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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.
 Fall '08
 BELL,D

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