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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 onedimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computeraided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the KleinGordon and KortewegdeVries 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.
⚠️ WARNING (California Proposition 65):
This product may contain chemicals known to the State of California to cause cancer,
birth defects, or other reproductive harm.
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