The Mathematical Theory of Time-Harmonic Maxwell's Equations

Expansion-, Integral-, and Variational Methods

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book The Mathematical Theory of Time-Harmonic Maxwell's Equations by Andreas Kirsch, Frank Hettlich, Springer International Publishing
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Author: Andreas Kirsch, Frank Hettlich ISBN: 9783319110868
Publisher: Springer International Publishing Publication: November 20, 2014
Imprint: Springer Language: English
Author: Andreas Kirsch, Frank Hettlich
ISBN: 9783319110868
Publisher: Springer International Publishing
Publication: November 20, 2014
Imprint: Springer
Language: English

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.

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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.

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