Linear Integral Equations

  • Rainer Kress

Part of the Applied Mathematical Sciences book series (AMS, volume 82)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Rainer Kress
    Pages 1-12
  3. Rainer Kress
    Pages 13-24
  4. Rainer Kress
    Pages 25-35
  5. Rainer Kress
    Pages 36-49
  6. Rainer Kress
    Pages 50-57
  7. Rainer Kress
    Pages 58-81
  8. Rainer Kress
    Pages 82-107
  9. Rainer Kress
    Pages 108-131
  10. Rainer Kress
    Pages 132-141
  11. Rainer Kress
    Pages 142-153
  12. Rainer Kress
    Pages 154-167
  13. Rainer Kress
    Pages 168-183
  14. Rainer Kress
    Pages 184-205
  15. Rainer Kress
    Pages 206-220
  16. Rainer Kress
    Pages 221-242
  17. Rainer Kress
    Pages 243-258
  18. Rainer Kress
    Pages 259-269
  19. Rainer Kress
    Pages 270-288
  20. Back Matter
    Pages 289-301

About this book

Introduction

I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equa­ tions of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also in­ troduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equa­ tions. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory.

Keywords

Hilbert space Integral calculus Integral equation Riesz-Fredholm theory calculus differential equation functional analysis numerical methods numerical solutions x integral equations

Authors and affiliations

  • Rainer Kress
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenFed. Rep. of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-97146-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-97148-8
  • Online ISBN 978-3-642-97146-4
  • Series Print ISSN 0066-5452
  • About this book