Bray (U. of Maine) offers a textbook for a one-semester course for upper-level undergraduate students of mathematics, the physical sciences, and engineering; and for graduate students in various other disciplines. Students should have a working knowledge of calculus in one and several variables, the theory and methods of solution for ordinary differential equations, and complex arithmetic and the complex exponential function. Some knowledge of linear algebra would also be handy, he says, but he uses it only once. Among the topics are first-order linear partial differential equations, Fourier expansions, diffusion and waves with boundaries, and Laplace's equation. Solutions are provided for selected exercises. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)