Chapter 4.2 gives the solutions to several different boundary conditions for an eigenvalue problem. All of the solutions provided are for inhomogeneous BC's though. Would the exam cover homogeneous BC? What would be the method in that case?

Also, point of clarification for the solution to previous TT2 #3

http://forum.math.toronto.edu/index.php?topic=841.0$ Y_m $ should depend upon the variable $ y $ correct? So the correct solution to Laplacian in the rectangle

${0<x<a,0<y<b} $ with Neumann boundary conditions should be?:

$$ u_{n,m}(x,y) = \cos(\frac{n\pi x}{a})\cos(\frac{m\pi y}{b}) $$