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partial-differential-equations

Orthogonality of Sturm-Liouville eigenfunctions

taught

Prove that eigenfunctions belonging to distinct eigenvalues of a regular Sturm-Liouville problem are orthogonal with respect to its weight function.

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Required by

Local knowledge map

Local knowledge map

Convergence of an eigenfunction expansion Solving the heat equation with a source term by eigenfunction… The Rayleigh quotient of a Sturm-Liouville operator Why Sturm-Liouville theory is the engine behind separation of… Eigenfunction expansions (generalized Fourier… Orthogonality of Legendre polynomials Reality and positivity of Sturm-Liouville eigenvalues Orthogonality of Sturm-Liouville eigenfunctions Fourier cosine series Fourier sine series From boundary conditions to a Sturm-Liouville… Legendre's equation and Legendre polynomials Parseval's equality Singular Sturm-Liouville problems, previewed Solving the heat equation on a finite rod with Robin… The separation-of-variables ansatz Orthogonality of the sine and cosine functions The regular Sturm-Liouville problem Boundary-value problems, contrasted with IVPs Eigenvalues and the characteristic equation Inner products: generalizing the dot product The linear differential operator L

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