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Author : Frank Penzel
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (116 download)
Download or read book On the Theory of Generalized Abel Integral Equations on the Half Line written by Frank Penzel and published by . This book was released on 1986 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank Penzel
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (11 download)
Download or read book On the theory of generalized Abel integral equations on the half-linie written by Frank Penzel and published by . This book was released on 1986 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Gorenflo
Publisher : Springer
ISBN 13 : 3540469494
Total Pages : 225 pages
Book Rating : 4.5/5 (44 download)
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Author : A. V. Bitsadze
Publisher : World Scientific
ISBN 13 : 9789810222635
Total Pages : 286 pages
Book Rating : 4.2/5 (226 download)
Download or read book Integral Equations of First Kind written by A. V. Bitsadze and published by World Scientific. This book was released on 1995 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies classes of linear integral equations of the first kind most often met in applications. Since the general theory of integral equations of the first kind has not been formed yet, the book considers the equations whose solutions either are estimated in quadratures or can be reduced to well-investigated classes of integral equations of the second kind.In this book the theory of integral equations of the first kind is constructed by using the methods of the theory of functions both of real and complex variables. Special attention is paid to the inversion formulas of model equations most often met in physics, mechanics, astrophysics, chemical physics etc. The general theory of linear equations including the Fredholm, the Noether, the Hausdorff theorems, the Hilbert-Schmidt theorem, the Picard theorem and the application of this theory to the solution of boundary problems are given in this book. The book studies the equations of the first kind with the Schwarz Kernel, the Poisson and the Neumann kernels; the Volterra integral equations of the first kind, the Abel equations and some generalizations, one-dimensional and many-dimensional analogues of the Cauchy type integral and some of their applications.
Author : I. G. Petrovskii
Publisher : Courier Corporation
ISBN 13 : 9780486697567
Total Pages : 142 pages
Book Rating : 4.6/5 (975 download)
Download or read book Lectures on the Theory of Integral Equations written by I. G. Petrovskii and published by Courier Corporation. This book was released on 1996-09-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Author : Ricardo Estrada
Publisher : Springer Science & Business Media
ISBN 13 : 1461213827
Total Pages : 433 pages
Book Rating : 4.4/5 (612 download)
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 433 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
Author : Harry Bateman
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.3/5 ( download)
Download or read book Report on the History and Present State of the Theory of Integral Equations written by Harry Bateman and published by . This book was released on 1911 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. G. Mikhlin
Publisher : Elsevier
ISBN 13 : 1483226271
Total Pages : 354 pages
Book Rating : 4.4/5 (832 download)
Download or read book Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-22 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.
Author : Donald Lee Schmidt
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (38 download)
Download or read book Generalized Abel's Integral Equation ... written by Donald Lee Schmidt and published by . This book was released on 1955 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maxime Bôcher
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.F/5 ( download)
Download or read book An Introduction to the Study of Integral Equations written by Maxime Bôcher and published by . This book was released on 1909 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ram P. Kanwal
Publisher : Academic Press
ISBN 13 : 1483262502
Total Pages : 311 pages
Book Rating : 4.4/5 (832 download)
Download or read book Linear Integral Equations written by Ram P. Kanwal and published by Academic Press. This book was released on 2014-05-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.
Author : Zabreyko
Publisher : Springer
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.:/5 (44 download)
Download or read book Integral Equations—a Reference Text written by Zabreyko and published by Springer. This book was released on 1975-01-09 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title 'Integral equations' covers many things which have very little connection with each other. However, they are united by the following important feature. In most cases, the equations involve an unknown function operated on by a bounded and often compact operator defined on some Banach space. The aim of the book is to list the main results concerning integral equations. The classical Fredholm theory and Hilbert-Schmidt theory are presented in Chapters II and III. The preceding Chapter I contains a description of the most important types of integral equations which can be solved in 'closed' form. Chapter IV is an important addition to Chapters II and III, as it contains the theory of integral equations with non-negative kernels. The development of this theory is mainly due to M. G. Krein. The content of the first four chapters is fairly elementary. It is well known that the Fredholm theory has been generalized for equations with compact operators. Chapter V is devoted tothis generalization. In Chapter VI one-dimensional (i.e. with one dependent variable) singular integral equations are considered. The last type of equations differ from that considered in the preceding chapters in that singular integral operators are not compact but only bounded in the usual functional spaces.
Author : Rudolf Gorenflo
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (755 download)
Download or read book An operational method for solving generalized Abel integral equations of second kind written by Rudolf Gorenflo and published by . This book was released on 1995 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : N. I. Muskhelishvili
Publisher : Courier Corporation
ISBN 13 : 0486462420
Total Pages : 466 pages
Book Rating : 4.4/5 (864 download)
Download or read book Singular Integral Equations written by N. I. Muskhelishvili and published by Courier Corporation. This book was released on 2008-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This high-level treatment considers one-dimensional singular integral equations involving Cauchy principal values, covering Hölder condition, Hilbert and Riemann-Hilbert problems, Dirichlet problems, inversion formulas for arcs, more. 1992 edition.
Author : Stephen M. Zemyan
Publisher : Springer Science & Business Media
ISBN 13 : 0817683496
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)
Download or read book The Classical Theory of Integral Equations written by Stephen M. Zemyan and published by Springer Science & Business Media. This book was released on 2012-07-10 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.
Author : Rudolf Gorenflo
Publisher :
ISBN 13 : 9783662201886
Total Pages : 232 pages
Book Rating : 4.2/5 (18 download)
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by . This book was released on 2014-01-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dang Dinh Ang
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (46 download)
Download or read book Regularization of a generalized Abel integral equation written by Dang Dinh Ang and published by . This book was released on 1990 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
