Introduction to the mathematical theory of waves
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TextLanguage: English Series: Student mathematical library, IAS/Park City mathematical subseries ; volume 3Publication details: Rhode Island : American Mathematical Society, 2000 Description: xiv, 196p. : ill. ; 22 cmISBN: 9780821887295Subject(s): Wave-motion, Theory ofDDC classification: 532.59 Online resources: Table of Contents | Reviews Summary: 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.
The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as Mathematica®, MATLAB®, or Maple® is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.
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NBHM Books
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NISER LIBRARY | 532.59:517.9 KNO-I (Browse shelf(Opens below)) | Available | N139 | |
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NBHM Books
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| 532 GUP-F Fluid mechanics and its applications | 532 KAM-E Elementary fluid mechanics | 532.5 MAR-T Time-domain scattering | 532.59 KNO-I Introduction to the mathematical theory of waves | 53:51 BIT-E Equations of mathematical physics | 53:51 COU-M Methods of mathematical physics, vol 2: partial differential equations | 53:51 COU-M Methods of mathematical physics, vol 1 |
Includes bibliographical references (p. 193-194) and index.
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.
The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as Mathematica®, MATLAB®, or Maple® is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.
Advanced undergraduates, graduate students, and research mathematicians interested in nonlinear PDEs.
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