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  3. Wave Motion
  • Cited by 33
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2001
Online ISBN:
9780511841033
DOI:
https://doi.org/10.1017/CBO9780511841033
Subjects:
Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Mathematical Modeling and Methods
Series:
Cambridge Texts in Applied Mathematics (24)
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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. 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.

Reviews

‘… 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.’

Source: European Journal of Mechanics

‘… the great strength of the book … lies in the clarity of exposition of the mathematical solution of the wave equations and of the physical interpretation of these solutions … this is an excellent book, which is thoroughly recommended … it ought to become the standard textbook for anyone taking an undergraduate course in mathematical wave theory.’

Source: Journal of Fluid Mechanics

‘… a clearly written book which covers a surprisingly wide variety of topics … an excellent introduction to this fascinating area of applied mathematics.’

A. Jeffrey Source: Zentralblatt für Mathematik

‘The rich material is presented in a quite digestible way with clear explanation of physical principles and properties and a formal apparatus which does not overwhelm everything else.’

H. Mathsam Source: Monatshefte für Mathematik

‘… Billingham and King … offer an attractive, thorough discussion of wave phenomena.’

J. H. Ellison Source: Choice

‘… written very clearly … will be valuable for students of mathematics who wish to apply their mathematics to physics and other fields.’

Source: EMS

‘Sections on non-linear wave motion and advanced topics extend the usefulness of this excellent text to the first year of graduate study.’

Source: Aslib Book Guide

‘… a text of great clarity … I warmly recommend this book as a useful source of reference material for applied mathematicians, physicists and engineers alike.’

A. Jueld Source: Contemporary Physics

‘Wave Motion has the potential to become the mathematical text for advanced undergraduate courses on the analytical aspects of waves.’

Christopher Howls - University of Southampton

' … very accessible for a reader with some background in applied mathematics. The style and the exercises after each chapter make it perfectly fit as lecture notes for a course in applied mathematics.'

Source: Bulletin of the Belgian Mathematical Society

'I'm glad I bought a copy of this book as soon as it was published, because it has informed me, and will go on informing my lecture classes, for years to come.'

Mark J. Cooker Source: The Mathematical Gazette

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