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partial-differential-equations

Laplace's equation by separation of variables on a disk

taught

Solve the Dirichlet problem for Laplace's equation on a disk using periodicity in the angular variable and boundedness at the origin in place of ordinary boundary conditions.

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Required by

Local knowledge map

Local knowledge map

Bessel's equation and Bessel functions Iterative solvers: Jacobi, Gauss-Seidel, SOR Separating the Laplacian eigenvalue problem in spherical… The Green's function for the Dirichlet problem, revisited Deriving the Poisson kernel Finite differences for Laplace's equation: the five-point stencil Laplace's equation on a wedge and an annulus Separating the Laplacian eigenvalue problem in polar… Laplace's equation by separation of variables on a disk Complex Fourier series Convergence of a Fourier series at a point Even, odd, and periodic extensions From boundary conditions to a Sturm-Liouville… Laplace's equation by separation of variables on a… Parseval's equality Solving the heat equation on a finite rod with Neumann… Solving the heat equation on a finite rod with Robin… Solving the vibrating-string problem by separation… Term-by-term differentiation and integration of a… Why numerical methods, and what can go wrong The full Fourier series The separation-of-variables ansatz Fourier cosine series Fourier sine series The regular Sturm-Liouville problem

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