Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems 2001 Edition Contributor(s): Nedelec, Jean-Claude (Author) |
|
![]() |
ISBN: 0387951555 ISBN-13: 9780387951553 Publisher: Springer OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: March 2001 Annotation: This self-contained book is devoted to the study of the acoustic wave equations and the Maxwell system, the two most common waves equations that are encountered in physics or in engineering. It presents a detailed analysis of their mathematical and physical properties. In particular, the author focuses on the study of the harmonic exterior problems, building a mathematical framework which provides the existence and uniqueness of the solutions. This book will serve as a useful introduction to wave problems for graduate students in mathematics, physics, and engineering. |
Additional Information |
BISAC Categories: - Mathematics | Applied - Science | Waves & Wave Mechanics - Medical |
Dewey: 530.124 |
LCCN: 00045038 |
Series: Applied Mathematical Sciences (Springer) |
Physical Information: 0.78" H x 6.41" W x 9.6" (1.22 lbs) 318 pages |
Descriptions, Reviews, Etc. |
Publisher 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. |