| Document Type
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BL
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| Record Number
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667568
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| Doc. No
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dltt
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| Main Entry
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Kress, Rainer,1941-
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| Title & Author
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Linear integral equations /\ Rainer Kress
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| Edition Statement
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Third edition
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Third edition
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| Series Statement
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Applied mathematical sciences ;; volume 82
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| Page. NO
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1 online resource (xvi, 412 pages).
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| ISBN
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146149592X
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: 1461495938 (electronic bk.)
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: 9781461495925
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: 9781461495932 (electronic bk.)
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9781461495925
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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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
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| Abstract
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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 self-contained 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 two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation
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| Subject
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Integral equations.
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| Subject
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Analysis.
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| Subject
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Measure and Integration.
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| Subject
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Signal, Image and Speech Processing.
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| Dewey Classification
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515/.45
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| LC Classification
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QA431
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| Added Entry
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Ohio Library and Information Network.
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