By Maurice Roseau

ISBN-10: 0720423708

ISBN-13: 9780720423709

Asymptotic Wave idea investigates the asymptotic habit of wave representations and offers a few normal effects borrowed from hydrodynamics and elasticity concept. It describes innovations reminiscent of Fourier-Laplace transforms, operational calculus, detailed capabilities, and asymptotic equipment. It additionally discusses purposes to the wave equation, the weather of scattering matrix thought, difficulties regarding the wave equation, and diffraction.
Organized into 8 chapters, this quantity starts off with an outline of the Fourier-Laplace crucial, the Mellin rework, and certain capabilities equivalent to the gamma functionality and the Bessel capabilities. It then considers wave propagation, with emphasis on representations of aircraft, cylindrical or round waves. It methodically introduces the reader to the reflexion and refraction of a aircraft wave on the interface among homogeneous media, the asymptotic enlargement of Hankel's capabilities in the community of the purpose at infinity, and the asymptotic habit of the Laplace rework. The ebook additionally examines the tactic of steepest descent, the asymptotic illustration of Hankel's functionality of enormous order, and the scattering matrix conception. the remainder chapters concentrate on difficulties of move in open channels, the propagation of elastic waves inside of a layered round physique, and a few difficulties in water wave concept.
This ebook is a worthy source for mechanics and scholars of utilized arithmetic and mechanics.

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