Eigenvalues of the Laplacian on a square
SMRTR summary
The eigenvalues of the Laplacian on a unit square are explored, revealing solutions of the form sin(mπx)sin(nπy) with λ = (m² + n²)π². These eigenvalues are compared to Pólya's bounds, considering their multiplicities and distribution. Analysis shows the kth eigenvalue is approximately 4πk for large k, aligning with Pólya's lower bound for a region of area 1.
SMRTR provides this summary for quick context. The original article belongs to John D. Cook.
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