The Mathematical Theory of Time-Harmonic Maxwell's Equations

Expansion-, Integral-, and Variational Methods
Softcover Nachdruck of the original 1. Auflage 2015
ISBN: 978-3-319-37918-0
Verlag: Springer International Publishing

Buch, Englisch, Band 190, 337 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 5329 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Hettlich, Frank

Kirsch, Andreas

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder

Inhaltsverzeichnis

Introduction.- Expansion into Wave Functions.- Scattering From a Perfect Conductor.- The Variational Approach to the Cavity Problem.- Boundary Integral Equation Methods for Lipschitz Domains.- Appendix.- References.- Index.

Über Autor(innen)

Andreas Kirsch and Frank Hettlich are Professors of Mathematics at Karlsruher Institut für Technologie (KIT).