Solved: (a) Find the solution u(x, y) of Laplaces equation in the rectangle 0 < x < a, 0
Chapter 10, Problem 13(choose chapter or problem)
(a) Find the solution u(x, y) of Laplaces equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the boundary conditions u(0, y) = 0, u(a, y) = f(y), 0 < y < b, u(x, 0) = 0, uy(x, b) = 0, 0 x a. Hint: Eventually, it will be necessary to expand f(y) in a series that makes use of the functions sin(y/2b), sin(3y/2b), sin(5y/2b), ... (see of Section 10.4). (b) Find the solution if f(y) = y(2b y). (c) Let a = 3 and b = 2; plot the solution in several ways.
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