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.

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.

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