Operator Theory for Electromagnetics | 
 enlarge | Authors: George W. Hanson, Alexander B. Yakovlev
Publisher: Springer
Category: Book
List Price: $135.00
Buy New: $84.96
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Rating:  1 reviews
Sales Rank: 672092
Media: Hardcover
Edition: 1
Pages: 656
Number Of Items: 1
Shipping Weight (lbs): 2.4
Dimensions (in): 9.3 x 6.2 x 1.4
ISBN: 0387952780
Dewey Decimal Number: 530.141
EAN: 9780387952789
Publication Date: October 12, 2001
Availability: Usually ships in 1-2 business days
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Product Description
While there are many excellent books available on fundamental and applied electromagnetics, most introduce operator concepts in an ad hoc manner, and few discuss the subject within the general framework of operator theory. This is in contrast to quantum theory, where the use of operators and concepts from functional analysis is common. However, casting electromagnetic problems in terms of operator theory produces useful insights into the mathematical properties and physical characteristics of solutions. For instance, the commonly used modal expansion of fields in waveguides are immediately justified upon identifying the differential operators as being of the appropriate Sturm-Liouville type. As another example, existence, uniqueness and solvability of integral formulations can often be settled by appealing to the theory of Fredholm operators. Many other examples that illustrate the value of abstracting problems to an operator level are provided. Although the book focuses on mathematical fundamentals, it is written from the perspective of engineers and applied scientists working in electromagnetics. The book begins with a review of electromagnetic theory, including a discussion of singular integral operators commonly encountered in applications. It then turns to a self-contained introduction to operator theory, including basic functional analysis, linear operators, Greenand Green spectral theory, and Sturm-Liouville operators. The discussion is at an introductory mathematical level, presenting definitions and theorems, as well as proofs of the theorems when these are particularly simple or enlightening. The tools developed in this first part of the book are then applied to problems in classical electromagnetic theory: boundary-value problems and potential theory, transmission lines, waves in layered media, scattering problems in waveguides, and electromagnetic cavities.
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| Customer Reviews:
The missing link... at last August 2, 2006
Tareq Z. S. Salim (Birmingham, West Midlands, United Kingdom)
1 out of 1 found this review helpful
This book represents what I personally think is the missing link. Which link is that and between what?... well, the book introduces the reader to the very useful and easy, yet rigors theory of operators. This analytical tool is outstanding when someone wants to start proper analysis of an electromagnetic problem and wishes to do it in higher level of abstraction on the paper yet, with high level of details and physical understanding in mind. Therefore, The book is the link between the electromagnetism and theory of operators. The book is very useful for engineers and physicists who are not particularly interested in pure mathematics but instead, interested in the theory of operators as a powerful tool for both analytical and numerical formulations in electromagnetics. As a result, this book for advanced users and I suggest the beginners and intermediate readers to start with the book by Donald G. Dudley "Mathematical Foundations for Electromagnetic Theory ". Other sources that are of a great importance and support this book and make it perfect is the two by Ismo V. Lindell "Methods for Electromagnetic Field Analysis" and "Differential forms in Ellectromagnetics"
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