# Problem 3.7-12, heat equation on unit square F:=4x(1-x)y(1-y)sin(m*Pi*x)*sin(n*Pi*y); F:=4*x*(1-x)*y*(1-y)*sin(m*Pi*x)*sin(n*Pi*y); assume(m,integer);assume(n,integer); A:=unapply(int(int(F,x=0..1),y=0..1),(m,n)); 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); plot3d(u(x,y,0),x=0..1,y=0..1); plots[animate](plot3d,[u(x,y,t),x=0..1,y=0..1],t=0..0.05);