Wave Motion



By J. Billingham,&nbspA. C. King,

* Publisher: Cambridge University Press
* Number Of Pages: 475
* Publication Date: 2001-02-15
* Sales Rank: 4706420
* ISBN / ASIN: 0521632579
Djvu, 6.84 MB
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Book Description:

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.

Table of Contents

Introduction 1
Pt. 1 Linear Waves 5
1 Basic Ideas 7
2 Waves on a Stretched String 17
3 Sound Waves 36
4 Linear Water Waves 74
5 Waves in Elastic Solids 130
6 Electromagnetic Waves 173
Pt. 2 Nonlinear Waves 219
7 The Formation and Propagation of Shock Waves 221
8 Nonlinear Water Waves 269
9 Chemical and Electrochemical Waves 308
Pt. 3 Advanced Topics 355
10 Burgers' Equation: Competition between Wave Steepening and Wave Spreading 357
11 Diffraction and Scattering 378
12 Solitons and the Inverse Scattering Transform 405
App. 1 Useful Mathematical Formulas and Physical Data 451
Bibliography 455

Review:

Excellent Overview of Basic Wave Theory

This is book is a little strange but still very good. It could be thought of as a modern version of Lighthill's "Waves in Fluids". It first assumes that you are familiar with a pretty wide range of mathematical tools, and also that you have the necessary experience to handle long calculations. If you're comfortable with the method of stationary phase and contour integration but you've never studied acoustics or shocks, then this book is probably a worthwhile read. It's also good as an introduction to more advanced areas such as solitons, although the book by Johnson and Drazin (Solitons: An Introduction) is probably a better resource. I would have liked a chapter on waves of importance in geophysics though, such as internal gravity waves, Coriolis waves, and Rossby waves. It would have made the book an even better resource.

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