{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 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "SymbolPi" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot " -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "# G.H. George ENG I 5432 2008 02 05" }}{PARA 0 "" 0 "" {TEXT -1 40 "# 2008 Winter Problem Set 9 Question 5." }}{PARA 0 "" 0 "" {TEXT -1 60 "# Animation of the wave satisfying the heat equation on 0 < " }{TEXT 256 1 "x" } {TEXT -1 13 " < 100, with " }}{PARA 0 "" 0 "" {TEXT -1 32 "# the ends \+ held at temperatures " }{TEXT 257 1 "u" }{TEXT -1 3 "(0," }{TEXT 258 1 "t" }{TEXT -1 10 ") = 0 and " }{TEXT 259 1 "u" }{TEXT -1 5 "(100," } {TEXT 260 1 "t" }{TEXT -1 16 ") = 100 and with" }}{PARA 0 "" 0 "" {TEXT -1 31 "# initial temperature profile " }{TEXT 261 1 "u" }{TEXT -1 1 "(" }{TEXT 262 1 "x" }{TEXT -1 6 ",0) = " }{TEXT 263 2 "f " } {TEXT -1 1 "(" }{TEXT 264 1 "x" }{TEXT -1 5 ") = 2" }{TEXT 265 1 "x" } {TEXT -1 1 " " }{TEXT 267 1 "-" }{TEXT -1 2 " (" }{TEXT 266 1 "x" } {TEXT -1 7 "/10)^2." }}{PARA 0 "" 0 "" {TEXT -1 73 "# Only the first f our non-zero terms in the Fourier sine series are used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "y(x,t) := x + 800/Pi^3 * (sin(Pi*x/100)*exp(-Pi^2*t/2500)\n+ sin(3*Pi*x/100)*exp(-9 *Pi^2*t/2500)/27\n+ sin(5*Pi*x/100)*exp(-25*Pi^2*t/2500)/125\n+ sin(7* Pi*x/100)*exp(-49*Pi^2*t/2500)/343);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>-%\"yG6$%\"xG%\"tG,&F'\"\"\"*(\"$+)F*%#PiG!\"$,**&-%$sinG6#,$*(\"$+ \"!\"\"F-F*F'F*F*F*-%$expG6#,$*(\"%+DF7F-\"\"#F(F*F7F*F**&#F*\"#FF**&- F26#,$**\"\"$F*F6F7F-F*F'F*F*F*-F96#,$**\"\"*F*F=F7F-F>F(F*F7F*F*F**&# F*\"$D\"F**&-F26#,$*(\"#?F7F-F*F'F*F*F*-F96#,$*(F6F7F-F>F(F*F7F*F*F**& #F*\"$V$F**&-F26#,$**\"\"(F*F6F7F-F*F'F*F*F*-F96#,$**\"#\\F*F=F7F-F>F( F*F7F*F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(plot s,animate):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "animate(y(x, t),x=0..100,t=0..1000,frames=50,color=blue,\nthickness=2);" }}{PARA 13 "" 1 "" {GLPLOT2D 285 218 218 {PLOTDATA 2 "6&-%(ANIMATEG6T7#-%'CURV ESG6$7S7$$\"\"!F-F,7$$\"+LLL$3#!\"*$\"3'f*o\"42ho0%!#<7$$\"+nmmmTF1$\" 3uj46#[Fa3)F47$$\"++++]iF1$\"3]v>)GO()f?\"!#;7$$\"+LLLL$)F1$\"3!**fP\\ +$*ef\"F?7$$\"+nmmT5!\")$\"3CXiqhvsw>F?7$$\"++++]7FH$\"3cU\"3`m/wM#F?7 $$\"+LLLe9FH$\"39e5aBJC3FF?7$$\"+nmmm;FH$\"3C6.:Dv%)eIF?7$$\"++++v=FH$ \"35#eHopN**R$F?7$$F0FH$\"3\"\\?k>^Y@t$F?7$$\"+nmm\"H#FH$\"3I$HK^$G1cS F?7$$\"+++++DFH$\"3#ev`%)4z?P%F?7$$\"+LLL3FFH$\"31r$zGSK.o%F?7$$\"+nmm ;HFH$\"3![)f#>R-2)\\F?7$$\"++++DJFH$\"3_1E%)p7(GF&F?7$$\"+LLLLLFH$\"39 Qg#e+Ckb&F?7$$\"+nmmTNFH$\"3Sq:i4$eF?7$$\"++++]PFH$\"3y-VG.S?'4'F?7 $$\"+LLLeRFH$\"3?/VJ@([?N'F?7$$F7FH$\"3==zE[=f)f'F?7$$\"++++vVFH$\"3:5 +c+64OoF?7$$\"+LLL$e%FH$\"3GRv65J*[1(F?7$$\"+nmm\"z%FH$\"3C'>E$H.M&G(F ?7$$\"+++++]FH$\"3!pS%*3T\"o(\\(F?7$$\"+LLL3_FH$\"3QjG*f*p+-xF?7$$\"+n mm;aFH$\"3at3XVkA)*yF?7$$\"++++DcFH$\"3e6+c+64'3)F?7$$\"+LLLLeFH$\"3u' eM\\^e_E)F?7$$\"+nmmTgFH$\"3\\Qwka?QN%)F?7$$F9bs*F?7$$\"+nmmT&)FH$\"3+\"RuoXw:z*F?7$$\"++++]()FH$\"3cU\" 3`m/w%)*F?7$$\"+LLLe*)FH$\"3'4\"HPGUR$*)*F?7$$\"+nmmm\"*FH$\"3AK4FQjAH **F?7$$\"++++v$*FH$\"3Wu>)GO()f&**F?7$$\"+LLL$e*FH$\"3chx([T4_(**F?7$$ \"+nmm\"z*FH$\"3QA]US%>!*)**F?7$$\"+++++5!\"($\"2')***************!#:- %'COLOURG6&%$RGBGF,F,$\"*++++\"FH7#-F(6$7SF+7$F/$\"3m>+5Cg'*RPF47$F6$ \"3S8\\e]QsouF47$F;$\"3\"HLl+UNv6\"F?7$FA$\"3sOw(oT\\\\[\"F?7$FF$\"3WI C7Bk:[=F?7$FL$\"3/z*=E/%H1AF?7$FQ$\"3[YQzOjgeDF?7$FV$\"3-]2nQ#[W!HF?7$ Fen$\"3e(zi!RRGVKF?7$Fjn$\"3/Jlf@-ouNF?7$F^o$\"3g/>:ogH)*QF?7$Fco$\"3] \">b5+qQ@%F?7$Fho$\"33mGdxl?@XF?7$F]p$\"33#)*G*RK;?[F?7$Fbp$\"3W\\&z^S Q16&F?7$Fgp$\"3%eu5$=8c#R&F?7$F\\q$\"39RAo]Q)em&F?7$Faq$\"3NSO%H:u0$fF ?7$Ffq$\"3U%)Q.&*=h'='F?7$F[r$\"3mbgN^Z)RV'F?7$F_r$\"3S.%3>!eosmF?7$Fd r$\"3qyp>\"f6F!pF?7$Fir$\"3a!3z!eoAzF?7$Fbt$\"3ACF-=9l+ \")F?7$Fgt$\"39?sOG_%*p#)F?7$F\\u$\"3xTO%H:u0V)F?7$F`u$\"3s2*[t^]De)F? 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