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)
