# 3.9-3, Asmar, Poisson problem with zero conditions, f=sin(PI x)
# a=1, b=1 Poisson problem with zero BC
assume(m,integer,m>0); assume(n,integer,n>0);
# Required for subsequent summations.
lambda:=(m,n)->(m*Pi)^2+(n*Pi)^2;
f:=(x,y)->sin(Pi*x);
F:=-4*(1/lambda(m,n))*f(x,y)*sin(m*Pi*x)*sin(n*Pi*y);
EE:=unapply(int(int(F,x=0..1,'AllSolutions'),y=0..1,'AllSolutions'),(m,n));
# Special option 'AllSolutions' insures that maple does not skip over
# any subcases, like m=1, in this example.
N:=10: u:=(x,y)->sum(sum(EE(m,n)*sin(m*Pi*x)*sin(n*Pi*y),m=1..N),n=1..N);
plot3d(u(x,y),x=0..1,y=0..1);