This book on integral equations and the calculus of variations is intended for use by senior
undergraduate students and first-year graduate students in science and engineering. Basic familiarity with theories of linear algebra, calculus, differential equations, and complex analysis
on the mathematics side, and classical mechanics, classical electrodynamics, quantum mechanics including the second quantization, and quantum statistical mechanics on the physics side,
is assumed. Another prerequisite for this book on the mathematics side is a sound understanding of local and global analysis.
This book grew out of the course notes for the last of the three-semester sequence of
Methods of Applied Mathematics I (Local Analysis), II (Global Analysis) and III (Integral
Equations and Calculus of Variations) taught in the Department of Mathematics at MIT. About
two-thirds of the course is devoted to integral equations and the remaining one-third to the
calculus of variations. Professor Hung Cheng taught the course on integral equations and the
calculus of variations every other year from the mid 1960s through the mid 1980s at MIT.
Since then, younger faculty have been teaching the course in turn. The course notes evolved
in the intervening years. This book is the culmination of these joint efforts.
There will be the obvious question: Why yet another book on integral equations and the
calculus of variations? There are already many excellent books on the theory of integral
equations. No existing book, however, discusses the singular integral equations in detail; in
particular, Wiener–Hopf integral equations and Wiener–Hopf sum equations with the notion
of the Wiener–Hopf index. In this book, the notion of the Wiener–Hopf index is discussed in
detail.