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IDENT
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http://dx.doi.org/10.1007/978-1-4614-9593-2
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標題および責任表示
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Linear Integral Equations / by Rainer Kress
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特定資料種別コード
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リモートファイル
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版事項
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3rd ed. 2014
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出版・頒布事項
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New York, NY : Springer New York : Imprint: Springer , 2014
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形態事項
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XVI, 412 p. 1 illus : online resource
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巻号情報
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書誌構造リンク
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Applied Mathematical Sciences <> 82//a
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内容著作注記
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Normed Spaces
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内容著作注記
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Bounded and Compact Operators
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内容著作注記
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Riesz Theory
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内容著作注記
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Dual Systems and Fredholm Alternative
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内容著作注記
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Regularization in Dual Systems
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内容著作注記
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Potential Theory
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内容著作注記
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Singular Integral Equations
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内容著作注記
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Sobolev Spaces
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内容著作注記
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The Heat Equation
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内容著作注記
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Operator Approximations .-Degenerate Kernel Approximation
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内容著作注記
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Quadrature Methods
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内容著作注記
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Projection Methods
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内容著作注記
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Iterative Solution and Stability
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内容著作注記
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Equations of the First Kind
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内容著作注記
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Tikhonov Regularization
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内容著作注記
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Regularization by Discretization
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内容著作注記
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Inverse Boundary Value Problems
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内容著作注記
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References
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内容著作注記
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Index
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注記
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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 Hahn?Banach 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. 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)
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学情ID
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9781461495925
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本文言語コード
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英語
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著者標目リンク
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*Kress, Rainer <> author
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著者標目リンク
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SpringerLink (Online service) <>
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分類標目
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DC23:515
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件名標目等
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Mathematics
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件名標目等
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Mathematical analysis
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件名標目等
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Analysis (Mathematics)
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件名標目等
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Measure theory
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件名標目等
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Numerical analysis
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件名標目等
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Mathematics
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件名標目等
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Analysis
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件名標目等
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Numerical Analysis
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件名標目等
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Measure and Integration
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件名標目等
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Signal, Image and Speech Processing
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