Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. Beyond the usual model problems, the presentation includes a number of realistic applications that illustrate the power and usefulness of the ideas behind these techniques. This complete, self-contained book includes numerous exercises and error estimates, as well as a rigorous approximation and computational tool.
Potential, Heat, and Wave Equations. Basic Approximation Theory. Sturm–Liouville Problems. Fourier Series. Eigenfunction Expansions for Equations in Two Independent Variables. One-Dimensional Diffusion Equation. One-Dimensional Wave Equation. Potential Problems in the Plane. Multidimensional Problems. Bibliography. Index.