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The Mathematical Theory of Time-Harmonic Maxwell's Equations

Expansion-, Integral-, and Variational Methods

  • Textbook
  • © 2015

Overview

Authors:
  1. Andreas Kirsch

    1. Karlsruhe Institute of Technology (KIT) Department of Mathematics, Karlsruhe, Germany

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  2. Frank Hettlich

    1. Department of Mathematics, Karlsruhe Institute of Technology (KIT), karlsruhe, Germany

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    You can also search for this author in PubMed   Google Scholar

  • 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

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Andreas Kirsch, Frank Hettlich
    Pages 1-20

  3. Expansion into Wave Functions

    • Andreas Kirsch, Frank Hettlich
    Pages 21-94

  4. Scattering from a Perfect Conductor

    • Andreas Kirsch, Frank Hettlich
    Pages 95-163

  5. The Variational Approach to the Cavity Problem

    • Andreas Kirsch, Frank Hettlich
    Pages 165-225

  6. Boundary Integral Equation Methods for Lipschitz Domains

    • Andreas Kirsch, Frank Hettlich
    Pages 227-311

  7. Back Matter

    Pages 313-337
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Keywords

About this book

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.

Reviews

“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 Rădulescu, zbMATH 1342.35004, 2016)

Authors and Affiliations

  • Karlsruhe Institute of Technology (KIT) Department of Mathematics, Karlsruhe, Germany

    Andreas Kirsch

  • Department of Mathematics, Karlsruhe Institute of Technology (KIT), karlsruhe, Germany

    Frank Hettlich

About the authors

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

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