Wave Motion

J. Billingham (University of Birmingham), A. C. King (University of Birmingham)

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English

Cambridge University Press
21 March 2001

Applied mathematics; Fluid mechanics; Quantum physics (quantum mechanics & quantum field theory)

Series: Cambridge Texts in Applied Mathematics

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.

By: J. Billingham (University of Birmingham), A. C. King (University of Birmingham)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 24
Dimensions: Height: 229mm, Width: 152mm, Spine: 30mm
Weight: 870g
ISBN: 9780521632577
ISBN 10: 0521632579
Series: Cambridge Texts in Applied Mathematics
Pages: 476
Publication Date: 21 March 2001
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Replaced By: 9780521634502
Format: Hardback
Publisher's Status: Active

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.

Reviews for Wave Motion

'... 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 '... 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.' 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, Zentralblatt fur 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, Monatshefte fur Mathematik '... Billingham and King ... offer an attractive, thorough discussion of wave phenomena.' J. H. Ellison, Choice '... written very clearly ... will be valuable for students of mathematics who wish to apply their mathematics to physics and other fields.' EMS 'Sections on non-linear wave motion and advanced topics extend the usefulness of this excellent text to the first year of graduate study.' 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, 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.' 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, The Mathematical Gazette