# Linear Integral Equations

• Rainer Kress
Textbook

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

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

### 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
• Print ISBN 978-3-642-97148-8
• Online ISBN 978-3-642-97146-4
• Series Print ISSN 0066-5452
• Buy this book on publisher's site