{"product_id":"an-introduction-to-the-mathematical-theory-of-waves-9780821820391","title":"An Introduction to the Mathematical Theory of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction: 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.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50577670635863,"sku":"9780821820391","price":46.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821820391.jpg?v=1746096100","url":"https:\/\/bookcurl.com\/products\/an-introduction-to-the-mathematical-theory-of-waves-9780821820391","provider":"Book Curl","version":"1.0","type":"link"}