Asymptotic Wave Theory (Mathematics & Mechanics) - download pdf or read online

By Maurice Roseau

Asymptotic Wave concept investigates the asymptotic habit of wave representations and offers a few ordinary effects borrowed from hydrodynamics and elasticity thought. It describes recommendations reminiscent of Fourier-Laplace transforms, operational calculus, certain services, and asymptotic tools. 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 summary of the Fourier-Laplace vital, the Mellin remodel, and specified services comparable 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 airplane wave on the interface among homogeneous media, the asymptotic enlargement of Hankel's features in the community of the purpose at infinity, and the asymptotic habit of the Laplace rework. The publication additionally examines the strategy of steepest descent, the asymptotic illustration of Hankel's functionality of enormous order, and the scattering matrix idea. the remainder chapters specialize in difficulties of circulation in open channels, the propagation of elastic waves inside a layered round physique, and a few difficulties in water wave thought.
This publication is a precious 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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