{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Math 304, Aug. 29, 2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eps := 1-evalf(1/3)*3; # fi nding the machine precision" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$epsG $\"\"\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "The program: (copy-paste \+ from Notepad, using courier new font" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 434 "\nsine := proc( x :: numeric # input\n \+ )\n local k, s, eps, t;\n\n # default error tolerance\n eps := 1.0 - evalf(1/3)*3; \n\n s := 0; # initialize the sum\n t := x; # the first term;\n\n for k from 1 to 10000 while abs(t) > eps do \n\n # add the new term in the series\n s := s + t;\n \+ \n # prepare the next term \n t := (-1)^k * x^(2*k+1)/(2*k+1 )!;\n\n end do;\n\n return s; # output\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "read( \"c:/304/sine.txt\");" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%sineGf*6#' %\"xG%(numericG6&%\"kG%\"sG%$epsG%\"tG6\"F/C'>8&,&$\"#5!\"\"\"\"\",$*& \"\"$F7-%&evalfG6##F7F:F7F7F6>8%\"\"!>8'9$?(8$F7F7\"&++\"2F2-%$absG6#F CC$>F@,&F@F7FCF7>FC*()F6FFF7)FD,&*&\"\"#F7FFF7F7F7F7F7-%*factorialG6#F SF6OF@F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "z := sine(1 .23);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$\"+?!))[U*!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "sin(1.23); # maple built-i n sine program" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+>!))[U*!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "Th e order of accuracy" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "taylor(sin(0+h),h=0,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"hG\"\"\"F%#!\"\"\"\"'\"\"$#F%\"$?\"\"\"&-%\"OG6 #F%\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "We use Taylor's series for h to be small. For example, \+ h=0.2;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "h := 0.2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG$\" \"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "h^7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$G\"!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "for x f rom 1 by 0.5 to 3 do\n evalf(sin(x))\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+[)4ZT)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+m) \\\\(**!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+oU(H4*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+T9s%)f!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"3+7T\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "x := Vector([1,1.5,2,2.5,3]) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6%\"*_!=e9-%'MATR IXG6#7'7#\"\"\"7#$\"#:!\"\"7#\"\"#7#$\"#DF27#\"\"$&%'VectorG6#%'column G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y := Vector([0.84,1,0. 9,0.6,0.14]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%'RTABLEG6%\"* s\"=e9-%'MATRIXG6#7'7#$\"#%)!\"#7#\"\"\"7#$\"\"*!\"\"7#$\"\"'F67#$\"#9 F0&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " A := Matrix(5,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6 %\"*WX1Y\"-%'MATRIXG6#7'7'\"\"!F.F.F.F.F-F-F-F-%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "for k from 1 to 5 do\n for j from 1 to 5 do\n A[j,k] := x[j]^(k-1)\n end do\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'RTABLEG6%\"*WX1Y\"-%'MATRIXG6#7'7'\"\"\"F,F,F,F,7'$F,\"\"!$\"#:! \"\"$\"$D#!\"#$\"%vL!\"$$\"&D1&!\"%7'F,\"\"#\"\"%\"\")\"#;7'F.$\"#DF2$ \"$D'F5$\"&Dc\"F8$\"'D1RF;7'F,\"\"$\"\"*\"#F\"#\")%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "c := LinearAlgebra:-LinearSo lve(A,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'RTABLEG6%\"*))Ga Y\"-%'MATRIXG6#7'7#$!3y*)************f!#=7#$\"3#QmmmmmmR#!#<7#$!3.kmmm mm;6F47#$\"37BLLLLLLLLLLLL8!#>&%'VectorG6#%'columnG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "g := c[1] + c[2]*t + c[3]*t^ 2 + c[4]*t^3 + c[5]*t^4;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"gG,,$ \"3y*)************f!#=!\"\"*&$\"3#QmmmmmmR#!#<\"\"\"%\"tGF.F.*&$\"3.km mmmm;6F-F.)F/\"\"#F.F)*&$\"37BLLLLLLLLLLLL8!# >F.)F/\"\"%F.F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot1 := plot(sin(t),t=1..3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pl ot2 := plot(g,t=1..3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "p lots[display](\{plot1,plot2\});" }}{PARA 13 "" 1 "" {GLPLOT2D 431 266 266 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"\"\"\"!$\"30l*y![)4ZT)!#=7$$\" 3ALLL3VfV5!#<$\"3#f&)zHk\"=U')F-7$$\"3smm\"H[D:3\"F1$\"3fwysPyvE))F-7$ $\"3XLL$e0$=C6F1$\"3[.S7f/:>!*F-7$$\"3QLL$3RBr;\"F1$\"37fjCeZC'>*F-7$$ \"3imm\"zjf)47F1$\"33.T)zTkcN*F-7$$\"3WLLe4;[\\7F1$\"3w#=CwJ5#)[*F-7$$ \"3-++Dmy]!H\"F1$\"3IAWE1ov4'*F-7$$\"3>LLezs$HL\"F1$\"3%y0VTeY%=(*F-7$ $\"31++D@1Bv8F1$\"3K6Rtx*y$4)*F-7$$\"3pmmm@Xt=9F1$\"3akI%>k3Y))*F-7$$ \"3MLL$3y_qX\"F1$\"3]$*y\"4u\"QN**F-7$$\"3'******\\1!>+:F1$\"35H5`KT3v **F-7$$\"3*******\\Z/Na\"F1$\"3)Rf'G0gF'***F-7$$\"35+++NfC&e\"F1$\"33L vFig&*)***F-7$$\"3LLLez6:B;F1$\"3AF==xzH')**F-7$$\"3_mmm\"=C#o;F1$\"3a Us$ffwD&**F-7$$\"3gmmmEpS1*4I]d'*F-7$$\"3!****\\(3zMu=F1$\"3R!=Z#>!4Ga*F-7$$\"3emm;H_?<>F 1$\"3emWVE.)fS*F-7$$\"3mmm\"zihl&>F1$\"3%*fEmau5l#*F-7$$\"3KLL$3#G,**> F1$\"3G@\"3=&z2(4*F-7$$\"39w7>0*)F-7$$\"3o***\\PQ#\\ \"3#F1$\"3-J)[3(\\/C()F-7$$\"3BLL$e\"*[H7#F1$\"3M0(R)pT(R^)F-7$$\"3#** *****pvxl@F1$\"3solT?,f\"G)F-7$$\"3z****\\_qn2AF1$\"3hHK6\"pY&R!)F-7$$ \"3%)***\\i&p@[AF1$\"3!Q-S]??>z(F-7$$\"3#)****\\2'HKH#F1$\"3dgRfq.*>]( F-7$$\"3_mmmwanLBF1$\"3]M^F6]\\GsF-7$$\"3u*****\\2goP#F1$\"3e&e_rgSM#p F-7$$\"3CLLeR<*fT#F1$\"3CzW%p1^ej'F-7$$\"3'******\\)HxeCF1$\"3zN,n)=I) 4jF-7$$\"3Cmm\"H!o-*\\#F1$\"3#yW1?J:D*fF-7$$\"3))***\\7k.6a#F1$\"3s\"p n;0g/l&F-7$$\"3emmmT9C#e#F1$\"3.CK]rRO1`F-7$$\"3\"****\\i!*3`i#F1$\"32 0*e%)y;l$\\F-7$$\"3;LLL$*zymEF1$\"3mTTUUskrXF-7$$\"30LL$3N1#4FF1$\"3/ \\3A4oQ!>%F-7$$\"3kmm\"HYt7v#F1$\"3voB'4=O[!QF-7$$\"3%*******p(G**y#F1 $\"3dJ?=*Q.YW$F-7$$\"3Umm;9@BMGF1$\"3`'=]\")HRa-$F-7$$\"3/LLL`v&Q(GF1$ \"33uyj*4zak#F-7$$\"30++DOl5;HF1$\"3>u6q+?!eB#F-7$$\"3/++v.UacHF1$\"3u c*fTcT*R=F-7$$\"\"$F*$\"38s')f!3+7T\"F--%'COLOURG6&%$RGBG$\"#5!\"\"$F* F*F`[l-F$6$7S7$F($\"3o*************R)F-7$F/$\"3/;VrvK)=m)F-7$F5$\"3i[$ Q6(3Gp))F-7$F:$\"3%**p*R`zE!3*F-7$F?$\"3wjxFh,Qp#*F-7$FD$\"31v0>5o$\\V *F-7$FI$\"31$[,*>moo&*F-7$FN$\"3E[=\"f5*f(o*F-7$FS$\"3'>!H]?l3!z*F-7$F X$\"3ACN+9X(>()*F-7$Fgn$\"3L8%3'o[dN**F-7$F\\o$\"3[(G6.d[Y(**F-7$Fao$ \"3d5iQ]p++5F17$Ffo$\"36aocP\\i+5F17$F[p$\"3])[zF[#G%***F-7$F`p$\"3/q` 'y@4&o**F-7$Fep$\"3jF)*eV_!)>**F-7$Fjp$\"3E<(Q,FGN')*F-7$F_q$\"31m+JXK 7\"y*F-7$Fdq$\"3gM*ygm/Lp*F-7$Fiq$\"3)y:(F-7$Fju$\"3YFsf6BQ**oF-7$F_v$\"3SUZ+=9FC mF-7$Fdv$\"3e*3^LKP?J'F-7$Fiv$\"3P$3$)zh!\\2gF-7$F^w$\"3-ju\"pCz\"ycF- 7$Fcw$\"3SQ%z11RbM&F-7$Fhw$\"3%>.;Ne^h)\\F-7$F]x$\"3p(f!=$4%RHYF-7$Fbx $\"3o)e*z0=#RD%F-7$Fgx$\"31*)RN(oq5(QF-7$F\\y$\"3moV67*o,^$F-7$Fay$\"3 kVMJW>$f3$F-7$Ffy$\"3oi:(>L!*pp#F-7$F[z$\"39DSi>(4DF#F-7$F`z$\"3;l]7fR %o&=F-7$Fez$\"3C,++++++9F-Fiz-%+AXESLABELSG6%Q\"t6\"Q!F[el-%%FONTG6#%( DEFAULTG-%%VIEWG6$;F(FezF`el" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(t=2.231,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+NEnLy!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sin(2.231 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'Rt')*y!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "for t from 2 by 0.25 to 4 do\n evalf(ln (t))\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1=ZJp!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+i@I4\")!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+>t!H;*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+74 g65!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*G7')4\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'*\\ly6!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+oHw_7!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Se v@8!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+hVH'Q\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "use the 3 digits for each number above. \+ " }}}}{MARK "27 0 0" 42 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 145818052 145818172 146064544 146542888 }{RTABLE M7R0 I6RTABLE_SAVE/145818052X*%)anythingG6"6"[gl!#%!!!"&"&"""$"#:!""""#$"#DF*""$F& } {RTABLE M7R0 I6RTABLE_SAVE/145818172X*%)anythingG6"6"[gl!#%!!!"&"&$"#%)!"#"""$""*!""$""'F-$" #9F)F& } {RTABLE M7R0 I6RTABLE_SAVE/146064544X,%)anythingG6"6"[gl!"%!!!#:"&"&"""$F'""!F'F(F'F'$"#:!"" 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