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Waves are a ubiquitous and important feature of the physical world, and, throughout history, it has been a major challenge to understand them. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, 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 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.Read more
- Lots of worked examples and exercises with solutions
- Clear mathematical exposition carefully relating the mathematics to the physics of waves
- Contemporary treatment with many illustrations, some in colour, of interesting and broad range of wave phenomena
Reviews & endorsements
"This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists, or engineers. The first part addresses linear waves, including waves on a stretched string, sound waves, linear water waves, waves in elastic solids, and electromagnetic waves. The second part examines nonlinear waves, including the formation and propagation of shock waves, nonlinear water waves, and chemical and electrochemical waves. The third part considers advanced topics, including the Burger equation, diffraction and scattering, solitons, and the inverse scattering transform." International Aerospace Abstracts (IAA)See more reviews
"The writing is clear, the references are adequate, and the book is a useful addition to the literature in this rapidly expanding field." Mathematical Review
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- Date Published: January 2001
- format: Hardback
- isbn: 9780521632577
- length: 476 pages
- dimensions: 229 x 152 x 30 mm
- weight: 0.87kg
- contains: 13 b/w illus. 1 table 98 exercises
- availability: Available
Table of Contents
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
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