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Answer by JohnD for Laplace's Equation in Polar Coordinates - PDE
Yes, except $f(x)$ should be $1$ in the last line:$$b_n={2\over \pi}\int_0^\pi 1\cdot \sin(\sqrt{\lambda_n}\theta)\,d\theta={2\over \pi}\int_0^\pi \sin(n\theta)\,d\theta,\ n=1,2,\dots$$Side note: good...
View ArticleLaplace's Equation in Polar Coordinates - PDE
Find the bounded solution of Laplace's equation in the region $\Omega=\{(r,\theta):r>1,0<\theta<\pi\}$ subject to the boundary conditions $u(r,\pi)=u(r,0)=0$ for $r>1$ and $u(1,\theta)=1$...
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