Operator Theory for Electromagnetics

An Introduction
2002. Auflage 2001
ISBN: 978-0-387-95278-9
Verlag: Springer

Buch, Englisch, 634 Seiten, Format (B × H): 161 mm x 241 mm, Gewicht: 1230 g

The purpose of this book is to describe methods for solving problems in applied electromagnetic theory using basic concepts from functional anal ysis and the theory of operators. Although the book focuses on certain mathematical fundamentals, it is written from an applications perspective for engineers and applied scientists working in this area. Part I is intended to be a somewhat self-contained introduction to op erator theory and functional analysis, especially those elements necessary for application to problems in electromagnetics. The goal of Part I is to ex plain and synthesize these topics in a logical manner. Examples principally geared toward electromagnetics are provided. With the exception of Chapter 1, which serves as a review of basic electromagnetic theory, Part I presents definitions and theorems along with associated discussion and examples. This style was chosen because it allows one to readily identify the main concepts in a particular section. A proof is provided for all theorems whose proof is simple and straightforward. A proof is also provided for theorems that require a slightly more elaborate proof, yet one that is especially enlightening, being either constructive or illustrative. Generally. theorems are stated but not proved in cases where either the proof is too involved or the details of the proof would take one too far afield of the topic at hand, such as requiring additional lemmas that are not clearly useful in applications.

Zielgruppe

Graduate

Autoren/Hrsg.

Hanson, George W

Yakovlev, Alexander B

Fachgebiete

• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik

Inhaltsverzeichnis

I: Basic Theory.- 1 Electromagnetic Fundamentals.- 2 Introductory Functional Analysis.- 3 Introductory Linear Operator Theory.- 4 Spectral Theory of Linear Operators.- 5 Sturm—Liouville Operators.- 6 Poisson’s and Laplace’s Boundary Value Problems: Potential Theory.- 7 Transmission-Line Analysis.- 8 Planarly Layered Media Problems.- 9 Cylindrical Waveguide Problems.- 10 Electromagnetic Cavities.- A Vector, Dyadic, and Integral Relations.- A.1 Vector Identities.- A.2 Dyadic Identities.- A.3 Dyadic Analysis.- A.4 Integral Identities.- A.5 Useful Formulas Involving the Position Vector and Scalar Green’s Functions.- A.6 Scalar and Vector Differential Operators in the Three Principal Coordinate Systems.- B Derivation of Second-Derivative Formula (1.59).- C Gram—Schmidt Orthogonalization Procedure.- D Coefficients of Planar-Media Green’s Dyadics.- E Additional Function Spaces.