From density dips of compressible gas to the crest of a chemical wave

Wave Motion covers all the types of waves commonly encountered in an applied mathematics degree programme. The first half discusses linear, string, acoustic, water, elastic and electromagnetic waves. The section dealing with nonlinear waves is a blend of examples from the formation of shocks in water waves or traffic flow to compressible gas dynamics and chemical and electrochemical waves, including the propagation of nerve impulses. Topics are self-standing, as, for the most part, the authors provide clear introductions to the underlying physics and governing equations.

The sometimes abrupt style may annoy some, but the extensive range of topics covered compensates. Combined with the variety of examples, the book has the flexibility for a number of undergraduate courses, not just those dedicated to waves.

The last quarter deals with advanced topics such as Burgers' equation, diffraction, solitons and inverse scattering, making it a useful introductory text for mathematically able postgraduates. Physicists or chemists looking for discussions of quantum mechanical waves, eigenvalue problems and associated asymptotic techniques will, however, have to look elsewhere.

Solutions to the exercises are available from the publishers for overburdened exam-setters. The text is amply furnished with illustrations, although one or two could have been better chosen. For example, to show the bunching of traffic waves, the authors managed to find a rare instant when a Birmingham motorway was devoid of traffic.

Nevertheless, Wave Motion has the potential to become the mathematical text for advanced undergraduate courses on the analytical aspects of waves.

Christopher Howls is lecturer in applied mathematics, University of Southampton.