Integral Equations: Theory and Numerical Treatment (International Series of Numerical Mathematics) - Softcover

Hackbusch, Wolfgang

Softcover

ISBN 10: 3034899475 ISBN 13: 9783034899475

Publisher: Birkhäuser, 2011

Synopsis

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.

About this title

Language Notes

Text: English (translation)
Original Language: German

Edition details

• Publisher: Birkhäuser
• Publication date: 2011
• Language: English
• ISBN 10: 3034899475
• ISBN 13: 9783034899475
• Binding: Paperback
• Number of pages: 376