Extra Credit. (10 points) Let a > 0 be given. Use spherical harmonics to find the solution of Laplace's equation u(r, 0,

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Extra Credit 10 Points Let A 0 Be Given Use Spherical Harmonics To Find The Solution Of Laplace S Equation U R 0 1 (39.84 KiB) Viewed 25 times

Extra Credit. (10 points) Let a > 0 be given. Use spherical harmonics to find the solution of Laplace's equation u(r, 0,6) in three-dimensions in the exterior of the ball, namely N = {(r,0,0): r > a, 0 < < 27,0 <O<} = with = u(a,0,0) = sin’(0) on the boundary where & is the polar angle (i.e., z = r cos 6). In particular, your solution must satisfy lim (u(r, 0,0) = 0 = 100 for all 0 < < 27,0 < < .