a. Find the solution u( x, y) of Laplaces equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the boundary conditions ux(0, y) = 0, ux (a, y) = 0, 0 < y < b, u( x, 0) = 0, u( x, b) = g( x), 0 < x < a. b. Find the solution if g( x) = 1 + x2( x a)2. G c. Let a = 3 and b = 2; plot several different views of the solution.

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