000 04130nam a22004935i 4500
001 978-1-4614-9593-2
003 DE-He213
005 20140220082505.0
007 cr nn 008mamaa
008 131204s2014 xxu| s |||| 0|eng d
020 _a9781461495932
_9978-1-4614-9593-2
024 7 _a10.1007/978-1-4614-9593-2
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aKress, Rainer.
_eauthor.
245 1 0 _aLinear Integral Equations
_h[electronic resource] /
_cby Rainer Kress.
250 _a3rd ed. 2014.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2014.
300 _aXVI, 412 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v82
505 0 _aNormed 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.
520 _aThis 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)  
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aNumerical Analysis.
650 2 4 _aMeasure and Integration.
650 2 4 _aSignal, Image and Speech Processing.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461495925
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v82
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-9593-2
912 _aZDB-2-SMA
999 _c92400
_d92400