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Summary
Table of Contents
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 | |
Table of Contents provided by Publisher. All Rights Reserved. |
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