The theory of integral equations has been an active research field for
many years and is based on analysis, function theory, and functional
analysis. On the other hand, integral equations are of practical
interest because of the boundary integral equation method, which
transforms partial differential equations on a domain into integral
equations over its boundary. This book grew out of a series of lectures
given by the author at the Ruhr-Universitat Bochum and the
Christian-Albrecht-Universitat zu Kiel to students of mathematics. The
contents of the first six chapters correspond to an intensive lecture
course of four hours per week for a semester. Readers of the book
require background from analysis and the foundations of numeri- cal
mathematics. Knowledge of functional analysis is helpful, but to begin
with some basic facts about Banach and Hilbert spaces are sufficient.
The theoretical part of this book is reduced to a minimum; in Chapters
2, 4, and 5 more importance is attached to the numerical treatment of
the integral equations than to their theory. Important parts of
functional analysis (e. g., the Riesz-Schauder theory) are presented
without proof. We expect the reader either to be already familiar with
functional analysis or to become motivated by the practical examples
given here to read a book about this topic. We recall that also from a
historical point of view, functional analysis was initially stimulated
by the investigation of integral equations.