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It runs over the range [st,en]" }}{PARA 0 "" 0 "" {TEXT -1 44 "and we find the maximum value in that range." }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 9 "u:=b*a/2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "d:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for nn from 1 to n do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "dd:=2*a*u*Pi^2*nn*(u^2+Pi^2*(1-nn)^2)^(-1)*(u^2+Pi^2*(1+nn)^2) ^(-1)*(1+exp(-u)*(-1)^nn);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "d:=evalf(d+2*exp(-(b/4+Pi^2*nn^2/(b *a^2))*t+b*x/2)*sin(Pi*x*nn/a)*dd/a);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "decay:=decay,[x,evalf(d ,9)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "maxdecay:=max(maxdecay,d); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "print(de cay);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "print(t,evalf(maxdecay,9)) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot([decay]);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#]" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG\" \")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"$+#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#stG$\"%0)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#enG$\"%2)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&decayG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)maxdecayG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%0)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&^!)* !\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&_!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&`!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"& a!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&b!)*!\"%" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"&c!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"&d!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&e!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&f!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&g!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&h!)*!\"%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&i!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&j!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&k!) *!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&l!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&m!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"&n!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&o!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&p!)*!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"&q!)*!\"%" }}{PARA 12 "" 1 "" {XPPMATH 20 "677$$\"%0)*!\"$$\" *CX=1&!\"*7$$\"&^!)*!\"%$\"*')\\=1&F)7$$\"&_!)*F-$\"*+a=1&F)7$$\"&`!)* F-$\"*md=1&F)7$$\"&a!)*F-$\"*%3'=1&F)7$$\"&b!)*F-$\"*`j=1&F)7$$\"&c!)* F-$\"*ul=1&F)7$$\"&d!)*F-$\"*Yn=1&F)7$$\"&e!)*F-$\"*po=1&F)7$$\"&f!)*F -$\"*Wp=1&F)7$$\"&g!)*F-$\"*qp=1&F)7$$\"&h!)*F-$\"*Zp=1&F)7$$\"&i!)*F- $\"*uo=1&F)7$$\"&j!)*F-$\"*`n=1&F)7$$\"&k!)*F-$\"*#e'=1&F)7$$\"&l!)*F- $\"*ij=1&F)7$$\"&m!)*F-$\"*$4'=1&F)7$$\"&n!)*F-$\"*ud=1&F)7$$\"&o!)*F- $\"*1a=1&F)7$$\"&p!)*F-$\"*()\\=1&F)7$$\"&q!)*F-$\"*>X=1&F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\")$\"*qp=1&!\"*" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$777$$\"%0)*!\"$$\"*CX =1&!\"*7$$\"&^!)*!\"%$\"*')\\=1&F-7$$\"&_!)*F1$\"*+a=1&F-7$$\"&`!)*F1$ \"*md=1&F-7$$\"&a!)*F1$\"*%3'=1&F-7$$\"&b!)*F1$\"*`j=1&F-7$$\"&c!)*F1$ \"*ul=1&F-7$$\"&d!)*F1$\"*Yn=1&F-7$$\"&e!)*F1$\"*po=1&F-7$$\"&f!)*F1$ \"*Wp=1&F-7$$\"&g!)*F1$\"*qp=1&F-7$$\"&h!)*F1$\"*Zp=1&F-7$$\"&i!)*F1$ \"*uo=1&F-7$$\"&j!)*F1$\"*`n=1&F-7$$\"&k!)*F1$\"*#e'=1&F-7$$\"&l!)*F1$ \"*ij=1&F-7$$\"&m!)*F1$\"*$4'=1&F-7$$\"&n!)*F1$\"*ud=1&F-7$$\"&o!)*F1$ \"*1a=1&F-7$$\"&p!)*F1$\"*()\\=1&F-7$$\"&q!)*F1$\"*>X=1&F--%'COLOURG6& %$RGBG$\"#5!\"\"\"\"!Fdr-%+AXESLABELSG6$%!GFhr-%%VIEWG6$%(DEFAULTGF\\s " 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }