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Mathematical methods of electromagnetic theory. (English) Zbl 1308.78001

Courant Lecture Notes in Mathematics 25. Providence, RI: American Mathematical Society (AMS); New York, NY: Courant Institute of Mathematical Sciences (ISBN 978-1-4704-1711-6/pbk). x, 145 p. (2014).
The book under review provides a mathematical introduction to the classical electromagnetic theory and wave propagation. The volume also includes a brief introduction to special relativity. Some of the main features of this book are the following: (i) it gives a rigorous derivation and very nice interpretations of the interaction of electromagnetic waves with matter; and (ii) the volume provides a thorough discussion about how to use the variational principles in order to solve problems in electrostatics and magnetostatics.
The content of the book is divided into nine chapters, as follows: 1. Preliminaries; 2. Electrostatics; 3. Currents and Ohm’s Law; 4. Magnetostatics; 5. Electromagnetic Fields Changing in Time; 6. Transmission Lines. Method of the Laplace Transformation; 7. Electromagnetodynamics of Moving Bodies and the Principle of Relativity; 8. Electromagnetic Wave Propagation; 9. The Scattering Problem.
This volume is mainly addressed to undergraduate students, graduate students, and research mathematicians interested in electromagnetics.

MSC:

78-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory
78-03 History of optics and electromagnetic theory
01A75 Collected or selected works; reprintings or translations of classics
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
00A79 Physics
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