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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. 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.
List of contents
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.
Summary
This introduction to the mathematics of waves is for undergraduates in mathematics, physics or engineering. Further material on linear and nonlinear waves is also included for the benefit of graduates. The context and underlying physics is clearly explained; worked examples and exercises are supplied throughout, with solutions available to teachers.
Report
'... an excellent advanced introduction to the mathematical theory of wave motion. it is ideally suited to advanced undergraduate students and beginning postgraduate students ... one attractive feature of the book is the abundance of worked examples and exercises (with solutions available to teachers) ... this is a wonderful book whose reading I would recommend to any scientist interested in learning the mathematical theory of wave motion.' European Journal of Mechanics
