. (a) Find the solution u(x, y) of Laplaces equation in
Chapter 10, Problem 12(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 conditionsu(0, y) = 0, u(a, y) = 0, 0 < y < b,uy(x, 0) = 0, u(x, b) = g(x), 0 x a.Note that this is neither a Dirichlet nor a Neumann problem, but a mixed problem inwhich u is prescribed on part of the boundary and its normal derivative on the rest.(b) Find the solution ifg(x) =x, 0 x a/2,a x, a/2 x a.(c) Let a = 3 and b = 1. By drawing suitable plots, compare this solution with the solutionof 1.
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