The Resource Linear Integral Equations, by Rainer Kress, (electronic resource)
Linear Integral Equations, by Rainer Kress, (electronic resource)
Resource Information
The item Linear Integral Equations, by Rainer Kress, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Linear Integral Equations, by Rainer Kress, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as selfcontained as possible, 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 itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the HahnBanach extension theorem and the Banach open mapping theorem are now included in the text.The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for twodimensional hypersingular boundary integral equations and a collocation method for the threedimensional LippmannSchwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
 Language
 eng
 Edition
 Third edition 2014.
 Extent
 XVI, 412 pages 1 illustrations
 Contents

 Normed Spaces
 Bounded and Compact Operators
 Riesz Theory
 Dual Systems and Fredholm Alternative
 Regularization in Dual Systems
 Potential Theory
 Singular Integral Equations
 Sobolev Spaces
 The Heat Equation
 Operator Approximations .Degenerate Kernel Approximation
 Quadrature Methods
 Projection Methods
 Iterative Solution and Stability
 Equations of the First Kind
 Tikhonov Regularization
 Regularization by Discretization
 Inverse Boundary Value Problems
 References
 Index
 Isbn
 9781461495932
 Label
 Linear Integral Equations
 Title
 Linear Integral Equations
 Statement of responsibility
 by Rainer Kress
 Language
 eng
 Summary
 This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as selfcontained as possible, 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 itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the HahnBanach extension theorem and the Banach open mapping theorem are now included in the text.The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for twodimensional hypersingular boundary integral equations and a collocation method for the threedimensional LippmannSchwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorDate
 1941
 http://library.link/vocab/creatorName
 Kress, Rainer
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement

 Applied Mathematical Sciences,
 Springer eBooks
 Series volume
 82
 http://library.link/vocab/subjectName

 Mathematics
 Global analysis (Mathematics)
 Numerical analysis
 Label
 Linear Integral Equations, by Rainer Kress, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent.
 Contents
 Normed Spaces  Bounded and Compact Operators  Riesz Theory  Dual Systems and Fredholm Alternative  Regularization in Dual Systems  Potential Theory  Singular Integral Equations  Sobolev Spaces  The Heat Equation  Operator Approximations .Degenerate Kernel Approximation  Quadrature Methods  Projection Methods  Iterative Solution and Stability  Equations of the First Kind  Tikhonov Regularization  Regularization by Discretization  Inverse Boundary Value Problems  References  Index
 Control code
 9781461495932
 Dimensions
 unknown
 Edition
 Third edition 2014.
 Extent
 XVI, 412 pages 1 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781461495932
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code
 c
 Other control number
 10.1007/9781461495932
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086528973
 Label
 Linear Integral Equations, by Rainer Kress, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent.
 Contents
 Normed Spaces  Bounded and Compact Operators  Riesz Theory  Dual Systems and Fredholm Alternative  Regularization in Dual Systems  Potential Theory  Singular Integral Equations  Sobolev Spaces  The Heat Equation  Operator Approximations .Degenerate Kernel Approximation  Quadrature Methods  Projection Methods  Iterative Solution and Stability  Equations of the First Kind  Tikhonov Regularization  Regularization by Discretization  Inverse Boundary Value Problems  References  Index
 Control code
 9781461495932
 Dimensions
 unknown
 Edition
 Third edition 2014.
 Extent
 XVI, 412 pages 1 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9781461495932
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code
 c
 Other control number
 10.1007/9781461495932
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086528973
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