Singular Integral Equations

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Publisher : Springer Science & Business Media
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ISBN 10 : 0817640851
Pages : 444 pages
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Summary Book Review Singular Integral Equations :

Download or read book Singular Integral Equations written by Ricardo Estrada and published by Springer Science & Business Media. This book was released on 2000 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Singular Integral Equations is an ideal text for a beginning graduate level course or for self-study in a variety of scientific disciplines."--BOOK JACKET.

Singular Integral Equations

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Publisher : Springer
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ISBN 10 : 9400999968
Pages : 441 pages
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Rating : 4.9/5 (999 users download)


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Summary Book Review Singular Integral Equations :

Download or read book Singular Integral Equations written by N.I. Muskhelishvili and published by Springer. This book was released on 2011-12-25 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: In preparing this translation for publication certain minor modifications and additions have been introduced into the original Russian text, in order to increase its readibility and usefulness. Thus, instead of the first person, the third person has been used throughout; wherever possible footnotes have been included with the main text. The chapters and their subsections of the Russian edition have been renamed parts and chapters respectively and the last have been numbered consecutively. An authors and subject index has been added. In particular, the former has been combined with the list of references of the original text, in order to enable the reader to find quickly all information on anyone reference in which he may be especially interested. This has been considered most important with a view to the difficulties experienced outside Russia in obtaining references, published in that country. Russian names have been printed in Russian letters in the authors index, in order to overcome any possible confusion arising from transliteration.

Singular Integral Equations

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Publisher : Springer Science & Business Media
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ISBN 10 : 9781461213826
Pages : 427 pages
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Summary Book Review Singular Integral Equations :

Download or read book Singular Integral Equations written by Ricardo Estrada and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0

Singular Integral Equations and Discrete Vortices

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Publisher : Walter de Gruyter GmbH & Co KG
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ISBN 10 : 9783110926040
Pages : 484 pages
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Summary Book Review Singular Integral Equations and Discrete Vortices :

Download or read book Singular Integral Equations and Discrete Vortices written by I. K. Lifanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Singular Integral Equations

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ISBN 10 : 9783662042915
Pages : 552 pages
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Summary Book Review Singular Integral Equations :

Download or read book Singular Integral Equations written by E.G. Ladopoulos and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Applied Singular Integral Equations

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Publisher : CRC Press
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ISBN 10 : 9781439876213
Pages : 270 pages
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Summary Book Review Applied Singular Integral Equations :

Download or read book Applied Singular Integral Equations written by B. N. Mandal and published by CRC Press. This book was released on 2016-04-19 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

Singular Integral Equations

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Publisher : Courier Corporation
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ISBN 10 : 9780486145068
Pages : 464 pages
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Summary Book Review Singular Integral Equations :

Download or read book Singular Integral Equations written by N. I. Muskhelishvili and published by Courier Corporation. This book was released on 2013-02-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div

Wavelet Based Approximation Schemes for Singular Integral Equations

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Publisher : CRC Press
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ISBN 10 : 9780429534287
Pages : 290 pages
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Summary Book Review Wavelet Based Approximation Schemes for Singular Integral Equations :

Download or read book Wavelet Based Approximation Schemes for Singular Integral Equations written by Madan Mohan Panja and published by CRC Press. This book was released on 2020-09-25 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.

Multidimensional Weakly Singular Integral Equations

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Publisher : Springer
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ISBN 10 : 9783540477730
Pages : 168 pages
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Summary Book Review Multidimensional Weakly Singular Integral Equations :

Download or read book Multidimensional Weakly Singular Integral Equations written by Gennadi Vainikko and published by Springer. This book was released on 2006-11-15 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.

Toeplitz Matrices and Singular Integral Equations

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Publisher : Birkhäuser
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ISBN 10 : 9783034881999
Pages : 328 pages
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Summary Book Review Toeplitz Matrices and Singular Integral Equations :

Download or read book Toeplitz Matrices and Singular Integral Equations written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.

One-dimensional Linear Singular Integral Equations

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Publisher : Springer Science & Business Media
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ISBN 10 : 3764327960
Pages : 246 pages
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Summary Book Review One-dimensional Linear Singular Integral Equations :

Download or read book One-dimensional Linear Singular Integral Equations written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 1992 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 6 Preliminaries.- 6.1 The operator of singular integration.- 6.2 The space Lp(?, ?).- 6.3 Singular integral operators.- 6.4 The spaces $$L_{p}^{ + }(\Gamma, \rho ), L_{p}^{ - }(\Gamma, \rho ) and \mathop{{L_{p}^{ - }}}\limits^{^\circ } (\Gamma, \rho )$$.- 6.5 Factorization.- 6.6 One-sided invertibility of singular integral operators.- 6.7 Fredholm operators.- 6.8 The local principle for singular integral operators.- 6.9 The interpolation theorem.- 7 General theorems.- 7.1 Change of the curve.- 7.2 The quotient norm of singular integral operators.- 7.3 The principle of separation of singularities.- 7.4 A necessary condition.- 7.5 Theorems on kernel and cokernel of singular integral operators.- 7.6 Two theorems on connections between singular integral operators.- 7.7 Index cancellation and approximative inversion of singular integral operators.- 7.8 Exercises.- Comments and references.- 8 The generalized factorization of bounded measurable functions and its applications.- 8.1 Sketch of the problem.- 8.2 Functions admitting a generalized factorization with respect to a curve in Lp(?, ?).- 8.3 Factorization in the spaces Lp(?, ?).- 8.4 Application of the factorization to the inversion of singular integral operators.- 8.5 Exercises.- Comments and references.- 9 Singular integral operators with piecewise continuous coefficients and their applications.- 9.1 Non-singular functions and their index.- 9.2 Criteria for the generalized factorizability of power functions.- 9.3 The inversion of singular integral operators on a closed curve.- 9.4 Composed curves.- 9.5 Singular integral operators with continuous coefficients on a composed curve.- 9.6 The case of the real axis.- 9.7 Another method of inversion.- 9.8 Singular integral operators with regel functions coefficients.- 9.9 Estimates for the norms of the operators P?, Q? and S?.- 9.10 Singular operators on spaces H?o(?, ?).- 9.11 Singular operators on symmetric spaces.- 9.12 Fredholm conditions in the case of arbitrary weights.- 9.13 Technical lemmas.- 9.14 Toeplitz and paired operators with piecewise continuous coefficients on the spaces lp and ?p.- 9.15 Some applications.- 9.16 Exercises.- Comments and references.- 10 Singular integral operators on non-simple curves.- 10.1 Technical lemmas.- 10.2 A preliminary theorem.- 10.3 The main theorem.- 10.4 Exercises.- Comments and references.- 11 Singular integral operators with coefficients having discontinuities of almost periodic type.- 11.1 Almost periodic functions and their factorization.- 11.2 Lemmas on functions with discontinuities of almost periodic type.- 11.3 The main theorem.- 11.4 Operators with continuous coefficients - the degenerate case.- 11.5 Exercises.- Comments and references.- 12 Singular integral operators with bounded measurable coefficients.- 12.1 Singular operators with measurable coefficients in the space L2(?).- 12.2 Necessary conditions in the space L2(?).- 12.3 Lemmas.- 12.4 Singular operators with coefficients in ?p(?). Sufficient conditions.- 12.5 The Helson-Szegö theorem and its generalization.- 12.6 On the necessity of the condition a ? Sp.- 12.7 Extension of the class of coefficients.- 12.8 Exercises.- Comments and references.- 13 Exact constants in theorems on the boundedness of singular operators.- 13.1 Norm and quotient norm of the operator of singular integration.- 13.2 A second proof of Theorem 4.1 of Chapter 12.- 13.3 Norm and quotient norm of the operator S? on weighted spaces.- 13.4 Conditions for Fredholmness in spaces Lp(?, ?).- 13.5 Norms and quotient norm of the operator aI + bS?.- 13.6 Exercises.- Comments and references.- References.

Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift

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ISBN 10 : 9789401143639
Pages : 378 pages
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Summary Book Review Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift :

Download or read book Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift written by Georgii S. Litvinchuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857). In particular, such problems exhibit as boundary conditions relations among values of the unknown analytic functions which have to be evaluated at different points of the boundary. Singular integral equations with a shift are connected with such boundary value problems in a natural way. Subsequent to Riemann's work, D. Hilbert (1905), C. Haseman (1907) and T. Carleman (1932) also considered problems of this type. About 50 years ago, Soviet mathematicians began a systematic study of these topics. The first works were carried out in Tbilisi by D. Kveselava (1946-1948). Afterwards, this theory developed further in Tbilisi as well as in other Soviet scientific centers (Rostov on Don, Ka zan, Minsk, Odessa, Kishinev, Dushanbe, Novosibirsk, Baku and others). Beginning in the 1960s, some works on this subject appeared systematically in other countries, e. g. , China, Poland, Germany, Vietnam and Korea. In the last decade the geography of investigations on singular integral operators with shift expanded significantly to include such countries as the USA, Portugal and Mexico. It is no longer easy to enumerate the names of the all mathematicians who made contributions to this theory. Beginning in 1957, the author also took part in these developments. Up to the present, more than 600 publications on these topics have appeared.

Multidimensional Singular Integrals and Integral Equations

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Publisher : Elsevier
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ISBN 10 : 9781483164496
Pages : 172 pages
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Summary Book Review Multidimensional Singular Integrals and Integral Equations :

Download or read book Multidimensional Singular Integrals and Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-10 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Hypersingular Integral Equations and Their Applications

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Publisher : CRC Press
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ISBN 10 : 9780203402160
Pages : 416 pages
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Summary Book Review Hypersingular Integral Equations and Their Applications :

Download or read book Hypersingular Integral Equations and Their Applications written by I.K. Lifanov and published by CRC Press. This book was released on 2003-12-29 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co

One-Dimensional Linear Singular Integral Equations

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Publisher : Springer Science & Business Media
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ISBN 10 : 3764325844
Pages : 280 pages
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Summary Book Review One-Dimensional Linear Singular Integral Equations :

Download or read book One-Dimensional Linear Singular Integral Equations written by I. Gohberg and published by Springer Science & Business Media. This book was released on 1992-01-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.

Singular Integral Operators

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ISBN 10 : 3540159673
Pages : 530 pages
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Rating : 4.1/5 (596 users download)


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Summary Book Review Singular Integral Operators :

Download or read book Singular Integral Operators written by Solomon Grigor'evich Mikhlin and published by Springer Science & Business Media. This book was released on 1987 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

Handbook of Integral Equations

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Publisher : CRC Press
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ISBN 10 : 9780203881057
Pages : 1144 pages
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Rating : 4.2/5 (38 users download)


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Summary Book Review Handbook of Integral Equations :

Download or read book Handbook of Integral Equations written by Polyanin Polyanin and published by CRC Press. This book was released on 2008-02-12 with total page 1144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa