Acoustic and Electromagnetic Equations

Integral Representations for Harmonic Problems

By:

Jean-Claude Nedelec

Format:

Hardback

Series:

Applied Mathematical Sciences,

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Description

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.

Release date NZ

March 30th, 2001

Author

Jean-Claude Nedelec

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Illustrations

X, 318 p.

Pages

318

Series

Applied Mathematical Sciences,

Dimensions

156x234x19

ISBN-13

9780387951553

Product ID

2844282

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