Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.
This undergraduate textbook on the physics of wave motion in optics and acoustics avoids presenting the topic abstractly in order to emphasize real-world examples. While providing the needed scientific context, Dr. Espinoza also relies on students' own experience to guide their learning. The book's exercises and labs strongly emphasize this inquiry-based approach. A strength of inquiry-based courses is that the students maintain a higher level of engagement when they are studying a topic that they have an internal motivation to know, rather than solely following the directives of a professor. "Wave Motion" takes those threads of engagement and interest and weaves them into a coherent picture of wave phenomena. It demystifies key components of life around us--in music, in technology, and indeed in everything we perceive--even for those without a strong math background, who might otherwise have trouble approaching the subject matter.
Author: Herbert berall,Ardshir Guran,D. J. Inman
Publisher: World Scientific
This book is a collection of papers on the subject of applied system dynamics and control written by experts in this field. It offers the reader a sampling of exciting research areas in three fast-growing branches: (i) Wave Motion (ii) Intelligent Structures (iii) Nonlinear Mechanics. The topics covered include flow instability, nonlinear mode localization autoparametric systems with pendula, and geometric stiffening in multibody dynamics. Mathematical methods include perturbation methods, modern control theory, nonlinear neural nets, and resonance scattering theory of berall-Ripoche-Maze. Applications include sound-induced structural vibrations, fiber acoustic waveguides, vibration suppression of structures, linear control of gyroscopic systems, and nonlinear control of distributed systems.This book shows how applied system dynamics and control is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
Proceedings of a Conference in Honor of the 60th Birthday of Peter D. Lax
Author: AlexandreJ. Chorin,Andrew J. Majda
Publisher: Springer Science & Business Media
The 60th birthday of Peter Lax was celebrated at Berkeley by a conference entitled Wave Motion: theory, application and computation held at the mathematical Sciences Research Institute, June 9-12, 1986. Peter Lax has made profound and essential contributions to the topics described by the title of the conference, and has also contributed in important ways to many other mathematical subjects, and as a result this conference volume dedicated to him includes research work on a variety of topics, not all clearly related to its title.
Book 3 is written for the compulsory part "Wave Motion". It is a useful supplement to textbook. The questions appear in the order of the syllabus for easy reference. All questions are carefully selected to cover various question types requiring different levels of skills. Solutions to calculations and explanations of different options in most multiple choice questions and full marking schemes for conventional questions are provided to help students consolidate their concepts and master their skills in answering examination type questions.
This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.