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)"
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