**TI92P*Group file dated 02/29/00, 09:56lac\BlaplaceBcheckeydenom1Dfold1form1helpJilaplaceq ilapsub64lapsubW4laplace4lapsubEEmenubGnum1bNsimultdSsolvedWwronskiamZ/RRt:tՀ~lfs/cblcc(-b)-l+-*/,-creadlclfs/c/*-+(-:c;c;cdccclfs0c b(-aaaad at1tt1tύ ttttEXPR- ;dt1tcba}rend0]lf2/(-:rend/:ltlf1/: lf1/(-;lf1/)-(-:lf10lf20(-Ї;}readچread}ܹacabbcacabbc abababababx/_laplace\laplacelaplace\laplaceڏlaplace\ilaplace܈" ++++++,,+++,,,,,,,,,,,,,/ old0/exp1----write - (Mlaplace\-expexp1Working...- (MSolveD(equ,{x(t),0,1})-Solving equation:-(x(t),t,2)+1=^(t)equ-Storing equation:-write 0-Index 1-Back--page1ld0/1key:key1keyx(0)=0 and x'(0)=1---z%Solving diff. eq.:-writeSolveD((x(t),t,2)+1=^(t),{x(t),0,1})-exp 1-Back 2-PgDn--page1ld20ls0/exp3 M - (M exp2laplace\simultdexp3Working...- (M0-exp3 ;SimultD(eq,[x(t),0;y(t),1])-M 1-SimultD 3-PgUp--page1ls30ls0/eq-Mexp2 MStoring equ's in a var.-writeexp1expexp2 1-SimultD 2-PgUp 4-PgDn--page1ls20ls0/x(0)=0 and y(0)=1---exp1-expEquations:-write ŋexp1 ڋexp 1-Back 3-PgDn--page1ls10li/ls3/4key:ls2/3key:ls1/2key:ls/1key:key1keyls00x(0),.. initial conditions- find-x(t);y(t);.. functions to-eq;eq;.. diff./integral eq.- [x(t),x(0);y(t),y(0)])-Syntax: SimultD([eq;eq],-Simult. Diff. equ. solver-write 0-Index 2-Example--page1ls0Rld2/2key:ld1/1key:li/0key:key1keyld00f(0),.. initial conditions-x : independent var-f(x) : function to find-SolveD(equ,{f(x),f(0),..})-Syntax:-Differential equ. solver-write 0-Index 2-Example--page1ld10ll0/exp1---write - (Mlaplace\-expexp1Working...- (MexpExample: -Modulation ^(a*s)*f(s)-writeiLaplace(s/(s-b)*^(a*s),s)-exp 1-Back--page1ll20Rll2/2key:ll1/1key:li/0key:key1keyll00exp1-----write - 0Mlaplace\-expexp1Working...- 0MexpExample:-s : variable to transform-F(s) : LaPlace expression-Syntax: iLaplace(F(s),s)-writeiLaplace(a*s/(s^2+b^2),s)-exp0-Index 2-^(a*s)--page1ll10l0/exp1----write - ,Mlaplace\-expexp1Working...- ,MExam: -exp-  ڇDirac Delta function:-writelaplace(t*(t-a),t)-exp1-Back 2-Heaviside--page1l30l0/exp1----write - ,Mlaplace\-expexp1Working...- ,MExam: -exp-  ڇHeaviside function:-writelaplace(t*u(t-a),t)-exp1-Back 3-Delta--page1l20Rl3/3key:l2/2key:l1/1key:li/0key:key1keyl00exp1----write - ,Mlaplace\-expexp1Working...- ,MExample: -expt : variable to transform-f(t) :func. in time domain.-Syntax: Laplace(f(t),t)-writeLaplace(sin(t),t)-exp0-Index 2-Heaviside 3-Delta--page1l10lf0/exp1--write - (Mlaplace\-expexp1Working...- (MexpSolving integral:-write 0-Index 1-Back--page1li/3key:lf0/1key:key1keyg(x)=u(t)-f(x)=u(t)-u(t-3)-Rewriting to Heaviside--ڇ-ڇwritefold(u(t)-u(t-3),u(t),t)-exp0-Index 1-Back 3-PgDn--page1li/2key:lf/1key:key1keylf00t : the variable- convolute.-f(t),g(t) : expressions to-Syntax: Fold(f(t),g(t),t)-Solving conv. integral f*g-write 0-Index 2-Example--page1lf0lc0/is satisfied.-Zero indicate, that equ.-exp1explaplace\check Check(-exp ,res)-Checking result:-exp1 res-Store result in a var:-writeCheck(-exp ,-exp1 )-exp2 0-Index 1-Back--page1lc20lc0/exp1(M - (Mexplaplace\solvedexp1Working...- (MLaPlace(-exp ,{f(t)})-MSolving equatio for f(t):--expwriteexp 0-Index 1-Back 3-PgDn--page1lc10li/lc2/3key:lc1/2key:lc/1key:key1keylc00 from SolveD/SimultD.-res:is the result returned- of equations to check.-equ:is the equ. or matrix-SolveD/SimultD.-Checking the results of-Syntax: Check(equ,res)-write 0-Index 2-Example-Function: Check-page1lc0li/key1key perez-franco@iname.com-E-mail:- Roberto Perez-Franco-Ti-89 support:-E-mail: ask@post8.tele.dk-Author: Lars Frederiksen-LaPlace Help TI-89 v. 1.0-writePress any key--page1laut0RHome-Split 1 App-Graph-Split 1 App-laut/7key:lc/6key:ls/5key:ld1/4key:l1/3key:ll1/2key:lf/1key:key1key 6. Check- 5. SimultD- 4. SolveD- 3. Laplace- 2. iLaplace- 1. Fold 7. About-Index-write Press 1-7 Q-Quit--page1li0exp3exp4exp3exp2exp1}expkey}RADIAN-Angle-RECTANGULAR-Complex Format-AUTO-Exact/Approx-laplace On-Pretty Print-l1/:l10}key1چkey1}e22 2 21;12Ml1t221}writeچwrite}2CM----------------------------=M21page1چpage1}=3پlaplace\ilapsubPlease set mode: Angle=RADIAN-RRADIAN-Angle- :Please set mode: Complex Format=RECTANGULAR-RRECTANGULAR-Complex Format- :Please set mode: Exact/Approx=AUTO-RAUTO-Exact/Approx- :f1Rleqs/1tf:ffrf1Հlneq01 1ڏ;gendr0iendr/:real-ggglgg;real-g gendp0enext0SedYeddcc-a-cdd-a-c;gtbddbncbd%bn bn^bnbn]bd%vbn0- ;>-a-㍏gtaa;test20next/g: lx1/aa0- ;gegae0-g :glx10cbalaplace\num1laplace\denom1ՑYag9balaplace\num1laplace\denom1ՑYag9alaplace\num1laplace\denom1Ցag;;glaplace\form1 g;+ ve0- ;ganext/%aS1a1ڏŋa 1ڏ0- ;;1ڏ ;elgՍendp/l:test0end0l1/---Ї:-end/:/(-d1-dlld)-Հ%SՀ*/-dreads-d+-- readdtestx0;s-ll1/:SՀՀl;ll2/ *-l;1- bd1-bd; 1-bn bd1-bnbd;bn;bdllbntestll2/ls-;+-*/)-read-Ї:;)-Ї(-Ї;l;l+-*/)-read;^-ll20-ll10l+--readՀ/-Ї;end/:1-l+-/-readend/:l10-llneq/0-;r s- :lln2/cclln1/ttz1lneq/can't solve this!-t; +-*/-cread;dcd;ctan(-dd:cln(-dlln20c lln10tf1leqs0ft}hgfedcbdbna}rend0]lf2/(-:rend/:ltlf1/: lf1/(-;lf1/)-(-:lf10lf20(-Ї;}readچread}******************************* Email : ask@post8.tele.dk Author : Lars Frederiksen Date : 9.7.98 Version : 1.2.2 Function : Inverse Laplace sp.*******************************11ܵhz% z q eڏf-f(s)-laplace\lapsub*)ylus/caf aldlcaaif fhkhhkh hhkhkhu; can't solve this!-Riu;fPiifk ffPuifhu;0-f ;kifkidk)-careaddluf0ls/0-a0-i 9kzaz% aifk0-fstrinfڊ;kifkidkca1-aldlcaa)-careaddlf0start/lcklcՀmk k^n*mkn9Qkfmŋk k+k^(n-f)*(m,,f)knftkn;bndmŋb%kmSnkmdflicfd dl1f fdficlՅ;difftdca1-al+-*/)-careadlcaklff1/ca/*-+(-:c;lff0lis/cad/-al)-careadlcaa,-caread dlif0lds/cadif *-dalflcaad ddif)-kjfreaddifk:,-)-jfreadkdifdlj,-diffreadd9difdif-diffЇ=dif+-*/-careadfldf0rcab٭Rendp0start/atzztkŏaazh%ākli/atat; aazh%čali0t;saashaa0-h ;start/btztzaŏb;atzat:lt2/znm;%*/-gfreadSntts-k;lt1/flg:g*/-gfreadlgs-k;*/^-gfreadklt10c fg0-f ;cfmicmmlt20a]a^inmtaaluf/c:u(-aclus0lf/c:(-acls0lff/c:inString(a,1[l])cclicaclff10cndltlif/c:-aclis0lds0ldf/c:-ac-aa--jЇ:j;balbbj+--breadaendp/lb:bbdifuhstart0ndncbabictnd rcba}nmgtlnddifuihjkfdcba}rend0]lf2/(-:rend/:ltlf1/: lf1/(-;lf1/)-(-:lf10lf20(-Ї;}readچread}******************************* Email : ask@post8.tele.dk Author : Lars Frederiksen Date : 9.7.98 Version : 1.1.0 Function : Laplace sp.*******************************1icRADIAN-Angle-RECTANGULAR-Complex Format-laplace Menu()-WSetFold(laplace)-WSetFold(Main)-WCustmOff-WNewProb-WClrHome-WSet Up-VHelp()-WHelp-VFold(x(t),y(t),t)-WFold-Vlap( )-WiLaplace(F(s),s)-WLaplace(f(t),t)-WLaplace-VWronskia()-WCheck(eq,result)-WSimultD([;],[;])-WSolveD(eq,{,})-WDiff Eq-VVacabca%ababca%acaba%bcabcb%bcc%abbcccb%zbbcccc%abbcb%cbbccc%abbcccb%czbbbcccc%bbccb%cbbcccc%aba%zaca%ab%c%b%cbc%aba%aba%aba%Haba%a%aabab babbZbbbbHbb%aba% aba%<aba%xa%aababbb b<bxb%aba%aba% a%aabbb b%aba%a%abb%a%b%a%a%a%a%a%a%a%a%ٽeqREfeqf2ՇfeqՀndftcrndeqӰlaplace\ilapsubeqndieqeqizfrՀ1cffύlaplace\lapsubindfteqndr(-iif1ՀifՀci iif2Հfindft12ndn1)-lcclcfirst column has to be functions-Rc:(-lc lerror dimension-Rtnd:tndsimultd([eq;eq;..],[x(t),f(0),..;y(t),..])-RMAT- MAT- ㊃:Please set mode: Angle=RADIAN-RRADIAN-Angle- :Please set mode: Complex Format=RECTANGULAR-RRECTANGULAR-Complex Format- :Please set mode: Exact/Approx=AUTO-RAUTO-Exact/Approx- :reqcilndf21}******************************* Email : ask@post8.tele.dk Author : Lars Frederiksen Date : 18.7.98 Version : 1.2.0 Function :Mul. Diff. Solve*******************************ܖcbzbՑlaplace\ilapsublacύlaplace\lapsubbcՁ Հ)-lcclcclafirst argument in the list has to be a function name-Rc:(-lc lsecond argument has to be a list-RLIST- :first argument has to be an equatio-R=- :Please set mode: Angle=RADIAN-RRADIAN-Angle- :Please set mode: Complex Format=RECTANGULAR-RRECTANGULAR-Complex Format- :Please set mode: Exact/Approx=AUTO-RAUTO-Exact/Approx- :lcba}******************************* Email : ask@post8.tele.dk Author : Lars Frederiksen Date : 18.7.98 Version : 1.0.1 Function : Diff.eq. solversolvedif(equation,{f(x),initial conditions})*******************************b() Prgm Lbl lbl DelVar x Local a,b,c,d,e,f,g,h,i,j,n,,temp1,temp2 ClrIO Dialog Title "Wronskian Solver" Text "Input the # of functions in the wronskian." Text "(variable with respect to X), (up to 7)" Text "" Request "number",n EndDlog expr(n)n If n=2 Then Goto lbl2 ElseIf n=3 Then Goto lbl3 ElseIf n=4 Then Goto lbl4 ElseIf n=5 Then Goto lbl5 ElseIf n=6 Then Goto lbl6 ElseIf n=7 Then Goto lbl7 EndIf Lbl lbl2 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b EndDlog expr(a)a expr(b)b det([[a,b][(a,x),(b,x)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls2 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b) Goto lblq Lbl lbl3 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b Request "function:3",c EndDlog expr(a)a expr(b)b expr(c)c det([[a,b,c][(a,x),(b,x),(c,x)][(a,x,2),(b,x,2),(c,x,2)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&","&string(c)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls3 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b)&"+C3*"&string(c) Goto lblq Lbl lbl4 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b Request "function:3",c Request "function:4",d EndDlog expr(a)a expr(b)b expr(c)c expr(d)d det([[a,b,c,d][(a,x),(b,x),(c,x),(d,x)][(a,x,2),(b,x,2),(c,x,2),(d,x,2)][(a,x,3),(b,x,3),(c,x,3),(d,x,3)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&","&string(c)&","&string(d)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls4 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b)&"+C3*"&string(c)&"+C4*"&string(d) Goto lblq Lbl lbl5 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b Request "function:3",c Request "function:4",d Request "function:5",e EndDlog expr(a)a expr(b)b expr(c)c expr(d)d expr(e)e det([[a,b,c,d,e][(a,x),(b,x),(c,x),(d,x),(e,x)][(a,x,2),(b,x,2),(c,x,2),(d,x,2),(e,x,2)][(a,x,3),(b,x,3),(c,x,3),(d,x,3),(e,x,3)][(a,x,4),(b,x,4),(c,x,4),(d,x,4),(e,x,4)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&","&string(c)&","&string(d)&","&string(e)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls5 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b)&"+C3*"&string(c)&"+C4*"&string(d)&"+C5*"&string(e) Goto lblq Lbl lbl6 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b Request "function:3",c Request "function:4",d Request "function:5",e Request "function:6",f EndDlog expr(a)a expr(b)b expr(c)c expr(d)d expr(e)e expr(f)f det([[a,b,c,d,e,f][(a,x),(b,x),(c,x),(d,x),(e,x),(f,x)][(a,x,2),(b,x,2),(c,x,2),(d,x,2),(e,x,2),(f,x,2)][(a,x,3),(b,x,3),(c,x,3),(d,x,3),(e,x,3),(f,x,3)][(a,x,4),(b,x,4),(c,x,4),(d,x,4),(e,x,4),(f,x,4)][(a,x,5),(b,x,5),(c,x,5),(d,x,5),(e,x,5),(f,x,5)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&","&string(c)&","&string(d)&","&string(e)&","&string(f)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls6 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b)&"+C3*"&string(c)&"+C4*"&string(d)&"+C5*"&string(e)*"+C6*"&string(f) Goto lblq Lbl lbl7 Dialog Title "Enter the functions with respect to X" Request "function:1",a Request "function:2",b Request "function:3",c Request "function:4",d Request "function:5",e Request "function:6",f Request "function:7",g EndDlog expr(a)a expr(b)b expr(c)c expr(d)d expr(e)e expr(f)f expr(g)g det([[a,b,c,d,e,f,g][(a,x),(b,x),(c,x),(d,x),(e,x),(f,x),(g,x)][(a,x,2),(b,x,2),(c,x,2),(d,x,2),(e,x,2),(f,x,2),(g,x,2)][(a,x,3),(b,x,3),(c,x,3),(d,x,3),(e,x,3),(f,x,3),(g,x,3)][(a,x,4),(b,x,4),(c,x,4),(d,x,4),(e,x,4),(f,x,4),(g,x,4)][(a,x,5),(b,x,5),(c,x,5),(d,x,5),(e,x,5),(f,x,5),(g,x,5)][(a,x,6),(b,x,6),(c,x,6),(d,x,6),(e,x,6),(f,x,6),(g,x,6)]])temp1 Disp "The Wronskian is:" Disp "W("&string(a)&","&string(b)&","&string(c)&","&string(d)&","&string(e)&","&string(f)&","&string(g)&")=" Output 25,0,temp1 Pause x temp1temp2 Goto lbl Lbl lbls7 DelVar x Disp "The fundamental set is:" Disp "y=C1*"&string(a)&"+C2*"&string(b)&"+C3*"&string(c)&"+C4*"&string(d)&"+C5*"&string(e)*"+C6*"&string(f)*"+C7*"&string(g) Goto lblq Lbl lbl If temp20 Then Goto lbli Else Goto lbld EndIf Lbl lbli Disp "Linearly Independent" If n=2 Then Goto lbls2 ElseIf n=3 Then Goto lbls3 ElseIf n=4 Then Goto lbls4 ElseIf n=5 Then Goto lbls5 ElseIf n=6 Then Goto lbls6 ElseIf n=7 Then Goto lbls7 EndIf Goto lblq Lbl lbld Disp "Linearly dependent, " Disp "the fundamental set " Disp "is non existent." Goto lblq Lbl lblq Pause PopUp {"Run Again","About","Exit Program"}, If =1 Then Goto lbl ElseIf =2 Then Goto lbl ElseIf =3 Then Goto lbl EndIf Lbl lbl Dialog Title "Wronskian Solver for the TI-89" Text " Copyright 1999, Eric P. Esterle" Text "This Wronskian Solver will solve Wronskians" Text "which consist of up to seven functions. It will" Text "give you the linear criterion and when possi-" Text "ble, the fundamental set of solutions. Web:" Text "http://pages.preferred.com/~pesterle/eric" Text "frames.htm.email:eesterle@preferred.com" EndDlog Lbl lbl DispHome EndPrgm\