The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc. This book presents a clear and systematic treatment of the mathematical methods of wave phenomena in solids and fluids that will be readily accessible to physicists, engineers, and applied mathematicians. The emphasis is on developing the necessary mathematical techniques and on showing how they can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, stress waves in solids, etc. One of the unique features of this book is the treatment of the Hamilton-Jacobi theory in the setting of variational methods. This theory is fundamental to the treatment of the partial differential equations of wave propagation; it bridges the gap between classical mechanics and geometric optics and sets the scene for the development of the quantum mechanics. Another interesting feature of this book is that it organizes some of the more advanced material such as nonlinear theory and asymptotic expansion methods, now scattered in the literature, into a systematic presentation. Front Matter....Pages i-x Oscillatory Phenomena....Pages 1-33 The Physics of Wave Propagation....Pages 34-49 Partial Differential Equations of Wave Propagation....Pages 50-83 Transverse Vibrations of Strings....Pages 84-107 Water Waves....Pages 108-158 Sound Waves....Pages 159-191 Fluid Dynamics....Pages 192-273 Wave Propagation in Elastic Media....Pages 274-311 Variational Methods in Wave Phenomena....Pages 312-379 Back Matter....Pages 381-386 Contents: Oscillatory Phenomena The Physics of Wave Propagation Partial Differential Equations of Wave Propagation Transverse Vibrations of Strings Water Waves Sound Waves Fluid Dynamics Wave Propagation in Elastic Media Variational Methods in Wave Phenomena Bibliography Index.
