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Linear Integral Equations / by Rainer Kress.
Math/Physics/Astronomy Library QA1 .A647 v.1-61,63-65,67-80,83-v.205,v.208-v.215,v.218-v.223
Available
Chemistry Library - Books QA1 .A647 v.38,44,46,51-52,55
Mixed Availability
LIBRA QA1 .A647 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Kress, Rainer., Author.
- Series:
- Applied Mathematical Sciences, 0066-5452 ; 82
- Language:
- English
- Subjects (All):
- Mathematical analysis.
- Analysis (Mathematics).
- Numerical analysis.
- Measure theory.
- Signal processing.
- Image processing.
- Speech processing systems.
- Analysis.
- Numerical Analysis.
- Measure and Integration.
- Signal, Image and Speech Processing.
- Local Subjects:
- Analysis.
- Numerical Analysis.
- Measure and Integration.
- Signal, Image and Speech Processing.
- Physical Description:
- 1 online resource (XVI, 412 p. 1 illus.) online resource.
- Edition:
- 3rd ed. 2014.
- Place of Publication:
- New York, NY : Springer New York : Imprint: Springer, 2014.
- Language Note:
- English
- 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 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) .
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 1-4614-9593-8
- OCLC:
- 865475046
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