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Introduction to the Mathematical Theory of Waves

AUTHOR: Roger A. Knobel
ISBN: 0821820397
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	HOME--->> Science --->>Physics --->>Waves & Wave Mechanics

	Waves & Wave Mechanics

Editorial Review

Introduction to the Mathematical Theory of Waves
- Book Review, by Roger A. Knobel

Book News, Inc.
Based on the author's undergraduate course at the summer Institute for Advanced Studies/Park City Mathematics Institute, the monograph treats waves as central to the theory of partial differential equations. Models of traffic flow illustrate conservation laws and wave phenomena. Exercises favor MATLAB software. -- Copyright © 1999 Book News, Inc., Portland, OR All rights reserved Book News, Inc.®, Portland, OR

Book Description
This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series. The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow.

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Book Review

Introduction to the Mathematical Theory of Waves
- Book Reviews, by Roger A. Knobel

Introduction to the Mathematical Theory of Waves

FROM THE PUBLISHER

Linear and nonlinear waves are a central part of the theory of PDEs. This book begins with a description of one-dimensional waves and their visualization through computer-aided techniques. Next, traveling waves are covered, such as solitary waves for the Klein-Gordon and KdV equations. Finally, the author gives a lucid discussion of waves arising from conservation laws, including shock and rarefaction waves. As an application, interesting models of traffic flow are used to illustrate conservation laws and wave phenomena.. "This book is based on a course given by the author at the IAS/Park City Mathematics Institute. It is suitable for independent study by undergraduate students in mathematics, engineering, and science programs.

FROM THE CRITICS

Booknews

Based on the author's undergraduate course at the summer Institute for Advanced Studies/Park City Mathematics Institute, the monograph treats waves as central to the theory of partial differential equations. Models of traffic flow illustrate conservation laws and wave phenomena. Exercises favor MATLAB software. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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