Solutions for homework assignment #4
Substituting the series into the boundary condition u(b,θ) = f(θ), we get f(θ) = X ∞ n=1 c n b a 2n − a b sin2nθ. The right-hand side is a Fourier sine series on the interval [0,π/2]. Therefore the boundary condition is satisfied if the right-hand side coincides with the Fourier sine series X ∞ n=1 b n sin2nθ of the function f(θ ...
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