Students in applied mathematics and the physical sciences will benefit from this text. It gives a concise treatment of the theory of integral equations and of some integral equations that frequently arise in applications. The text is accessible to anyone with a good background in mathematics and, in particular, a good knowledge of the theory of analytic functions of a complex variable.
The book is divided into three parts. The first part, on Fredholm and Hilbert-Schmidt theory, is mostly theoretical. Much of this discussion is presented in terms of finite-dimensional matrices and vectors. The last two parts emphasize problem solving using complex variables. The solution of convolution equations by using one- and two-sided Laplace transforms is covered in the second part. This second part includes (as preparation for the material on convolution equations) a short introduction to the Laplace transform. A short chapter covers the Wiener-Hopf method. The third part, in which the use of analytic function theory continues, deals with Cauchy principal value integrals.
These three parts comprise 12 chapters:
Fredholm Theory
Fredholm Theory with Integral Norms
Hilbert-Schmidt Theory
Laplace Transforms
Volterra Equations
Reciprocal Kernels
Smoothing and Unsmoothing
Wiener-Hopf Equations
Evaluation of Principal Value Integrals
Cauchy Principal Value Equations on a Finite Interval
Principal Value Equations on a Semi-infinite Interval
Principal Value Equations on an Infinite Interval
Many examples and problems for solution by the student are an integral part of the text. The book is well organized and suitable for introducing students to the fundamental methods in the theory of integral equations.
