Linear Integral Equations

  • Rainer Kress

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Rainer Kress
    Pages 1-14
  3. Rainer Kress
    Pages 15-27
  4. Rainer Kress
    Pages 28-38
  5. Rainer Kress
    Pages 39-54
  6. Rainer Kress
    Pages 55-66
  7. Rainer Kress
    Pages 67-93
  8. Rainer Kress
    Pages 94-124
  9. Rainer Kress
    Pages 125-151
  10. Rainer Kress
    Pages 152-162
  11. Rainer Kress
    Pages 163-176
  12. Rainer Kress
    Pages 177-196
  13. Rainer Kress
    Pages 197-217
  14. Rainer Kress
    Pages 218-246
  15. Rainer Kress
    Pages 247-264
  16. Rainer Kress
    Pages 265-289
  17. Rainer Kress
    Pages 290-307
  18. Rainer Kress
    Pages 308-319
  19. Rainer Kress
    Pages 320-346
  20. Back Matter
    Pages 347-367

About this book

Introduction

In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me. Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book. As in the first edition, the main motivation is to present the fundamental theory of integral equations, some of their main applications, and the basic concepts of their numerical solution in a single volume. This is done from my own perspective of integral equations; I have made no attempt to include all of the recent developments. In addition to making corrections and adjustments throughout the text and updating the references, the following topics have been added: In Sec­ tion 4.3 the presentation of the Fredholm alternative in dual systems has been slightly simplified and in Section 5.3 the short presentation on the index of operators has been extended. The treatment of boundary value problems in potential theory now includes proofs of the jump relations for single-and double-layer potentials in Section 6.3 and the solution of the Dirichlet problem for the exterior of an arc in two dimensions (Section 7.6). The numerical analysis of the boundary integral equations in Sobolev space settings has been extended for both integral equations of the first kind in Section 13.4 and integral equations of the second kind in Section 12.4.

Keywords

Boundary value problem Integral Equations Integral calculus Integral equation Linear Integral Equations Sobolev space calculus compactness functional analysis logarithm minimum numerical methods

Authors and affiliations

  • Rainer Kress
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0559-3
  • Copyright Information Springer-Verlag New York, Inc. 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6817-8
  • Online ISBN 978-1-4612-0559-3
  • Series Print ISSN 0066-5452
  • About this book