Linear Integral Equations

Linear Integral Equations

by Rainer Kress
     
 

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… See more details below

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.

Product Details

ISBN-13:
9780387506166
Publisher:
Springer-Verlag New York, LLC
Publication date:
07/28/1989
Series:
Applied Mathematical Sciences Series, #82
Pages:
299
Product dimensions:
6.30(w) x 9.45(h) x (d)

Table of Contents

Preface to the Second Edition
Preface to the First Edition
1Normed Spaces1
2Bounded and Compact Operators15
3Riesz Theory28
4Dual Systems and Fredholm Alternative39
5Regularization in Dual Systems55
6Potential Theory67
7Singular Integral Equations94
8Sobolev Spaces125
9The Heat Equation152
10Operator Approximations163
11Degenerate Kernel Approximation177
12Quadrature Methods197
13Projection Methods218
14Iterative Solution and Stability247
15Equations of the First Kind265
16Tikhonov Regularization290
17Regularization by Discretization308
18Inverse Boundary Value Problems320
References347
Index361

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