A Course on Integral Equations

Authors: Allen C. Pipkin



Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe- matical Sciences ( AMS) series, which will focus on advanced textbooks and research level monographs. Foreword This book is based on a one-semester course for graduate students in the physical sciences and applied mathematics. No great mathematical back- ground is needed, but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is on problem- solving rather than theorem-proving, the main requirement is that the stu- dent should be willing to work out a large number of specific examples.

Table of contents (12 chapters)

Front Matter

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

Back Matter