An Introduction to the Mathematical Theory of Waves [UK ed] 0-8218-2039-7, 9780821820391
This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and non
546 50 3MB
English Pages 196 [208] Year 2000
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Table of contents :
Content: Introduction: Introduction to waves A mathematical representation of waves Partial differential equation Traveling and standing waves: Traveling waves The Korteweg-de Vries equation The Sine-Gordon equation The wave equation D'Alembert's solution of the wave equation Vibrations of a semi-infinite string Characteristic lines of the wave equation Standing wave solutions of the wave equation Standing waves of a nonhomogeneous string Superposition of standing waves Fourier series and the wave equation Waves in conservation laws: Conservation laws Examples of conservation laws The method of characteristics Gradient catastrophes and breaking times Shock waves Shock wave example: Traffic at a red light Shock waves and the viscosity method Rarefaction waves An example with rarefaction and shock waves Nonunique solutions and the entropy condition Weak solutions of conservation laws Bibliography Index.
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