Show how to find the solution u(x, y) of Laplaces equation in the rectangle 0 < x < a, 0
Chapter 10, Problem 4(choose chapter or problem)
Show how to 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) = k(y), u(a, y) = f(y), 0 < y < b, u(x, 0) = h(x), u(x, b) = g(x), 0 x a. Hint: See 3. 5. Find the solution u(r, ) of Laplaces equation urr + (1/r)ur + (1/r2 )u = 0 outside the circle r = a, that satisfies the boundary condition u(a, ) = f(), 0 < 2, on the circle. Assume that u(r, ) is single-valued and bounded for r > a.
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