Asymptotic Wave Theory (Mathematics & Mechanics) by Maurice Roseau

By Maurice Roseau

Asymptotic Wave concept investigates the asymptotic habit of wave representations and provides a few average effects borrowed from hydrodynamics and elasticity thought. It describes options resembling Fourier-Laplace transforms, operational calculus, distinct features, and asymptotic equipment. It additionally discusses functions to the wave equation, the weather of scattering matrix thought, difficulties on the topic of the wave equation, and diffraction.
Organized into 8 chapters, this quantity starts off with an outline of the Fourier-Laplace imperative, the Mellin remodel, and targeted features akin to the gamma functionality and the Bessel features. It then considers wave propagation, with emphasis on representations of airplane, 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 growth 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 huge order, and the scattering matrix idea. the remainder chapters concentrate on difficulties of circulation in open channels, the propagation of elastic waves inside a layered round physique, and a few difficulties in water wave concept.
This ebook is a helpful source for mechanics and scholars of utilized arithmetic and mechanics.

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