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

G. B. Whitham (Author)

Book Description

ISBN-10: 0471359424 | ISBN-13: 978-0471359425 | Publication Date: July 1, 1999

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Editorial Reviews

Review

The re-issue of this excellent book on linear and nonlinear waves in paperback form is to be welcomed. (Zentralblatt Math, Volume 940, No 15, 2000)

From the Back Cover

INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS With Emphasis on Wave Propagation and Diffusion G. L. Lamb Jr.

Geared to scientists and engineers seeking to hone their mathematical skills, this book draws on such phenomena as heat conduction and wave motion to show how partial differential equations are used to obtain specific information about the phy-sical world. Topics include one-dimensional problems, Laplace Transform method, Green's functions, spherical geometry, and first order equations. 1995 (0-471-31123-5) 496 pp.

APPLIED MATHEMATICS Second Edition J. David Logan. This highly acclaimed book provides readers from diverse scientific and engineering fields with an easily accessible, up-to-date treatment of mathematical methods. Coverage ranges from such standard topics as fluid mechanics and calculus of variations to modern methods--dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.

Also in this series...ORTHOGONAL SETS AND POLAR METHODS IN LINEAR ALGEBRA. Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming Enrique Castillo, Angel Cobo, Francisco Jubete, and Rosa Eva Pruneda 1999 (0-471-32889-8) 440 pp.

ALGEBRA Pierre Grillet 1999 (0-471-25243-3) 694 pp.

Product Details

• Paperback: 660 pages
• Publisher: Wiley-Interscience (July 1, 1999)
• Language: English
• ISBN-10: 0471359424
• ISBN-13: 978-0471359425
• Product Dimensions: 9.1 x 6.1 x 1.6 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #337,593 in Books (See Top 100 in Books)
  • #62 in Books > Professional & Technical > Professional Science > Physics > Waves & Wave Mechanics

Customer Reviews

Most Helpful Customer Reviews

15 of 16 people found the following review helpful:

5.0 out of 5 stars The most understandable treatment of waves I have read!, June 29, 1998

By A Customer

This review is from: Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) (Hardcover)

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.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Good book, September 20, 2007

By 

Don C. Fletcher "Maverick" (Mountain View, CA) - See all my reviews
(REAL NAME)   

This review is from: Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Paperback)

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.

18 of 28 people found the following review helpful:

4.0 out of 5 stars good backround, March 6, 2000

By 

"pyramidl" - See all my reviews

This review is from: Linear and Nonlinear Waves (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) (Paperback)

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.