# The Mathematical Theory of Time-Harmonic Maxwell's Equations

## Expansion-, Integral-, and Variational Methods

Part of the Applied Mathematical Sciences book series (AMS, volume 190)

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Textbook

Part of the Applied Mathematical Sciences book series (AMS, volume 190)

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave propagation problems. The students should have some knowledge on vector analysis (curves, surfaces, divergence theorem) and functional analysis (normed spaces, Hilbert spaces, linear and bounded operators, dual space).

Written in an accessible manner, topics are first approached with simpler scale Helmholtz Equations before turning to Maxwell Equations. There are examples and exercises throughout the book. It will be useful for graduate students and researchers in applied mathematics and engineers working in the theoretical approach to electromagnetic wave propagation.

Electromagnetic Theory Helmholtz Equations Lipschitz Domains Maxwell Equation Partial Differential Equations Sobolev Spaces

- DOI https://doi.org/10.1007/978-3-319-11086-8
- Copyright Information Springer International Publishing Switzerland 2015
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-11085-1
- Online ISBN 978-3-319-11086-8
- Series Print ISSN 0066-5452
- Series Online ISSN 2196-968X
- Buy this book on publisher's site