Assignment:
Consider the heat equation for a rectangular region, 0 < x < a, 0 < y < b, t > 0
ut = k(uxx + uyy) , 0 < x < a, 0 < y < b, t > 0
subject to the initial conditions: u(x,y) = f(x,y)
a) ux (0, y, t) = 0, ux (a, y, t) = 0, 0 < y < b, t > 0
uy (x, 0, t) = 0, uy (x, b, t) = 0, 0 < x < a, t > 0
b) u (0, y, t) = 0, ux (a, y, t) = 0, 0 < y < b, t > 0
uy (x, 0, t) = 0, uy (x, b, t) = 0, 0 < x < a, t > 0