10.8 Laplace equation

Exercise 1, page 611.

> with(plots):

> a:=4:b:=2:

> c:=n->1/(sinh(n*Pi*b/a))*2/a*(int(x*sin(n*Pi*x/a),x=0..a/2)+int((-x+a)*sin(n*Pi*x/a),x=a/2..a));

> u:=sum(c(n)*sin(n*Pi*x/a)*sinh(n*Pi*y/a),n=1..20):

> plot3d([x,y,u],x=0..a,y=0..b,numpoints=200,axes=frame,labels=["x","y","u(x,y)"]);