Applied Mathematical Sciences

Linear Integral Equations

Authors: Kress, Rainer

  • 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
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About this Textbook

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) 

Reviews

“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)


Table of contents (18 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-9593-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4614-9592-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4939-5016-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Linear Integral Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
82
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4614-9593-2
DOI
10.1007/978-1-4614-9593-2
Hardcover ISBN
978-1-4614-9592-5
Softcover ISBN
978-1-4939-5016-4
Series ISSN
0066-5452
Edition Number
3
Number of Pages
XVI, 412
Number of Illustrations and Tables
1 b/w illustrations
Topics