The Mathematical Theory of Time-Harmonic Maxwell's Equations: Expansion-, Integral-, and Variational Methods

ISBN-13: 9783319379180 / Angielski / Miękka / 2016 / 337 str.

Andreas Kirsch; Frank Hettlich

Opis

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.

Recenzje

"This book is devoted to the study of the Maxwell equations in relationship with the basic techniques for a thorough mathematical analysis of these equations. ... Numerous examples and exercises illustrate the abstract content of this book. The volume under review is useful to graduate students and researchers in applied mathematics and engineers working in the theoretical approach to electromagnetic wave propagation." (Teodora-Liliana Radulescu, zbMATH 1342.35004, 2016)

Spis treści

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.

O autorze

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