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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "# Problem 3.9-3 in \+
Nakhle Asmar's textbook on pde\n" }{MPLTEXT 1 0 105 "# a=1, b=1 Poisso
n problem with zero BC\n# Asmar calls the answer u_1(x,y) in section 3
.9 of his textbook." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "assu
me(m,integer,m>0); assume(n,integer,n>0);\n" }{MPLTEXT 1 0 37 "# Requi
red for subsequent summations." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 33 "lambda:=(m,n)->(m*Pi)^2+(n*Pi)^2;" }}}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 20 "f:=(x,y)->sin(Pi*x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "F:=-4*(1/lambda(m,n))*f(x,y)*sin(m*Pi*x)*sin(n*Pi*y);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "EE:=unapply(int(int(F,x
=0..1,'AllSolutions'),y=0..1,'AllSolutions'),(m,n));\n" }{MPLTEXT 1 0 
70 "# Special option 'AllSolutions' insures that maple does not skip o
ver\n" }{MPLTEXT 1 0 42 "# any subcases, like m=1, in this example." }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "N:=10: u:=(x,y)->sum(sum(E
E(m,n)*sin(m*Pi*x)*sin(n*Pi*y),m=1..N),n=1..N);" }}}{EXCHG {PARA 0 "> 
" 0 "" {MPLTEXT 1 0 29 "plot3d(u(x,y),x=0..1,y=0..1);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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