close {x}? Does it depend upon the cardinality of cl {x}? Warning: do not try to open {x} or it will vanish. === Subject: Re: Riddle of the day On 2007-11-22 10:49:57 -0500, Dik T. Winter said: > ... > > Give R the cocountable topology. The first time I saw this sentence I read coconutable. Aoccdrnig to a rscheearch at an Elingsh uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae we do not raed ervey lteter by it slef but the wrod as a wlohe. Hree, the two wrods cocountable and coconutable are scuh eamlxpe. -- -kira === Subject: Re: Riddle of the day >... Give R the cocountable topology. The first time I saw this sentence I read coconutable. Makes as much sense as the rest of this thread :> -- Patrick Hamlyn posting from Perth, Western Australia Windsurfing capital of the Southern Hemisphere Moderator: polyforms group (polyforms-subscribe@egroups.com) === Subject: Re: Riddle of the day posting-account=qN8jXgoAAADYUCiIfKAgmpC5L2L_xGmX AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) > How long does it take to close an open set? What is the sound of one set closing? === Subject: Re: Riddle of the day How long does it take to close an open set? What is the sound of one set closing? > The sound of the open unit disk closing would be boing The sound of the open unit interval closing would be bink, bink. The sound of an open clopen set closing would be a quite hum. The sound of a closed set closing would be the sound of silence. ---- === Subject: Re: Riddle of the day > How long does it take to close an open set? Why should I answer that - I just don't see the point? Are you trying to make a pun on the word point? Or are you just annoyed? > Will this nonsense ever end? William - I would like to see the answer to your riddle. Please don't > keep us in suspense too long. Why didn't you notice the end in my second question, given that you noticed the point in the first? Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Riddle of the day > How long does it take to close an open set? > Why should I answer that - I just don't see the point? > Are you trying to make a pun on the word point? Or are you just annoyed? > Will this nonsense ever end? > William - I would like to see the answer to your riddle. Please don't > keep us in suspense too long. Why didn't you notice the end in my second question, given > that you noticed the point in the first? Sorry! (And good job!) === Subject: Re: Riddle of the day > How long does it take to close an open set? > Why should I answer that - I just don't see the point? > Are you trying to make a pun on the word point? Or are you just annoyed? > Will this nonsense ever end? > William - I would like to see the answer to your riddle. Please don't > keep us in suspense too long. Why didn't you notice the end in my second question, given that you noticed the point in the first? Sorry! (And good job!) No problem, and obviously it was a bad job! They were very weak puns, but as I was fairly sure the thread wasn't going to head anywhere sensible anyway, so I thought 'what the heck...'. Phil -- -- Microsoft voice recognition live demonstration === Subject: High school problem Let f:[0,1]-->R be continuous. Then there exists an injective function g:[0,1]-->R such that |f(x)-g(x)|<1 (x in [0,1]). === Subject: Re: High school problem >Let f:[0,1]-->R be continuous. Then there exists an injective function g:[0,1]-->R such that |f(x)-g(x)|<1 (x in [0,1]). sure it's a high school problem!!!! Find me a high school TEACHER who could solve it!!!! === Subject: Another old high school problem Another one: Let f:[0,2]-->R be continuous, convex, non-negative, with f(0)=0. Then integral(0 to 2)[(x^2-1)f(x)dx]>=0. Have fun! Ady. === Subject: Re: Another old high school problem Another one: >Let f:[0,2]-->R be continuous, convex, non-negative, with f(0)=0. >Then integral(0 to 2)[(x^2-1)f(x)dx]>=0. Have fun! >Ady. pleas tell us what high school !!!!!!!!!!!!!!!!!! === Subject: Re: High school problem > Let f:[0,1]-->R be continuous. Then there exists an injective function g:[0,1]-->R such that |f(x)-g(x)|<1 (x in [0,1]). Wow - that is some high school that you attend! === Subject: Re: High school problem > Let f:[0,1]-->R be continuous. Then there exists an > injective function g:[0,1]-->R such that > |f(x)-g(x)|<1 (x in [0,1]). Let h : [0,1] --> R be a step function such that |f-h|<1/4. So, h(x) = b_k, for x in I_k, k=1..n, where I_k =[a_(k-1), a_k), for k said: > Let f:[0,1]-->R be continuous. Then there exists an injective function > g:[0,1]-->R such that |f(x)-g(x)|<1 (x in [0,1]). This is one way to try: For each point x in [0,1], use the definition of continuity to find an interval I_x containing x such that the range of values of f over I_a does not exceed 1. Do this for every point in [0,1] and you get an opening covering of [0,1]. Note that [0,1] is compact. Then try to construct a piece-wise linear function over some intervals each with a sufficiently small non-zero slope. -- -kira === Subject: A new resource for inventors, scientists and students - and R&D departments everywhere posting-account=2fkjZQoAAADqujYPhJDDt63m8LL6BtoO AppleWebKit/523.12 (KHTML, like Gecko) Version/3.0.4 Safari/523.12,gzip(gfe),gzip(gfe) hi everyone, my apologies if this is not the correct place to post this notice. I am writing to announce a new company that I thought may be of interest to you and your members. http://www.SearchandDevelop.com is a global web-based community where research and development problems and various challenges can be solved. Our goal is to bring together researchers, inventors, brilliant minds and creative thinkers with Searcher companies looking for answers. Once a member of SearchandDevelop.com, Searcher companies can post Quests, effectively increasing their R&D department staff by thousands, but paying only for results Developers can sign up free at http://www.searchanddevelop.com and will be able to view Quests as they arrive and offer solutions. A solution that is accepted by the Searcher company will earn the Developer a cash Award (the amount depends on the complexity of the Quest). We also offer a generous Affiliate system where Affiliates (signing up as an Affiliate is also free) earn $1000 when they sign up a Searcher company, plus a percentage of any Award paid out by the Searcher company they signed up. Affiliates also earn a percentage of the Award given to Developers upon successful completion of a Quest (full details on our web site). We are also looking for Searcher companies who have R&D problems - sign up now to get the benefit of our experts and get answers to your R&D problems. Please visit htt://searchanddevelop.com now for full information. thank you, we look forward to seeing you soon at SearchandDevelop.com === Subject: Units of the ring of algebraic integers What are the units of the ring of algebraic integers ? === Subject: Re: Units of the ring of algebraic integers days. My association with the Department is that of an alumnus. >What are the units of the ring of algebraic integers ? They are exactly the roots of monic irreducible polynomials with integer coefficients and constant term equal to 1 or -1. Their structure is a bit more difficult, though Dirichlet's Unit Theorem tells you what the structure of U(A)/K is for every K that is a finite extension of Q (where U(A) is the units of the algebraic integers): they form a finitely generated abelian group of the form V x W, where W is the finite cyclic group of roots of 1 in K, and V is a free abelian group of rank r+s-1, where r is the number of real embeddings of K into C, and 2s is the number of nonreal embeddings of K into C. In particular, the unit group of A contains free abelian groups of arbitrarily large rank, contains copies of the Prufer p-infinity group for every prime p, and so on. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Difficulty with a Spiral Equation ! posting-account=UmxzHAoAAADiGn5q_OAJNdqryOZkrQSe 1.1.4322),gzip(gfe),gzip(gfe) > > 1) Your latest plot is perfect if I can only reproduce it > computationally!! > > 2) The automatic procedure I've developed based on your earlier > approach works fine and produces very nice-looking spirals for most of > the data sets. The exception, however, includes quite a few sets! > Polynomials fitted through sets of points are notorious for not doing what you want them to do, or what you might reasonably expect them to do from looking at the points. I'm surprised it works well for most of the data sets; that's good. Sometimes adding additional control points helps, but sometimes it makes the curve go even more haywire. > To get a smooth curve through a number of points many people use piecewise functions (such as Bezier curves). I'm not aware of a robust general way of deriving a single analytical expression for a curve through a set of points that you can control well enough so it always does what you want it to do -- other than time-consuming hand- crafting. Could be just my ignorance though. > > 3) For those exceptions, depending on the initial guess of the centre > C(f,g), the developed smooth spiral passes through all the data points > (as it always does) but shows one or more reflection points, which > ruin the display! > > 4) I suppose one could add a constraint to the changing of f & g in > the Solver, so that the 2nd derivative does not attain a zero value > anywhere within the spiral th range-of-interest th(1) to th(6). > (Keep in mind that one is restricted to <=, =, >= contraint operators > in Solver.) > But, for a given point (r,th) on the spiral, which 2nd derivative I > should check ?? Is it (d2r/dth2) or is it its transformed (d2y/ > dx2) ?? > > 5) Locally, based on the 6-pnt spiral equation: > r = a + b.th + c.th^2 + d.th^3 + h.th^4 + k.th^5 > where r is the radial ordinate from the centre of the spiral > C(f,g); and > th is the angle measured in the CLOCKWISE direction > from vector C --> pnt # 1 > (d2r/dth2) = 2c +th(6d +th(12h +th(20k))) ... which should not > vanish within the range th(1) to th(6) > > 6) Or, one must perform axis transformation to O(0,0) with +ve X to > the right and +ve Y upward, and identify where (d2y/dx2) = 0 as > true reflection points of the spiral curve. > A simple rotation of the spiral axis yields: > [ - sin(t1) + cos(t1).(dy/dx)] / [ cos(t1) + sin(t1).(dy/dx)] = > [ - r.cos(th) - sin(th).(dr/dth)] / [ - r.sin(th) + cos(th).(dr/ > dth)] > where tan(t1) is the slope of the line C(f,g) ---> pnt # 1, from > +ve X, +ve counter clockwise. > Then, do the axis translation from C(f,g) to O(0,0), differentiate > again, isolate the term (d2y/dx2), and make sure it doesn't vanish > within the range of interest. > > 7) I believe 6) above is the correct approach. Do you agree ?? > You talk about reflection points, but I assume you mean inflection points. At an inflection point you will have d^2y/dx^2 = 0. For brevity in the following I will write t for theta. I would just calculate dy/dx as (dy/dt)/(dx/dt), and then calculate d^2y/dx^2 as (d(dy/dx)/dt)/(dx/dt). Assuming the spiral's equation is x = f - r*cos(t + k), y = g + r*sin(t + k), where k is some rotational offset, I get the condition d^2y/dx^2 = 0 equivalent to > r*d^2r/dt^2 - 2*(dr/dt)^2 - r^2 = 0 > I think you should get something similar, or quite possibly identical, depending on the exact form of your equations for x and y. > Note that the condition d^2y/dx^2 = 0 does not necessarily correspond to an inflection point though. It could in theory be some other species of stationary point (such as the point (0,0) on the curve y = x^4 or y = x^4 + x). Given what you're doing it seems rather unlikely that you'll have any these other types of stationary points, but if it's a problem you can check that d^2y/dx^2 actually changes sign around the point at which it equals zero (check the values a suitably small distance away). > d^2y/dx^2 = 0 also won't find inflection points where the tangent is parallel to the y-axis (such as the point (0,0) on the curve y = x^(1/3)). Again, given the nature of what you're doing, it seems you'd be unlucky to have one of these, so you can probably ignore it. > > 8) The other difficulty is associated with the occasional crossings of > the spiral!. Having done some numerical experimentation, I'm still > unable to figure out the mathematical criterion that makes a smooth > spiral crosses over ?? If such criterion is established, then one may > solve the problem by adding a constraint in the solution of f & g. > Will keep trying !! > > Any thoughts ?? > Still assuming x = f - r*cos(t + k), y = g + r*sin(t + k), and assuming r = F(t), the spiral will intersect itself at the in-range solutions t_1 <> t_2 (if any) to the simultaneous equations > f - F(t_1)*cos(t_1 + k) = f - F(t_2)*cos(t_2 + k) g + F(t_1)*sin(t_1 + k) = g + F(t_2)*sin(t_2 + k) > or just > F(t_1)*cos(t_1 + k) = F(t_2)*cos(t_2 + k) F(t_1)*sin(t_1 + k) = F(t_2)*sin(t_2 + k) > Your equations should be similar or identical, depending on the exact form of your equations for x and y. If this proves difficult to check then you can instead check for in-range solutions to > F(t + 2*n*pi) = F(t) > where n is any integer (check separately for each in-range value of n). > If r can go negative then you also need to check for solutions to > F(t + (2*n + 1)*pi) = -F(t) > And, finally, to pick up intersections at the spiral's centre, you need to check for multiple solutions to F(t) = 0.- Hide quoted text - > - Show quoted text - > > matt271829; > > I'm working on the numerous difficulties as per your suggestions (with > minor adjustments). > Some progress, but nothing to write home about! > > I recall someone earlier had asked about the equations I'm using. Here > they are: > > Spiral equation: r = fn(th) > r = a + b.th + c.th^2 + d.th^3 + h.th^4 + k.th^5 > where > r is the radial ordinate from the centre of the spiral C(f,g); > th is the angle measured from vector C --> pnt # 1; > centre of spiral C(f,g) is in Rectangular (Cartesian) > Coordinates. > > X = f + r.cos(t1 - fac.th) > Y = g + r.sin(t1 - fac.th) > where: > X +ve to the right and Y +ve upward: > fac = 1 for clockwise spiral > fac = -1 for counter clockwise spiral > t1 is the angle of vector C(f,g) -->pnt # 1 > measured from +X, +ve in the counter clockwise direction > (atan2, -pi<>+pi) > > Monir- Hide quoted text - > > - Show quoted text - > Hello; Are there analytical expressions for the roots of the polynomial: y^5 +a.y^4 +b.y^3 + c.y^2 + d.y +e = 0 possibly similar to those for cubic equations ?? > Monir- Hide quoted text - > - Show quoted text - Klueless' reply and the links s/he provided: > analytically. Monir- Hide quoted text - - Show quoted text - matt271829; I'm still working on the problem and haven't given up yet! 1) In your latest reply, you kindly provided the following: >Assuming the spiral's equation is: >x = f - r*cos(t + k) >y = g + r*sin(t + k), where k is some rotational offset, >I get the condition d^2y/dx^2 = 0 equivalent to >r*(d^2r/dt^2) - 2*(dr/dt)^2 - r^2 = 0 >I think you should get something similar, or quite possibly identical, >depending on the exact form of your equations for x and y. 2) Earlier and after a quick check, I concurred with your derivation: ....(d2y/dx2) = 0 = r*(d2r/dt2) - 2*(dr/dt)^2 - r^2 at spiral inflection points. 3) Here's my full 2nd derivative as applied: Spiral equation: r = fn(th) r = [ a + b*(th/s) + c*(th/s)^2 + d*(th/s)^3 + h*(th/s)^4 + k*(th/ s)^5 ]*Exp(m*th/s) where r is the radial ordinate from the centre of the spiral C(f,g); th is the angle measured from vector C --> pnt # 1; s is a constant >0. coordinates of the spiral centre C(f,g) are in a Rectangular axis- system X +ve to the right and Y +ve upward: 4) The spiral Cartesian coordinates are given by: X = f + r.cos(t1 - fac.th/s) Y = g + r.sin(t1 - fac.th/s) where: fac = 1 for clockwise spiral fac = -1 for counter clockwise spiral t1 is the angle of vector C(f,g) -->pnt # 1 (start of the spiral), measured from +X, +ve in the counter clockwise direction (atan2, -pi<>+pi) ....(d2Y/dX2) = [(fac/s)^3*r^2 + 2*(fac/s)*(dr/dth)^2 - (fac/s)*r*(d2r/ dth2)] / [(fac/s)*r*sin(t1-fac/s*th)+cos(t1-fac/s*th)*(dr/ dth)]^3 5) For fac=1 (clockwise spiral) and s=1, the above expression yields: ....(d2Y/dX2) = [r^2 + 2*(dr/dth)^2 - r*(d2r/dth2)] / [r*sin(t1-th)+cos(t1-th)*(dr/dth)]^3 6) At inflection points: (d2Y/dX2) = 0.0 = r^2 + 2*(dr/dth)^2 - r*(d2r/ dth2) which agrees with 2) above. 7) Solving for th values at inflection points and ensure that the solution is free of such points within the spiral's th range-of-interest turned out to be a complicated/impractical task. 8) Instead, I decided (for mathematical convenience) to only examine numerically the change-of- sign of (d2Y/dX2) along the spiral 40 generated display points. (d2Y/dX2) change-of-sign between two points would indicate a possible inflection point been bracketed in that region, and Solver may be instructed to search for another values for f, g & m. 9) With a smooth spiral, the sign of (d2Y/dX2) is all-over the place!!! which suggests: a- either the relation 5) above is incorrect (incidentally, I suppose one can't just examine the change-of-sign of the numerator only used in 6 above); or b- (d2Y/dX2) change-of-sign does not necessarily mean an inflection point been bracketed, particularly since the spiral curve is (by default) represented by a set of non-monotonic data {consider the case of a circle for example, which's different from your examples of y = x^4, y = x^4 + x, y = x^(1/3) }! Your thoughts would be greatly appreciated. Monir === Subject: Tetration References Originator: bergv@math.uiuc.edu (Maarten Bergvelt) For those doing research on tetration, I have updated and edited my list of references on the subject with many new ones added, which were selected, compiled and sent to me courtesy of Dave L. Renfro. I believe this collection of references to be now the most extensive on the subject. http://ioannis.virtualcomposer2000.com/math/IERefs.html -- I.N. Galidakis === Subject: CFP: INTERNATIONAL WORKSHOP ON OPTICAL SUPERCOMPUTING (OSC'08) Originator: bergv@math.uiuc.edu (Maarten Bergvelt) --- CALL FOR PAPERS --- --------------------------------------------------------- INTERNATIONAL WORKSHOP ON OPTICAL SUPERCOMPUTING (OSC'08) --------------------------------------------------------- August 25-29, 2008, Vienna, Austria In conjunction with the 7th International Conference on Unconventional Computation (UC'08) WEB PAGE: http://www.cs.ubbcluj.ro/~moltean/osc2008 http://www.cs.bgu.ac.il/~osc2008 FORUM: SCOPE OCS, the International Workshop on Optical SuperComputing, is a new annual forum for research presentations on all facets of optical computing for solving hard computation tasks. Optical computing devices have the potential for being the very next computing infrastructure. Given the frequency limitations and cross-talk phenomena, as well as soft-errors of electronic devices on one hand, and the natural parallelism of optical computing devices, as well as the advance in fiber optics and optical switches on the other hand make optical computing commercial-able. Research contributions to the theory, design, specification, analysis, implementation, or application of optical supercomputers are solicited. Topics of interest include, but are not limited to: -Design of optical computing devices -Electro-optics devices for interacting with optical computing devices -Practical implementations -Analysis of existing devices and case studies -Optical and laser switching technologies -Applications and algorithms for optical devices -Alpha practical, X-Rays and nano-technologies for optical computing IMPORTANT DATES Submission deadline: May 1, 2008 Acceptance notification: June 1, 2008 Camera ready: June 15, 2008 Workshop: August 25-29, 2008 PUBLICATION The workshop POST-proceedings will be published by LNCS Springer Verlag. Selected best papers will be published in a special issue of the Natural Computing journal. Also, we plan to have an associated peer reviewed feature issue in Journal of the Optical Society of America A (JOSA A), and we have made preliminary inquiries concerning this. ORGANIZATION Shlomi Dolev, Ben-Gurion University Mihai Oltean, Babes-Bolyai University Wolfgang Osten, Stuttgart Universitat Tobias Haist, Stuttgart Universitat Hossin Abdeldayem (NASA-Goddard, USA) H. John Caulfield (Fisk University, USA) Shlomi Dolev (Chair) (Ben-Gurion University, Israel) Hen Fitoussi (Ben-Gurion University, Israel) Joseph W. Goodman (Stanford University, USA) Tobias Haist (Co-Chair) (Stuttgart Universitat, Germany) Lene Hau (Harvard University, USA) Jeremy O'Brien (University of Bristol, UK) Mihai Oltean (Co-Chair) (Babes-Bolyai University, Romania) Alastair McAulay (Lehigh University, USA) Stephane Messika (LRI, France) John Reif (Duke University, USA) Joseph Rosen (Ben-Gurion University, Israel) Natan T. Shaked (Ben-Gurion University, Israel) Damien Woods (University College Cork, Ireland) Mihai Oltean === Subject: Re: Jacobi Method for finding eigenvalues of symmetric matrix. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) H. P. M. van Kempen, On the convergence of the classical Jacobi method for real symmetric matrices with non-distinct eigenvalues. Numerische Mathematik 9(1966), 11-18. Summary: It is proved that the classical Jacobi method for real symmetric matrices with multiple eigenvalues converges quadratically. >I have been looking at the Jacobi Method for finding eigenvalues of a > converges with quadratic order when the eigenvalues are distinct. What is known about the speed of convergence when the eigenvalues are > not necessarily distinct?