Integral Equations Of First Kind PDF Download
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Author | : A V Bitsadze |
Publisher | : World Scientific |
Total Pages | : 274 |
Release | : 1995-10-12 |
Genre | : Science |
ISBN | : 9814500429 |
Download Integral Equations Of First Kind Book in PDF, ePub and Kindle
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 | : A. V. Bitsadze |
Publisher | : World Scientific |
Total Pages | : 286 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9789810222635 |
Download Integral Equations of First Kind Book in PDF, ePub and Kindle
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 | : G. Milton Wing |
Publisher | : SIAM |
Total Pages | : 141 |
Release | : 1991-01-01 |
Genre | : Mathematics |
ISBN | : 0898712637 |
Download A Primer on Integral Equations of the First Kind Book in PDF, ePub and Kindle
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.
Author | : Rainer Kress |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2013-12-04 |
Genre | : Mathematics |
ISBN | : 1461495938 |
Download Linear Integral Equations Book in PDF, ePub and Kindle
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)
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 1143 |
Release | : 2008-02-12 |
Genre | : Mathematics |
ISBN | : 0203881052 |
Download Handbook of Integral Equations Book in PDF, ePub and Kindle
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
Author | : George C. Hsiao |
Publisher | : Springer Nature |
Total Pages | : 783 |
Release | : 2021-03-26 |
Genre | : Mathematics |
ISBN | : 3030711277 |
Download Boundary Integral Equations Book in PDF, ePub and Kindle
This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
Author | : Rudolf Gorenflo |
Publisher | : Springer |
Total Pages | : 225 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540469494 |
Download Abel Integral Equations Book in PDF, ePub and Kindle
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 | : L. M. Delves |
Publisher | : CUP Archive |
Total Pages | : 392 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780521357968 |
Download Computational Methods for Integral Equations Book in PDF, ePub and Kindle
This textbook provides a readable account of techniques for numerical solutions.
Author | : Kendall E. Atkinson |
Publisher | : Cambridge University Press |
Total Pages | : 572 |
Release | : 1997-06-28 |
Genre | : Mathematics |
ISBN | : 0521583918 |
Download The Numerical Solution of Integral Equations of the Second Kind Book in PDF, ePub and Kindle
This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Author | : Abdul-majid Wazwaz |
Publisher | : World Scientific Publishing Company |
Total Pages | : 327 |
Release | : 2015-05-04 |
Genre | : Mathematics |
ISBN | : 9814675148 |
Download First Course In Integral Equations, A (Second Edition) Book in PDF, ePub and Kindle
This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Click here for solutions manual.