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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# Problem 3.7-12 in \+
Nakhle's textbook on pde" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 
"F:=4*x*(1-x)*y*(1-y)*sin(m*Pi*x)*sin(n*Pi*y);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "assume(m,integer);assume(n,integer);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "A:=unapply(int(int(F,x=0..1)
,y=0..1),(m,n));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "N:=10: \+
u:=(x,y,t)->sum(sum(A(m,n)*sin(m*Pi*x)*sin(n*Pi*y)*exp(-Pi^2*(m^2+n^2)
*t),m=1..N),n=1..N);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot3d(u(x,y,0),x=0..1,y=0..1);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plots[animate](plot3d,[u(x,
y,t),x=0..1,y=0..1],t=0..0.05);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "0 0 0" 24 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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