Linear Integral Equations

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Overview

This book originated from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter. For the second edition, in addition to corrections and adjustments throughout the text, as well as an updated reference section, new topics have been added.
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Editorial Reviews

Booknews
An advanced text combining theory, applications, and numerical methods for physicists and engineers. Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

Table of Contents

Preface to the Second Edition
Preface to the First Edition
1 Normed Spaces 1
2 Bounded and Compact Operators 15
3 Riesz Theory 28
4 Dual Systems and Fredholm Alternative 39
5 Regularization in Dual Systems 55
6 Potential Theory 67
7 Singular Integral Equations 94
8 Sobolev Spaces 125
9 The Heat Equation 152
10 Operator Approximations 163
11 Degenerate Kernel Approximation 177
12 Quadrature Methods 197
13 Projection Methods 218
14 Iterative Solution and Stability 247
15 Equations of the First Kind 265
16 Tikhonov Regularization 290
17 Regularization by Discretization 308
18 Inverse Boundary Value Problems 320
References 347
Index 361
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