Separation of Variables for Partial Differential Equations ― An Eigenfunction Approach

Writing for advanced undergraduates, Cain and Meyer (both mathematics emeriti, Georgia Institute of Technology) introduce a computable separation of variables solutions as an analytic approximate solution. They work through the notion of a general partial differential equation in two independent variables with a source term and subject to boundary and initial conditions. Using an eignefunction approach they give an algorithm for approximating and solving the problem and show applications and solutions to practical problems, covering such topics as potential, heat and wave equation, basic approximation theory, Sturm-Liouville problems, Fourier series, eigenfunction expansions for equations in two independent variables, the one-dimension diffusion equation, the one-dimensional wave equation, potential problems in the Plane, and multidimensional problems. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)