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By Maurice Roseau

Asymptotic Wave concept investigates the asymptotic habit of wave representations and provides a few ordinary effects borrowed from hydrodynamics and elasticity idea. It describes strategies similar to Fourier-Laplace transforms, operational calculus, precise features, and asymptotic tools. It additionally discusses purposes to the wave equation, the weather of scattering matrix thought, difficulties with regards to the wave equation, and diffraction.
Organized into 8 chapters, this quantity starts off with an outline of the Fourier-Laplace vital, the Mellin rework, and distinct features reminiscent of the gamma functionality and the Bessel services. 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 services in the community of the purpose at infinity, and the asymptotic habit of the Laplace remodel. The ebook additionally examines the tactic of steepest descent, the asymptotic illustration of Hankel's functionality of huge order, and the scattering matrix thought. the remainder chapters concentrate on difficulties of circulate in open channels, the propagation of elastic waves inside a layered round physique, and a few difficulties in water wave conception.
This e-book is a necessary source for mechanics and scholars of utilized arithmetic and mechanics.

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Asymptotic Wave Theory (Mathematics & Mechanics) by Maurice Roseau

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