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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.
- Sales Rank: #2233936 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2001-01-22
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.06" w x 5.98" l, 1.52 pounds
- Binding: Paperback
- 476 pages
- Used Book in Good Condition
Review
"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)
"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
About the Author
John Billingham is Chief of the Extraterrestrial Research Division at NASA Ames Research Center.
Previous books by this editor: Acta Numerica 1992 - 2003 (Vols 1 - 12); as author: First Course in the Numerical Analysis of Differential Equations (0521 553768), Approximation Theory and Optimization (0521 581907).
Andrew King is Killam Postdoctoral Fellow in English, Dalhousie University, Canada
Most helpful customer reviews
9 of 9 people found the following review helpful.
Excellent Overview of Basic Wave Theory
By M. Ward
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.
3 of 3 people found the following review helpful.
Wave Motion
By Maurice L. Adams, Jr./Mechanical Engineering Professor
This modern book has considerable breadth and depth, and is ideally suited as a reference text as well as a text for upper class under graduate and graduate courses. It treats acoustic waves, waves in elastic media, fluid dynamical waves, electromagnetic waves and more. The material is clearly presented, including excellent illustrations. At the same time, it is mathematically rigorous and thereby equally appropriate as a text for applied mathematics as well as engineering courses and study. Each of the book's twelve chapters ends with a set of homework problems, for which the authors have assembled a comprehensive well organized instructor's solution manual.
2 of 2 people found the following review helpful.
Not a good textbook for beginners in the subject
By Kindle Customer
This book is not for a person beginning to study waves. Even with a strong mathematical background, many of the physical explanations in the book are vague and often confusing. The authors need to spend a little more time developing the student's intuition. What seems obvious to them is not obvious to the novice. The book is well-written in the sense that the text flows well, and I imagine especially well for the expert. This book would make a good reference for someone with more experience in the subject matter.
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