Wave Motion

Textbook on wave phenomena for advanced undergraduate courses; worked examples, exercises and solutions for teachers.

J. Billingham (Author), A. C. King (Author)

9780521632577, Cambridge University Press

Hardback, published 29 January 2001

476 pages, 13 b/w illus. 1 table 98 exercises
22.9 x 15.2 x 3 cm, 0.87 kg

'I'm glad I bought a copy of this book as soon as it was published, because it has informed me, and will go on informing my lecture classes, for years to come.' Mark J. Cooker, The Mathematical Gazette

Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.

Introduction
Part I. Linear Waves: 1. Basic ideas
2. Waves on a stretched string
3. Sound waves
4. Linear water waves
5. Waves in elastic solids
6. Electromagnetic waves
Part II. Nonlinear Waves: 7. The formation and propagation of shock waves
8. Nonlinear water waves
9. Chemical and electrochemical waves
Part III. Advanced Topics: 10. Burgers' equation
11. Diffraction and scattering
12. Solitons and the inverse scattering transform
Appendix. Useful mathematical formulas and physical data
Bibliography
Index.

Subject Areas: Fluid mechanics [PHDF], Applied mathematics [PBW]