The Mathematical Theory of Time-Harmonic Maxwell's Equations

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.

Written by well known international researchers based on their lectures between 2007 and 2013 Accessible to broad audience with examples and exercises throughout Topics are first approached with simpler scalar Helmholtz equations before turning to Maxwell equations Appendix material includes results from functional analysis, vector calculus, and differential geometry

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

Inhalt
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.