(a) Show that u n = r n cos nθ, u n = r n sin nθ,...
Question:
(b) Solve the Dirichlet problem using (20) if R = 1 and the boundary values are u(θ) = -100 volts if -Ï < θ < 0, u(θ) = 100 volts if 0 < θ < Ï. (Sketch this disk, indicate the boundary values.)
(c) Show that the solution of the Neumann problem 2u = 0 if r < R, uN(R, θ) = f (θ) (where uN = u/N is the directional derivative in the direction of the outer normal) is
with arbitrary A0 and
(d) Solve 2u = 0 in the annulus 1 < r < 2 if ur (1, θ) = sin θ, ur (2, θ) = 0.
Transcribed Image Text:
u(r, 0) = Ao + Er"(An cos no + Bn sin nº) n=1 т An f (0) cos nө dӨ, -1 пnR- т Bn тnR*-1 f (0) sin nө dө. -т
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