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Integral Equations

Theory and Numerical Treatment

  • Wolfgang Hackbusch

Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 120)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Wolfgang Hackbusch
    Pages 1-24
  3. Wolfgang Hackbusch
    Pages 25-41
  4. Wolfgang Hackbusch
    Pages 201-215
  5. Wolfgang Hackbusch
    Pages 216-265
  6. Wolfgang Hackbusch
    Pages 266-317
  7. Wolfgang Hackbusch
    Pages 318-343
  8. Back Matter
    Pages 344-362

About this book

Introduction

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri­ cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

Keywords

Approximation Integral equation Interpolation

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

Bibliographic information

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