© 2014

Linear Integral Equations

  • Complete basis in functional analysis including the Hahn-Banach and the open mapping theorem

  • More on boundary integral equations in Sobolev spaces

  • New developements in collocation methods via trigononmetric polynomials


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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Rainer Kress
    Pages 17-32
  3. Rainer Kress
    Pages 33-44
  4. Rainer Kress
    Pages 45-62
  5. Rainer Kress
    Pages 63-74
  6. Rainer Kress
    Pages 75-102
  7. Rainer Kress
    Pages 103-140
  8. Rainer Kress
    Pages 141-170
  9. Rainer Kress
    Pages 171-182
  10. Rainer Kress
    Pages 183-198
  11. Rainer Kress
    Pages 199-218
  12. Rainer Kress
    Pages 219-240
  13. Rainer Kress
    Pages 241-278
  14. Rainer Kress
    Pages 279-296
  15. Rainer Kress
    Pages 297-322
  16. Rainer Kress
    Pages 323-349
  17. Rainer Kress
    Pages 351-364
  18. Rainer Kress
    Pages 365-398
  19. Back Matter
    Pages 399-412

About this book


This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter.



For this third edition in  order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text.The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods


Reviews of earlier editions:


"This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution."

(Math. Reviews, 2000)


"This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract."  (ZbMath, 1999)



Hölder spaces Nyström method Riesz-Fredholm therory Sobolev spaces boundary integral equations dual systems ill-posed problems inverse problems projection methods regularization

Authors and affiliations

  1. 1.Georg-August-Universität Göttingen Institut fuer Numerische und AngewandteGöttingenGermany

Bibliographic information

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“The book contains 18 well presented chapters with an extensive list of 249 references. … It also contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear, and in the proper modern framework. … It is recommended for study to students, teachers, and all others who are interested in the development of this useful, and live area of mathematics.” (K. C. Gupta, zbMATH 1328.45001, 2016)

“The book being reviewed is the third edition of a well received one on integral equations which combines theory, applications and also numerical methods. … the book is more suitable for graduate students. The writing is lucid and clear, and the presentation is excellent. … the book should appeal not just to mathematicians, but also to scientists and engineers who wish to learn the theory of integral equations, the methods used to solve them, and their applications.” (Peter Shiu, The Mathematical Gazette, Vol. 99 (544), March, 2015)