Differential Equations Lecture Work Solutions 64

Differential Equations Lecture Work Solutions 64 - 6 b. The...

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Unformatted text preview: 6 b. The only difference between this problem and the previous one is the boundary condition a0 u(a, θ) = f (θ) = + 2 ∞ n=1 (an a−n cos n θ + bn a−n sin n θ) ⇒ a0 , an a−n , bn a−n are coefficients of Fourier series of f a0 = 1 π an a−n = π −π 1 π f (θ ) d θ π −π f (θ) cos n θ d θ 1π f (θ) sin n θ d θ π −π Divide the last two equations by a−n to get the coefficients an and bn . bn a−n = 64 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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