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＜電子ブック＞
Acoustic and Electromagnetic Equations : Integral Representations for Harmonic Problems / by Jean-Claude Nedelec
(Applied Mathematical Sciences. ISSN:2196968X ; 144)

版	1st ed. 2001.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2001
本文言語	英語
大きさ	X, 318 p : online resource
著者標目	*Nedelec, Jean-Claude author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Electrodynamics LCSH:Acoustics LCSH:Computational intelligence LCSH:Electrical engineering FREE:Analysis FREE:Classical Electrodynamics FREE:Acoustics FREE:Computational Intelligence FREE:Electrical and Electronic Engineering
一般注記	1 Some Wave Equations -- 2 The Helmholtz Equation -- 3 Integral Representations and Integral Equations -- 4 Singular Integral Operators -- 5 Maxwell Equations and Electromagnetic Waves -- References This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier trans­ form reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the har­ monic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representa­ tions yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces HTTP:URL=https://doi.org/10.1007/978-1-4757-4393-7

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