Description
Book SynopsisPresents an overview of the concept of a wave, and describes one-dimensional waves using functions of two variables. This book also provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. It discusses traveling waves, leading to a description of solitary waves.
Table of ContentsIntroduction: 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.
