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partial-differential-equations

The regular Sturm-Liouville problem

taught

Recognize and rewrite a linear second-order ODE with boundary conditions in regular Sturm-Liouville form, and identify its weight function.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Choosing which series a boundary-condition pair calls for Eigenfunction expansions (generalized Fourier… Laplace's equation by separation of variables on a disk Laplace's equation by separation of variables on a… Orthogonality of Legendre polynomials Reality and positivity of Sturm-Liouville eigenvalues Solving the heat equation on a finite rod with Dirichlet… Solving the heat equation on a finite rod with Neumann… Solving the vibrating-string problem by separation… From boundary conditions to a Sturm-Liouville… Orthogonality of Sturm-Liouville eigenfunctions Singular Sturm-Liouville problems, previewed Solving the heat equation on a finite rod with Robin… The separation-of-variables ansatz The regular Sturm-Liouville problem Eigenvalue problems from boundary conditions Every operator on a complex space has an eigenvalue Homogeneous vs. nonhomogeneous equations Hyperbolicity: real, distinct eigenvalues IVPs vs. BVPs, revisited Multivariable first- and second-order optimality conditions Orthogonality of the sine and cosine functions Sturm-Liouville form The DFT, defined and as a matrix transformation The characteristic polynomial The eigenvalue method -- distinct real eigenvalues The power method for eigenvalues Boundary-value problems, contrasted with IVPs Eigenvalues and the characteristic equation The linear differential operator L Initial value problems and particular antiderivatives Second-order linear equations, standard form The eigenvector question

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