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We plot the results of taking x " }} {PARA 0 "" 0 "" {TEXT -1 70 "over a range of values, in order to find \+ which x leads to the maximum." }}{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 fro m 1 to n do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dd:=Pi*nn*(u^2+Pi^2 *nn^2)^(-1)*(1-exp(-u)*(-1)^nn);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "d:=evalf(d+2*exp(-(b/4+Pi^2*nn^2/(b*a^2))*t+b*x/2)*sin(Pi*x*nn/a)*dd) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "decay:=decay,[x,evalf(d,10)];" }}{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(decay);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "print(evalf(maxdecay,10));" }}{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 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"a G\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#?" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"tG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG \"$+$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&decayG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)maxdecayG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#)*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%0)*!\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%5)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%:)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%?)*! \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%D)*!\"$" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"%I)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%N) *!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%S)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%X)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%] )*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%b)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%g)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" %l)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%q)*!\"$" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"%v)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"%!))*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%&))*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%!*)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%&*)*!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%+**!\"$" }} {PARA 12 "" 1 "" {XPPMATH 20 "677$$\"#)*!\"\"$\"+a%[y!R!#57$$\"%0)*!\" $$\"+a)zo\"RF)7$$\"%5)*F-$\"+\"R&)[#RF)7$$\"%:)*F-$\"+\"pe<$RF)7$$\"%? )*F-$\"+4FQPRF)7$$\"%D)*F-$\"+j'G;%RF)7$$\"%I)*F-$\"+^[NWRF)7$$\"%N)*F -$\"+b`SXRF)7$$\"%S)*F-$\"+5'3Y%RF)7$$\"%X)*F-$\"+QexTRF)7$$\"%])*F-$ \"+9$*pORF)7$$\"%b)*F-$\"+o/:HRF)7$$\"%g)*F-$\"+\"zx)=RF)7$$\"%l)*F-$ \"+KXg0RF)7$$\"%q)*F-$\"+ph-*)QF)7$$\"%v)*F-$\"+?w!)oQF)7$$\"%!))*F-$ \"+x,eWQF)7$$\"%&))*F-$\"+Q\"Qf\"QF)7$$\"%!*)*F-$\"+$4NCy$F)7$$\"%&*)* F-$\"+Z)zNu$F)7$$\"%+**F-$\"+I>$))p$F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+b`SXR!#5" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$777$$\"#)*!\"\"$\"+a%[y!R!#57$$\"%0)*!\"$$ \"+a)zo\"RF-7$$\"%5)*F1$\"+\"R&)[#RF-7$$\"%:)*F1$\"+\"pe<$RF-7$$\"%?)* F1$\"+4FQPRF-7$$\"%D)*F1$\"+j'G;%RF-7$$\"%I)*F1$\"+^[NWRF-7$$\"%N)*F1$ \"+b`SXRF-7$$\"%S)*F1$\"+5'3Y%RF-7$$\"%X)*F1$\"+QexTRF-7$$\"%])*F1$\"+ 9$*pORF-7$$\"%b)*F1$\"+o/:HRF-7$$\"%g)*F1$\"+\"zx)=RF-7$$\"%l)*F1$\"+K Xg0RF-7$$\"%q)*F1$\"+ph-*)QF-7$$\"%v)*F1$\"+?w!)oQF-7$$\"%!))*F1$\"+x, eWQF-7$$\"%&))*F1$\"+Q\"Qf\"QF-7$$\"%!*)*F1$\"+$4NCy$F-7$$\"%&*)*F1$\" +Z)zNu$F-7$$\"%+**F1$\"+I>$))p$F--%'COLOURG6&%$RGBG$\"#5F*\"\"!Fcr-%+A XESLABELSG6$%!GFgr-%%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 }