Solution: (a) Find the solution u(x, y) of Laplaces equation in the rectangle 0 < x < a
Chapter 10, Problem 1(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) = 0, 0 < y < b, u(x, 0) = 0, u(x, b) = g(x), 0 x a. (b) Find the solution if g(x) = x, 0 x a/2, a x, a/2 x a. (c) For a = 3 and b = 1 plot u versus x for several values of y and also plot u versus y for several values of x. (d) Plot u versus both x and y in three dimensions. Also draw a contour plot showing several level curves of u(x, y) in the xy-plane.
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