Boundary conditions:
u(x,0) = f1(x)
u(0,y) = g1(y)
u(x,b) = f2(x)
u(a,y) = g2(x)
0
0
Use the method of separation of variables to derive u1 and An where
u1(x,y) = ∑ Ansin(nπx/a) sinh(nπ(b-y)/a)
and
h
h
h
h
= 2/a sinh(nπb/a) ∫ f1(x) sin(nπx/a) dx
**This problem consisting of Laplace’s equation on a region in the
plane together with specified boundary values is called a Dirichlet
problem.
∞
n=1
0
a
