TI-89T Lessons using OS 3.10 hardware version 2.00 ==== Useful urls http://en.wikipedia.org/wiki/TI-BASIC http://education.ti.com/educationportal/sites/US/sectionHome/download.html http://www.tc3.edu/instruct/sbrown/ti83/complx89.htm http://www.tc3.edu/instruct/sbrown/calc/ http://upload.wikimedia.org/wikipedia/en/8/89/Boxplot_vs_PDF.png http://tifreakware.net/ http://www.calc.org/ http://www.ticalc.org/ http://www.ticalc.org/pub/ http://education.ti.com/educationportal/downloadcenter/SoftwareDetail.do?website=US&appId=6129&tabId=2 TI-89 manual download http://www.turkeyland.net/ti-89.php http://tifreakware.net/tutorials/89/ http://www.rskey.org/buyguide.pdf compare calcs http://atlas64.selfip.net:8080/Mirrors/www.ticalc.org/ http://CalcG.org unitedti.org tifreakware.net calcg.org detachedsolutions.com http://education.ti.com/downloads/guidebooks/apps/89symbolic_math_guide/8992symbolicmathapp.pdf math tools manual 1-800-TI-CARES for problems ==== log(a,b) = log( a ) base b log(100,2.7182818) = ln(100)= 4.605 === impDif(x^2+y^2=2,x,y,2) -x^2/y^3-1/y gives second derivitive Implicit Differentiation == 1/oo=0 1/0 is undefined ti89 logic == All Memory reset homescreen type: exec 2A7800C8206D0A504E900000 Enter 2nd-left-right-on is an ordinary reset, not flash == | is WHERE to select root region solve(2*(cos(x))^2+cos(x)=0,x) | 0 < x < 2*pi x=pi/2 or x=2*pi/3 or 4=4*pi/3 or x=3*pi/2 == One difference in the TI-89 Titanium not on the old TI-89 In Graph formats menu Disconinuity Detection is not in the old TI-89 When off, Graph Order is active, otherwise grayed out. == Connection hints using a Mac computer I use TI Connect Turn on TI-89 and plug in cable. The first time you connect, choose TI-89 in CONNECTION menu at top of screen. Have it remember it. When 89 is connected you get a menu on the screen labeled TI-89 with Var Link menu. Most programs uploaded to calc will go to MAIN Folder. You can transfer them to other folders later Some programs have several sections and all parts must be sent together to other folders On the computer screen, you can click the name of a Basic progream to see list of steps You can download from TI to the computer, then drag to the 89 screen. You can drag a program from Var-Link screen to the computer screen to save it. The program on the computer screen can be edited , saved and the 89 will then have an edited program. If you save TI programs to the computer, put them in a folder titled with the name of the program, as the icon does not have the program name. == Exact mode n and x undefined, radian mode (n+zz*i)^x= (n^2+zz)^(x/2)*cos[tan-1(n/zz)*x- sign(zz)* (pi*x/2)] - (n^2+zz^2)^(x/2)*sin[tan-1(n/zz)*x - sign(zz)*(pi*x/2)]*i ln(n+zz*i)= [ln(n^2+zz^2)]/2 + [ ( sign(zz)*pi )/2 - tan-1(n/zz) ]*i === Replace any battery less than one volt. == solve(x^2<=4,x) results -2 <= x <= 2 == Simultaneous equation aa() Prgm Delvar x,y solve (x+y=3 and x-y=1,{x,y}) ->zz x=2 and y=1 part(zz,1)->zz1 x=2 part(zz,2)->zz2 y=1 part(zz1,2)->zz3 2 part(zz2,2)->zz4 1 Disp ³zz3,zz4², {zz3,zz4} zz3,zz4 EndPrgm {2 1} == Implicit Differentiation Defins z(tt)=-d(tt,x)/d(tt,y) x^3*y^3+x^2+y+4 z(tt) gives -x*(3*x*y^3+2)/(3*x^3*y^2+1) ImpDif(tt=0,x,y) gives same answer == Complex roots csolve(x^4=1,x) x=i or x=-i or x=-1 or x=1 Let yy0=-0.3265 yy1=-0.10091 degree mode solve(P|>Rx(yy0,ii)=yy1,ii) Results ii=360.*(@n1+.2) or ii=360.(@na-.2) @n1= 0,1,2,3... ii= is 72 degrees main solution === After graphing the TI-89T and finding area under the curve, save it by typing sysMath -> x to store area in x in active Folder. ==== http://64.233.169.104/search?q=cache:u7ykCl1NEvwJ:www.math.geneseo.edu/CURRENT_STUDENTS/TI89lin.pdf+ti89+multiply+matrix+vector&hl=en&ct=clnk&cd=2&gl=us Matrix on TI89 === http://www-s.ti.com/cgi-bin/discuss/sdbmessage.cgi?databasetoopen=calculator s&topicarea=TI-89/TI-89+Titanium/Voyage+200/TI-92+Plus&do_2=1 TI home http://www-s.ti.com/cgi-bin/discuss/sdbmessage.cgi?databasetoopen=calculators&topicarea=TI-89/TI-89+Titanium/Voyage+200/TI-92+Plus&do_2=1 TI-89 calculators === http://education.ti.com/guidebooks/graphing/89ti/TI89TitaniumGuidebook_Part2_EN.pdf TI-89T Manual === Integration problem S is integral sign sqrt is square root symbol S (sqrt(1/(1-x^2)),x) gives S(sqrt(-1/(x^2-1))x) no solution S(1/(sqrt(1-x^2)),x) gives sin-1(x) == Frozen TI-89 You could pull the batteries, but usually a soft reset will do. Try pressing 2nd+left+right+on (all at once, and press them in that order). That will usually fix your problem. The calculator will reload your OS, and you can use your calculator again. A serious problem can maybe be fixed by installing a new copy of the operating system. == Scientific and Engineering mode works only in Approximate mode === Choose Main in Mode diamond EE See keyboard menu APPS 7: Program Editor Enter 3: New Program main New --- Only programs in Main Folder use this Program main kbdprgm1 Enter :kbdprgm :Prgm :Disp "111" :EndPrgm HOME press diamond 1 See 111 === On the TI89T, entering y1=cos(x)|x<0 plots cos(x) when x<0 and plots nothing when x>=0. If you turn the axes off (F1, Format, Axes Off), you'll see that it really is plotting nothing, not 0, when false. The TI89T won't allow the multiply by a boolean trick as it has stricter type checking, treating true/false as a true boolean, not an integer. === Delvar a,b to delete variables a and b in a folder and only in selected folder. ----- ~ means not When using Boolean logic commands and, or, xor, not use 1 and 0 in exact mode or true and false in any mode a xor b -> ~a and b or a and ~b Demorgan's Theorem not ( a or b) -> ~a and ~b not ( a and b ) -> ~a or ~b a or a -> a a and a -> a a or a -> a not a ~a not ( a xor b ) -> ~a and ~b or a and b not not a -> a true or true -> true a and true -> a 1 or 1 -> 1 1 xor 1 -> 0 1 and 0 ->0 1 or 0 -> 1 === Ball collision Delvar v3,v4 m1*v1 + m2*v2 = m1*v3 + m4*v4 m1*v1^2 + m2*v2^2 = m1*v3^2 + m4*v4^2 Simultaneous equation will solve for v3 and v4 Assume m1=2 m2=10 v1=3 v2=-2 solve(m1*v1+m2*v2= m1*v3+m2*v4 and m1*v1^2+m2*v2^2= m1*v3^2+m2*v4^2,{v3,v4}) v3 = -5.333 and v4 = -0.333 or v3 = 3 and v4 = -2 ==== Path symbol \ Assume current folder is aaa Assume in folder bbb there is a program ccc type bbb\ccc() to run program ccc and variables generated by this program appear inside folder aaa in VAR LINK Expressions in bbb can be called. Assume there is an expression aa which is 45.22 in folder bbb bbb\aa shows 45.22 even if another folder is Current Folder bbb\aa->ax stores 45.22 in Current Folder and shows 45.22 in Home == Catalog F1- Gives information about selected catalog item. F2- Catalog list F3- List of all flash apps. If you select one and Enter, this app item will appear on the Home screen and can be worked by supplying needed elements and Enter. F4- User defined programs and the folder containing it. F5,F6.F7 nothing There is a description of the function at the bottom of the screen. == To add a description to a function or program It must be preceeded by @ and be the first line after Func and Prgm Example yy(x) Func @Description of function Return x^2 EndFunc yy(3) gives 9 yy(x) Func Return {³x x^2²,x^2,x^3} EndFunc yy(3) gives {³x, x^2² 3. 9.} 3 sto t This of type command is not allowed in a function -- Catalog F4 choose yy F1 --- See this ----- Help Description of function ----- This approach also works with a program. ====== Unit conversion 2nd mode key is convert symbol |> right triangle example 3_ft|>_cm gives 91.44*_cm === Graphing methods Mode radian Diamond F1 y1=sin(x) y2=Cos(x) F2 Window xmin=0 xmax=6.2832 xscl=1 ymin=-1 ymax=1 yscl=1 xres=1 F3 see two graphs F1 darken y1=sin(x) Diamond F1 F6-Style 4:Thick Enter F3 Graph see sine curve is dark and thick Diamond F1 F6-Style 4:Path Enter F3 Graph See sine wave has an initial circle Diamond F1 F6-Style 3:Square Enter F3 Graph See sine wave is made of squares Diamond F1 F6-Style 7:Above Enter F3 Graph See sine wave has vertical bars filling space above it Diamond F1 F6-Style 7:Above F3 Graph See sine wave has vertical bars filling space above it Diamond F1 F6-Style 8:Below F3 Graph See sine wave has vertical bars filling space below it Diamond F1 F6-Style 5:Animate F3 Graph See sine wave is traced out by a circle but no graph results Darken the function in F1 which is to be selected. Select Style with Enter for that curve as each curve can have a different style. It will retain that style until altered. In graphing a function, F8 8:Inflection occurs where the second derivitive of the curve is zero. ======== Select graph window diamond F2 set x range 0 to 1 set y range 0 to 1 deltasign is in CHAR GREEK menu /\ deltasignx is unit of x graph 1/deltax=158 = number of horizontal pixels deltasigny is unit of x graph 1/deltay=76 = number of vertical pixels deltasignx and deltasigny are not listed in variable list size of deltax and deltay varies with x range and y range in F2 ======= Underdefined Least square problem x y z | 2 4 5 | | 8 9 2 | = a | 25 | | 32 | = |b| aT*(a*aT)^(-1)*b=c | 0.909472212513 | x | 2.08808109053 | =c y a*c=b | 2.96574624257 | z HP48/49/50 in RPN b a LSQ gives c Another approach =============== Solve an overdefined system a*b=c a=| 1 1 | c=| x | b= | 7.1 | | 1 -1 | | y | | 11.2 | | 1 -2 | | 5.3 | (aT*a)^(-1)*aT*b=c both work aT*(a*aT)^(-1)*b=c c= | 9.185714 | x best values for x and y | -1.9785714 | y a*c=b ========================= Multiple Regression Solve an overdefined system k*p=m kT is transpose of k a =| 1 1 | c=| x | b= | 7.1 | | 1 -1 | | y | | 11.2 | | 1 -2 | | 5.3 | (aT*a)^(-1)*aT*b=c c= | 8.0142857142855 | best values for x and y | 0.2214285714285 | The Multiple regression program solves such systems ============ Solve a determined system least square a+b*x1+c*y1+d*z1=zz1 a+b*x2+c*y2+d*z2=zz2 a+b*x3+c*y3+d*z3=zz3 a+b*x4+c*y4+d*z4=zz4 assume a,b,c,d are unknown n x y z a+b*13+c*19+d*16=621 = zz1 1 13 19 16 a+b*23+c*21+d*33=1010 = zz2 2 23 21 33 a+b*41+c*46+d*42=1643 = zz3 3 41 46 42 a+b*27+c*55+d*66=1957 = zz4 4 27 55 66 1 x y z --------------------------------------------------------- 1 | sigma(n) sigma(xi) sigma(yi) sigma(zi) | x | sigma(xi) sigma(xi^2) sigma(xi*yi) sigma(xi*zi) | y | sigma(yi) sigma(xi*yi) sigma(yi^2) sigma(yi*zi) | z |sigma(zi) sigma(xi*zi) sigma(yi*zi) sigma(zi^2) --------------------------------------------------------- sigma(n) =4 sigma(xi)=(13+23+41+27) = 104 sigma(yi)=(19+21+46+55) = 141 sigma(zi)=(16+33+42+66) = 157 sigma(xi^2)=(13^2+23^2+41^+27^2) = 3108 sigma(yi^2)=(19^2+21^2+46^2+55^2) = 5943 sigma(zi^2)=(16^2+33^2+42^2+66^2) = 7465 sigma(xi*yi)=(13*19+23*21+41*46+27*55) = 4101 sigma(xi*zi)=(13*16+23*33+41*42+27*66) = 4471 sigma(yi*zi)=(19*16+21*33+46*42+55*66) = 6559 1 x y z ------------------------------------ 1 | 4 104 141 157 | x | 104 3108 4101 4471 = n1 | y | 141 4101 5943 6559 | z | 157 4471 6559 7465 ----------------------------------- sigma(zzi)= 621+1010+1643+1957 = 5231 sigma(zzi*xi)= 621*13+1010*23+1643*41+1957*27 = 151505 sigma(zzi*yi)= 621*19+1010*21+1643*46+1957*55 = 216222 sigma(zzi*zi)= 621*16+1010*33+1643*42+1957*66 = 241434 ------------------------------------ | 151505 | | 216222 | =n2 | 241434 | ----------------- n1^(-1)*n2=n3 | 10 | | 11 | | 12 | | 15 | a=10 b=11 c=12 d=15 ======== TI-89T statistics method APPS Stats.List Editor F4: Regressions D: Multireg list1 | list2 | list3 | list4 | yhat | resid | ----------------------------------------------- 621 | 13 | 19 | 16 | 621 | _ | 1010 | 23 | 21 | 33 | 1010 | 3E-12 | 1643 | 41 | 46 | 42 | 1643 | _ | 1957 | 27 | 55 | 66 | 1957 | 3E-12 | That is computed value using computed b0, b1, b2, b3 resid is difference between list1 and computed values === Define a function two ways Define f(x) = x^2 x^2 -> f(x) f(3) gives 9 ============= | 2 6 | | 5 3 | ->y y[1] is [ 2 6 ] y[1,1] is 2 y[2,2] is 3 y[2] is | 5 3 | y[1,2] is 6 y[2,1] is 5 ===== Adjoint[a]=a^(-1)*det(a)*identity(n) where n is rank of a |1 0 1| |0 2 1| ->a n=3 |1 1 1| | 1 1 -2 | | 1 0 -1 |= Adjoint[a] |-2 -1 2 | a=|a,i,j| adj|a| = | c[i,j] | c[i,j] are cofactors of c[1,1]= | 0 -1 | |-1 2 | Eliminate row and column i,j and remaining matrix is cofactor === Solve and extract solutions zeros(x^3-5*x^2-18*x+72,x)->t t is {-4 3 6} mid(t,1,1) gives {-4} mid(t,2,1) gives {3} mid(t,3,1) gives {6} Product({3}) gives 3, a computable number Solve and extract solutions Solve(x^2=4,x) -> x gives x=2. or x= -2. exp>list(Solve(x^2=4,x),x) -> t gives {-2, 2} mid(t,1,1) -> z gives {-2.} product(z) -> cc gives cc=-2. Be sure to be in Approximate mode. ======== Select folder a variables m,n are in Folder a DelVar m,n erases these in folder a === Edit a function function cc is in folder a APPS 7 2 See OPEN Type Program -> > V 2:Program Enter Folder main > rest of programs select a Variable -> List of Functions Select one :cc(n,xx) Make changes Home saves changes. Change now made. Edit Program the same way ===== Create a matrix j in folder af APPS 6 3: NEW NEW Type 1: Data 2: Matrix Select Enter 3: List Folder List of folders Select folder Enter Variable j (No alpha needed) Row Dimension 3 Col Dimension 3 3 by 3 matrix Enter Enter See a matrix filled with zeros Put in your values as it scans left to right HOME when finished ==== Edit a matrix APPS 6 2 Open OPEN Type 1: DATA 2: MATRIX Select Enter 3: LIST Folder Select af Variable Select af from list of matrices there Edit Home === Create a program hh in folder af (arbitrary name) Select folder af in MODE APPS 7 3: NEW Type Program Folder af Variable hh Enter Enter See :hh() :Prgm :Disp "999" :EndPrgm Put on blank line Enter to make more blank lines Use Catalog and menus to create program commands HOME when finished to store program Go to Var-Link Open af see hh Enter see hh( put in ) to make hh() Enter See 999 on screen ==== To select the number of history pairs hit diamond | select desired number. === Edit Matrix g in Folder a APPS 6 Data/Matrix Editor Open OPEN Type Data Matrix Select List Folder List of folders Select a Variable List of matrices Select g Enter See Matrix Edit it Enter Home ========= ElesIf example tu() tu() Enter observe c Prgm hit 1 see first 1. end ClrIO --- Input "c" c tu() Enter observe c If c=1 Then hit 2 see second 2. end Disp "first",c --- ElseIf c=2 Then tu() Enter observe c Disp "second",c hit 3 third 3. end ElseIf c=3 Then --- Disp "third",c tu() Enter observe c EndIf hit 8 8. end Disp "end" EndPrgm ================= Gamma function is associated with factorials 5!=5*4*3*2*1= 120 ! is Char Punctuation also use diamond alpha divide to make ! TI89T does factorials for positive integers and 0 Define gam(n)= S(e^(-x)*x^(n-1),x,0,40) This program works for n>0 The HP gives Gamma[n] for all n! not negative integers Define( gam(n)=S(e^(-x)*x^(n-1),x,0,40) 0!=1 1!=1 2!=2 3!=1*2*3=6 Gamma(1)=1 Gamma(2)=1 Gamma(3)=2 Gamma(4)=6 There is a Gamma function program in the this math list. TI_89_GammaFunc.txt Gamma[n]= integral { 0 to 1 } (ln(1/n))^(n-1) dx Gamma[x]*Gamma[-x]=-pi/(x*sin(pi*x)) Gamma[x]*Gamma[1-x]=+pi/(sin(pi*x)) Gamma(1-n)/(-n)=Gamma(-n) ===== Create a Custom Menu Create a Folder cstm(option) Create a program cst(option) cst() Prgm Custom Title "Progm" This gives F1 Progm as the title Item "cstmcst()" add any desired commands Title "Math" This gives F2 Math as the title Item "f(x)" add any desired commands Title "Calc" This gives F3 Calc as the title Item "S(" And so on. Add additional titles and items EndCustm Run this to set custom menu 2nd Custom shows custom menu Run CustmOff in F1 to return to standard menu ========= Eigenvector Create a folder called egn (arbitrary name) create a matrix called a (arbitrary name) |2 4 7| |8 3 5| |6 1 9| In Math/4: Matrix/9 eigVl( and eigVc( and in Catalog eigVl(a) -> t See {15.0044 -4.1328 3.12846 } ->t product(mid(t,1,1))->ee1 this is 15.004 product(mid(t,2,1))->ee2 this is -4.1328 product(mid(t,3,1))->ee3 this is 3.1284 eigVc(a) -> z see |-.51 -.73 -.288 | |-.59 .61 -.85 | |-.61 .28 .43 | Extract these three columns subMat(z,1,1,3,1) -> m1 | -.51 | | -.59 | | -.61 | -- subMat(z,1,2,3,2) -> m2 | -.73 | | -.61 | | -.28 | -- subMat(z,1,3,3,3) -> m2 | -.28 | | -.85 | | -.43 | --- these three cases are true a*m1=ee1*m1 | -7.72 | | -8.98 | | -9.21 | --- a*m2=ee2*m2 | 3.02 | | -2.55 | | -1.18 | -- a*m3=ee3*m3 | -.902 | | -2.66 | | 1.37 | === The product of the eigenvalues = det(matrix) ========= Given Eigenvectors of a and Eigenvalues of a, find a a=[[6.3] [2,7] eigVl(a)=(4,9) eigVc(a)= [-8.32 -.707] [ .554 -.707] c^(-1)=[ -.72 .72 ] [ -.56 -.84 ] bb=[ 4 0 ] [ 0 9 ] c*bb*c^(-1)=a ==== Eigenvalue problem | A11 A12 A13 | Assume a matrix A = | A21 A22 A23 | | A31 A32 A33 | | 4 3 7 | A= | 8 9 5 | Example | 6 2 4 | The goal is to find the groups A*C1 = C1*B1 A*C2 = C2*B2 A*C2 = C2*B2 | C11 | | C21 | | C31 | C1 = | C12 | C2 = | C22 | C3 = | C32 | | C13 | | C23 | | C33 | | A11-X A12 A13 | Assume a matrix AX = | A21 A22-X A23 | = 0 | A31 A32 A33-X | Compute determinate of AX = 0 Solve for X. The solutions will be C1, C2 and C3. Example -(X^3-17*X^2+12*X+168)=0 The three solutions of X are B1= 15.5308476265 B2= -2.63540657687 B3= 4.10455895037 We will solve for one case A*C1 = C1*B1 Multiply both sides by (INVERSE A) A*(INVERSE A)= IDENTITY MATRIX This gives C1=(INVERSE A)*C1*B1 The values C11, C12, C13 are to be determined. Assume C12=C21=C32=1, as any arbitrary value may be assumed. (INVERSE A)*C1*B1-C1=0 Let (INVERSE A)*B1=U1 | U11 U12 U13 | U1= | U21 U22 U23 | | U31 U32 U33 | | C11 | | U11 U12 U13 | | C11 | | C12 | * | U21 U22 U23 | - | C12 | = 0 | C13 | | U31 U32 U33 | | C13 | C13 * U13 + C12 * U12 + C11 * U11 = C11 C13 * U23 + C12 * U22 + C11 * U21 = C12 C13 * U33 + C12 * U32 + C11 * U31 = C13 Since C12=1, this leaves two unknowns, C11 and C13. Select any two of the above three equations and solve. | 0.534216183955 | | 1.0 | | -0.340890563392 | C1= | 1.0 | C2= | -0.243471887751 | C3= | 1.0 | | 0.451423630971 | | -0.800712987659 | | -0.4336633085 | | 8.29683015262 | | 1.0 | A*C1=C1*B1 = | 15.5308476265 | A*C2=C2*B2 = | -0.343471887751 | | 7.01099162761 | | -0.800712987659 | | -0.340890563392 | A*C3=C3*B3 = | 1.0 | | -0.4336633085 | == Program to run the Eigenvector program abc() (arbitrary name) Prgm ClrIO DelVar x,s12,s13,s22,s23,s32,s33 a^(-1)->a1 [[1][s12][s13]]->ss1 [[1][s22][s23]]->ss2 [[1][s32][s33]]->ss3 eigVl(a) ->va Find vectors b1,b2,b3 mid(va,1,1)->l1 mid(va,2,1)->l2 mid(va,3,1)->l3 product(l1)->b1 Disp "b1",b1 product(l2)->b2 Disp "b2",b2 product(l3)->b3 Disp "b3",b3 a1*b1*ss1-ss1-> k1 Solve for first vector ss1 subMat(k1,1,1,1,1)->sa1 subMat(k1,2,1,2,1)->sa2 det(sa1)->sb1 det(sa2)->sb2 solve(sb1=0 and sb2=0, s12,s13)->sk x(sk,1)->sk1 part(ss,2)->s13 part(sk,2)->s12 Disp "s12",s12 Disp "s13",s13 a1*b1*ss2-ss2-> k2 Solve for second vector ss2 subMat(k2,1,1,1,1)->sa1 subMat(k2,2,1,2,1)->sa2 det(sa1)->sb1 det(sa2)->sb2 solve(sb1=0 and sb2=0, s22,s23)->sk part(sk,1)->sk1 part(ss,2)->s23 part(sk,2)->s22 Disp "s22",s22 Disp "s23",s23 a1*b3*ss3-ss3-> k3 Solve for third vector ss3 subMat(k3,1,1,1,1)->sa1 subMat(k3,2,1,2,1)->sa2 det(sa1)->sb1 det(sa2)->sb2 solve(sb1=0 and sb2=0, s32,s33)->sk part(sk,1)->sk1 part(ss,2)->s33 part(sk,2)->s32 Disp "s32",s32 Disp "s33",s33 Note ss1=| 1 | | 1 | a*ss1=b1*ss1 = | 13.013 | | s12 | = | .5579 | | 7.201 | | s13 | | .9174 | | 11.939 | ss2=| 1 | | 1 | a*ss2=b2*ss2 = | 13.013 | | s22 | = | -.6692 | | -1.164 | | s23 | | -.0314 | | -.054 | ss3=| 1 | | 1 | a*ss3=b3*ss3 = | -6.754 | | s32 | = | .7261 | | -4.904 | | s33 | | -1.616 | | 10.91 | a= | 4 3 8 | | 1 3 5 | | 6 9 1 | ================================================ When you are editing and running a program, use 2nd APPS to go back and forth from running and observing the program. You have to use HOME to save changes in a program. in mode, Split 1 app Program Editor ==== Compute Chi Square statistics S is integral sign Gamma function n>0 Define gam(n)=S(e^(-x) * x^(n-1),x,0,40) gam(5) gives 24 Define v(n.xx) = 1 / (2^((n-1)/2)/2) * gam((n-1)/2)) * S(e^(-x/2) * x^((n-3)/2),x,xx,70) v(7,3) = .808846 n= number of cases xx= chi square value Degrees of freedom = n-1 ===== | 2+3*i 3+6*i | | 5-2*i 6-5*i | -> z zT = Transpose of z |2-3*i 5-2*i | |3-6*i 6-5*i | Note change in sign conj() is complex conjugate (conj(z))T is | 2+3*i 5+2*i | | 3+6*i 6-5*i | Note no change in sign ==== y=3x^2 | 0g lap() Prgm ClIO S(g*e^(-s*t),t,0,k)->d Disp d EndPrgm lap() Enter 1/(s^2+1) + ( k stuff) results. Ignore k stuff The EEPRO program has a list of Laplace Tranforms. The TI-89T math program list has Inverse Laplace programs. === Function notes Local internal variable names is vital before computation No ClIO allowed No call to a program allowed A call to another function is allowed Function Example with external function call xx(a,b) Func Local y,z yy(b)->t a+b+t=z Return z EndFunc yy(p) Func Local p Return p^2 RndFunc xx(1,7) Enter results in 57 = 1+7+49 === DrawInv y1=sin(x) xmin=-2 xmax=6.28 xscl=1 ymin=-2 ymax=2 yscl=1 F3 graph see sine wave Go to Home DrawInv(y1(x)) Enter See Sin(x) running vertical 2nd F6 has DrawInv and so does Catalog === Return x,y is illegal in a function Function with multiple variable output is illegal ---- xx(a,b) Func Local y,z a->y b->z Return {y,z} EndFunc ---- xx(2,3)->d d is {2 3} ======= To expand by partial fractions, use expand( Example expand( ( 6*x + 31)/( x^2 + 4 ) * ( x+2 )^2 ) This is useful in integration and solving Laplace Transform problems. Results -31*x/(16*(x^2+4) + 3/(2*(x^2+4)+31/(16*(x+2)) + 19/(8*(x+2)^2) There is a partial fraction program here I created. Partialfractions-TI-89 ===== Units Select MODE Unit System If you choose English, any selected item converts to English units 1_m Enter results 3.28*_ft Custom Units is grayed out If you choose SI, any selected item converts to SI(metric) 1_ft ENTER results .3048*_m If you choose CUSTOM, Set Defaults is available. Right Arrow See unit table Each type has options Select option for each, or NONE Custom Units ->Custom Units Defaults Example Choose Length _rod Enter to save selection 1_ft ENTER results .0606*_rod ======== Linear regression example Mode Approximate Graph Function Statistics Regressions LinReg(a+bx) Example x List {1,2,3,4} y List {5,4,5,7,7.1} Store Results y1(x)= for a plot of curve Enter See a=3.7 b=.88 r^2=.71439 r=.845 In list see resid=y data- computed y resid ---- .42 -.96 .66 -.12 --- Define r^2 y is y value in y List ym= is mean of y list yp=computed value of y from equation r^2= (sigma ((y-ym)^2)-sigma((y-yp)^2))/sigma((y-ym)^2) to compute r^2 list1 list2 ----- ----- 1 5 2 4.5 3 7 4 7.1 Darken list 3 list3=3.7*.88*list1 Enter list3 = yp ----- 4.58 5.46 6.34 7.22 Darken list4 list4=(list2-list3)^2 Enter this is sigma((y-yp)^2) list4 ----- .1764 .9216 .4356 .0144 Go to Home 0(list4) see 1.548 this is sigma((y-yp)^2) Go to Home sum(list2) see 23.6 compute 23.6/4=5.9 =y mean = ym Darken list5 list5=(list2-5.9)^2 list5 ----- .81 1.96 1.21 1.44 goto Home sum(list5) see 5.42 this is sigma((y-ym)^2) r^2=(5.42-1.548)/5.42= .71439 r=sqrt(r^2) = r= .845 -- Graph results Go to y1(x)= menu see y1(x)=3.7+.88*x Select Plot 1 Enter Plot Type Scatter Mark Box x list1 y list2 Use Freq and Categories NO Enter Window xmin=0 xmax=5 ymin=0 ymax=8 Graph See both line plot and scatter plot In y= menu, hit F1, 9:Format Enter to select plot options. A: Zoomfit fits cirve to window -- Program to compute r^2 in statistics results rr() Prgm ClrIO {1,2,3,4}->list1 {5,4.5,7.7.1}->list2 list1*.88+3.7->list3 (list2-list3)^2->list4 sum(list4)->l23 sum(list2)/4->m (list-m)^2->list5 sum(list5)->sym (sym-l23)/sym->rrr Disp "r2",rrr EndPrgm ======= Integration method S is Integrate sign S( 1/(x^2+r^2)^1.5 ,x) The TI-89T will not integrate this problem in this form S( 1/( (x^2+r^2) * (x^2+r^2)^.5) ,x) will integrate to x/(r^2 * sqrt(x^s+r^2) ) === define asnswer region with | where solve( (x-3)*(x+4)*x=0,x)|x>1 and x<5 answer x=3 solve( (x-3)*(x+4)*x=0,x)|x>-2 and x‚0 answer x=3 >= can be used equally with the single symbol found in catalog |x„3 <= can be used equally with the single symbol found in catalog |x„3 not= symbol found is catalog to eliminate a solution |x‚3 ======= Graph and Table operation Assume radian and approximate mode used, Diamond y= menu y1=sin(x) Diamond Window F2 xmin=0 xmax=10 xscl=1 ymin=-1 yscl=1 xres=1 -- Diamond F3 Graph See sine plot -- Diamond Tblset menu Diamond F4 tblstart set to 0 deltatbl .1 Graph (-) Table Off Independent Auto -- Diamond F5 See x y 0. 0. .1 .0998 --- Diamond F4 Graph (-) Table On Enter See x y 5. -.9589 tblstart 5 deltatbl .0632911392406 The first value of x is half the x range 10/.0632911392406 = 158 always this value -- Diamond 1 y= menu delete y1=sin(x) Diamond F4 Select Independent Select ASK Enter You now are transferred to F1 y= menu Enter new y= equation and continue ======= In UNITS menu choose CONSTANTS --- _c Speed of light _Cc stat units _g gravity _Gc Newton gravity _h Planck constant _k Boltzman constant _Me mass electron _Mn mass neutron _Mp mass proton _Na Avagadro number _q electron charge _Rb Boltzmann _Rc universal gas constant _Rdb Rydberg _Vm molar gas _e0 permitivity of vacuum _o Stefan-Boltzmann _o0 magnetic flux quantum _u0 permiability of vacuum _ub Bohr magnetron Example click _e0 See this on the home menu.. Put 1 in front of _e0. Hit enter. See 8.85419E-12 _F/_n ====== Vector dot and cross products v = [ 21.1, 5.51, -1.41 ] t=[ 3.55, 35.22, -1.9 ] v1 = 21.1 v2 = 5.51 v3 = -1.41 t1 = 3.55 t2 =35.22 t3 = -1.9 crossP(v,t) [ 39.191 35.085 723.58 ] = vp vp1= 39.191 vp2= 35.085 vp3= 723.58 dotP(v,t) 271.65 = dp (v dot p)/(|v|*|t|)= cos(th) = .3506 th=69.473 [vp1,vp2,vp3]>Sphere [725.49 angle 14.635 angle 93.699 ] [t1,t2,t3]>Sphere [ 35.449 angle 84.244 ] [v1,v2,v3]>Sphere [ 21.853 angle 14.635 angle 93.699 ] av=|v|=21.853 at=|t|=35.449 dp/(av*at)=cos(th) = 0.35066=cs th= 69.473 = angle between v and t |vp|=725.49 sin(th)=ap/(at*av)=0.34994=sn R>Ptheta(cs,sn)=69.473 v dot p= v1*t1+v2*t2+v3*t3 | i j k | | v1 v2 v3 | = dt | t1 t2 t3 | expand(det(dt)) 39.1912*i + 35.0845*j + 723.5815*k Note: Results of Sphere and Cylind can not have data operated on or saved. Contents can be copied and pasted to be used in math. crossP(x,y) = -crossP(y,x) ========== Partial Fraction Program The command expand(x/((x-1)*(x-2))) 1/(x-1)-1/(x-2) Partialfractions-TI-89T also works ==== Binomial expansion Define bb(n)=expand(a+b)^n) ========= Study of cosh[x/a]=(e^(x/a)+e^(-x/a))/2 Assume a=3 assume x1=-3 x2=2 y1=cosh(-3/3) = 1.543 y2 =cosh(2/3)=1.2305 arcLen(cosh(x/3),x,-3,2)=5.0842133=len Given len, x1,x2,len solve for a solve(arcLen(cosh(x/a),x,-3,2-len=0,a)|a>2.5 gives a=3 == Histogram plot Choose a folder with MODE, like ac APPS Data/Matrix NEW Type Data Folder ac Variable choose a letter, like k Enter See list c1 c2 c3 Under c1 1 Enter 2 E 3 E 5 E 7 E 7 E 5 E Home Diamond F1 Plot1 Enter Plot Type Histogram x c1 Hist bucket width 1 Use freq and catagories no Enter Diamond Window F2 xmin 0 xmax 8 ymin 0 ymax 3 Diamond Graph F3 See histogram == Function use x^2-4 sto f Define a(f)=solve(f=0,x) a(f) gives x=-2 or x=2 === Subscripts example |110. 120. 130.| |210. 220. 230.| sto a |310. 320. 330.| Define b(a,c,d)= det(subMat(a,c,d,c,d)) b(a,1,3) gives 130. ====== Plot x^2/3 You will get only right side. _|/ Plot x^2^(1/3) You will get both sides \|/ == rref function assume x=1, y=2, z=3 Use matrix method. 2*x+3*y+4*z=20 -x+2*y-5*z=-12 3*x-2*y+6*z=17 [[2,3,4][-1,2,-5][3,-2,6]]=a [[20][-12][17]]=b a^(-1)*b =c c=[[1][2][3]] --------- rref([2,3,4,20][-1,2,-5,-12][3,-2,6,17]]) rref([2,3,4,20;-1,2,-5,-12;3,-2,6,17]]) | 1 0 0 1 | | 0 1 0 2 | | 0 0 1 3 | answer [0,9,8]->a rref[a] gives [ 0 1 8/9 ] Divides rest by first non-zero number --------------------- [x,y,z,t] ->a rref(a) -> [1 y/x z/x t/x] divide all by first item == It is proper to put an equation in quotes to save it unevaluated. Remove quotes to use it as math. expr("2+3") gives 5 ====== Create a function Define n(x)=x^2 Enter n(5) gives 25 ------ APPS 7 3:New Enter Type 2:Function variable t Enter See : :t() :Func : :EndFunc put x into () to make :t(x) put :x^2 after :Func Home Results :t(x) :Func :x^2 :EndFunc t(5) gives 25 --- a() Prgm Disp t(6) EndPrgm a() givs 36 ====== TI references http://www.ticalc.org/pub/89/basic/ Many programs for TI-89 ti addresses 89 to 89 program set ftp://ftp.ti.com/pub/graph-ti/calc-apps/89/ TI-89 apps 89 manual.pdf http://education.ti.com/guidebooks/graphing/8992p/8992bookeng.pdf http://education.ti.com/educationportal/appsdelivery/download/download_eula.jsp?cid=us&displayMode=G&applicationid=6128&contentpaneid=17 Advanced Math Download Section http://www.paxm.org/symbulator/download/am.html Old TI-89 manual has more data http://education.ti.com/educationportal/sites/US/productDetail/us_ti89.html?bid=6 Assorted programs http://www.jvti.org/ assorted archives - ticalc.org http://www.ticalc.org/archives/ Assorted calcs http://www.shoreline.ctc.edu/precalc/ReferenceCenter/Tech.html assorted programs http://web.archive.org/web/20041013041757/http://www.ticalc.org/ calc files for assorted calcs http://www.ticalc.org/pub/ Circuits analysis http://www.paxm.org/symbulator/frontpage/ Detached Solutions - assorted http://www.detachedsolutions.com/main/ Detached Omnicalc User's Manual http://www.detachedsolutions.com/omnicalc/manual/ EE*Pro Download http://education.ti.com/educationportal/sites/US/productDetail/us_ee_pro_89.html Assorted Download http://calc.gregd.org/ =============== EEPro Download http://education.ti.com/educationportal/sites/US/productDetail/us_ee_pro_89.html EEPRO guidebook http://education.ti.com/educationportal/appsdelivery/download/download_eula.jsp?applicationId=6199&contentPaneId=25&cid=US ========= Kevin Kofler's Homepage http://ti89prog.kevinkofler.cjb.net/ kunjan.net/89 tips/glky url http://kunjan.net/archives/2005/12/06/tips-tricks-and-study-lessons-for-new-ti-89-titanium-users/ Parallel Link Plans - ticalc.org http://www.ticalc.org/hardware/cables/parallel.html teaching calculus with TI calc http://euler.slu.edu/courseware/TIProgs/TIProgs.html http://calcg.org/ ========= download statsle http://education.ti.com/educationportal/sites/US/productDetail/us_statslist_89.html --- http://facultyfiles.deanza.edu/gems/deansusan/statsle.pdf stats manual http://www.cbu.edu/~wschrein/media/Stat/statsle.pdf --- http://facultyfiles.deanza.edu/gems/bloomroberta/TI89StatInstructions.doc lessons http://www.engineering.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE3030/CalculatorNotes/ProbabilityFunctionsTI.pdf lessons http://www.cbu.edu/~wschrein/media/Stat/TI89man.pdf lessons http://mathforum.org/mathtools/tool/16322/ lessons http://www.howe-two.com/fhs/Calculus/regression89.html lessons http://education.ti.com/educationportal/sites/US/nonProductMulti/apps_latest.html?bid=6 ti-89 software ====== http://www.lakesideschool.org/people/homepages/fogerty/StatWeb/TI89Docs/TI89Help.htm statsle.pdf manual http://education.ti.com/guidebooks/apps/89stats_list_editor/stat-eng.pdf statsle.pdf manual http://iluvatar.ncssm.edu/~morrison/statsle.pdf good url statsle.pdf manual http://www.fayar.net/east/teacher.web/math/young/APPC/statsle.pdf Technical data 89T http://education.ti.com/educationportal/sites/US/productDetail/us_ti89ti.html?bid=7 TI-89 programs http://www.shoreline.ctc.edu/precalc/ReferenceCenter/TechFeat89.html Programs http://www.ticalc.org/archives/files/fileinfo/212/21274.html EE*Pro TI-89T DownL http://education.ti.com/educationportal/sites/US/productDetail/us_ee_pro_89.html Classes . http://education.ti.com/educationportal/sites/US/nonProductSingle/discover_hsalg.html http://www.prenhall.com/esm/app/calc_v2/frameset_89.html Texas Instruments OS & Apps http://education.ti.com/educationportal/sites/US/nonProductMulti/apps_latest.html?bid=4 Stats/List Editor DownL http://education.ti.com/educationportal/sites/US/productDetail/us_statslist_89.html TI-89 Titanium data/support http://education.ti.com/educationportal/sites/US/productDetail/us_ti89ti.html APPS http://education.ti.com/educationportal/sites/US/homePage/index.html TI Basic Lessons http://richfiles.solarbotics.net/Richfiles.html http://www.prenhall.com/divisions/esm/app/calculator/medialib/ReferenceCenter/framesets/TechFeat89.html http://www-s.ti.com/cgi-bin/discuss/sdbmessage.cgi?databasetoopen=calculators&topicarea=TI-89/TI89+Titanium/Voyage+200/TI-92+Plus&do_2=1 Discussion groups TI Topics http://richfiles.solarbotics.net/TITopics.html TI-89 interior http://richfiles.solarbotics.net/Turbo89.html TI Calculator Programs http://ostermiller.org/ti82/ TI Graphing Calculator FAQ http://www.technicalc.org/tifaq/ TI Connectivity kit Product http://education.ti.com/educationportal/sites/US/productDetail/us_ti_connectivity_kit.html TI Graphing Calculator FAQ http://www.technicalc.org/tifaq/?p3.htm App data http://www.ticalc.org/archives/news/articles/3/38/38694.html?p=1 TI-89 Assembly Math Programs http://www.ticalc.org/pub/89/asm/math/ http://www.rowan.edu/mars/depts/math/manuals/ti89.pdf http://www.covenantchristian.org/bird/Smart/Calc1/06_01_2006SummerTI-89primer.pdf TI-89 BASIC Science Programs http://www.ticalc.org/pub/89/basic/science/ TI-89 BASIC File http://www.ticalc.org/pub/89/basic/ TI-89 Guidebook http://education.ti.com/guidebooks/graphing/8992p/8992bookeng.pdf TI-89 vs HP49G+ http://alpage.ath.cx/hptute/compare.htm TI-89 Titanium - tech details http://www.ticalc.org/basics/calculators/ti-89-ti.html TI-89.org Forums - Edit Post http://www.ti-89.org/forum/editpost.php?post_id=4837&topic=1348&forum=4 TI-89.org Forums - Forum Index http://www.ti-89.org/forum/ TI-89.org Forums - View Topic http://www.ti-89.org/forum/viewtopic.php?topic=12&forum=10&9 TI-89 Games,ProgramsFAQ,Links,Func http://www.ti-89.org/ http://www.ticalc.org/archives/files/fileinfo/74/7484.html emulator for TI-89 http://www.shore.ctc.edu/precalc/ReferenceCenter/TechFeat89.html password required http://www.geocities.com/calculatorhelp/ti89.htm lessons TI-89T Guidebook http://education.ti.com/guidebooks/graphing/89ti/TI89TitaniumGuidebook_Part2_EN.pdf TI-TipList -- Examples: Fourier Series http://www.ibiblio.org/technicalc/examples/en/html/examples_index/fourierseries.html http://jcpti89.free.fr/programmesang.php TI-TipLis-Graphing Parametric Func http://www.ibiblio.org/technicalc/examples/en/html/examples_index/parametricfunctions.html http://dmoz.org/Computers/Hardware/Calculators/TI_Graphing_Calculators/TI-89/ TI-TipList -Examples: Half-Step Root Find http://www.ibiblio.org/technicalc/examples/en/html/examples_index/halfstep.html TI89 http://www.engineering.usu.edu/cee/faculty/gurro/Software_Calculators/TI_Docs/TI89.html TI89man.pdf http://www.cbu.edu/~wschrein/media/Stat/TI89man.pdf TI89manual.pdf http://hempy.dhs.org/classes/biom109/TI89man.pdf TICALCS-The TI Calculator Forum! - Home http://ticalcs.proboards41.com/index.cgi United-TI http://www.unitedti.org/index.php?showtopic=3438 Welcome - ticalc.org http://www.ticalc.org/ TI-89 Files - ticalc.org http://www.ticalc.org/pub/89/ TI-89 messages http://www.talkaboutcomputing.com/group/comp.sys.hp48/messages/195600.html http://www.math.armstrong.edu/ti92/ great programs http://bgo.netfirms.com/home.html TI 82/83 data =======