Customer Reviews

Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

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Linear and Nonlinear Waves provides an excellent treatment of the wave phenomena. This is a very complex and mathematically intesive subject, which Whitham conveys in an understandable and followable manner. He takes the approach that the reader has some knowlege of the subject, but writes at an introductory graduate level. This book will give any mathematician or engineer interested in waves an excellent introduction and bring them to a superior understanding.

I took some graduate level courses from Dr. Whitham at CalTech in 1973 while this book was still in draft form, and he was the head of the Applied Mathematics department. He was an excellent lecturer, and this book has long been an exemplar of that style as well as the pioneer book in the treatment of non linear waves. To my knowledege it was the first textbook to treat solitons. The book is very subtle in its treatment of physics, and the adept reader will note the bearing of dispersion relations on the foundations of quantum mechanics.

Most treatment of waves involves their role in electromagnetic spectra. The writer provides the historical account of the derivation of these algebraic (read numerical analysis) versions which implement in MathCad and Matlab well. The book's material on water waves is worth the price alone. However, only at the end,does the author venture into the world of non-linear dynamics which is so important to this area. Most of the book treats the wave phenomenology as most physicists will in the kinematical sense trying to linearize everything and avoiding the path if it can't be linearized. (In this sense most of the arguements and examples are structured in the conservation of mass and energy). This is great, however for the construction of first order linear diff. equations for implementation in Mathcad or Matlab. If one were not aware of bifurcations, limit-cycles or even total response waves from control theory, one would still be left feeling secure that water waves are standing waves. (They are not). Early research breaks them up into first part(Airy) long-standing(middle of the wave) and orgin to get around this problem. Book does not approach treatment as a diffusion problem.