This second edition of Linear Integral Equations continues the emphasis
that the first edition placed on applications. Indeed, many more
examples have been added throughout the text. Significant new material
has been added in Chapters 6 and 8. For instance, in Chapter 8 we have
included the solutions of the Cauchy type integral equations on the real
line. Also, there is a section on integral equations with a logarithmic
kernel. The bibliography at the end of the book has been exteded and
brought up to date. I wish to thank Professor B.K. Sachdeva who has
checked the revised man- uscript and has suggested many improvements.
Last but not least, I am grateful to the editor and staff of Birkhauser
for inviting me to prepare this new edition and for their support in
preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1.
Definition An integral equation is an equation in which an unknown
function appears under one or more integral signs Naturally, in such an
equation there can occur other terms as well. For example, for a s b; a:
( t: ( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) ]
ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the
function g(s) is the unknown function and all the other functions are
known, are integral equations. These functions may be complex-valued
functions of the real variables s and t.
