An introduction to the mathematical theory of waves

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An introduction to the mathematical theory of waves / Roger Knobel

資料種別:: 図書
出版情報:: Providence, R.I. : American Mathematical Society
Princeton, N.J. : Institute for Advanced Study, c2000
形態:: xiv, 196 p. ; 22 cm
シリーズ名:: Student mathematical library ; v. 3 . IAS/Park City mathematical subseries <BA42504671>
著者名:: Knobel, Roger, 1962- <DA12540934>
ISBN:: 9780821820391 [0821820397]
書誌ID:: BA43553934

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注記:

Includes bibliographical references and index

主題:

Wave motion, Theory of

言語:

英語

目次情報:

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

Introduction

Introduction to waves

A mathematical representation of waves

Partial differential equation

Traveling and standing waves: Traveling waves

The Korteweg-de Vries equation

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