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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.

Wave-motion, Theory of.

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Wave-motion, Theory of --- Wave-motion, Theory of. --- Wave-motion, theory of

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The theory of water waves has been a source of intriguing and often difficult mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and non-linear water-wave theory. This sets the ground for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and help to make this an ideal text for a beginning graduate course on water waves.

Wave-motion, Theory of. --- Water waves.

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Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

Wave-motion, Theory of. --- Nonlinear waves.

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Wave-motion, Theory of --- #WNAT:d.d. Prof. L. Bouckaert --- Undulatory theory --- Mechanics --- Wave-motion, Theory of. --- Acoustique --- Sound --- Sound. --- Antennes et propagation --- Wave-motion, theory of