Integral Equations Of First Kind

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Integral Equations Of First Kind

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Author : A. V. Bitsadze
language : en
Publisher: World Scientific
Release Date : 1995

Integral Equations Of First Kind written by A. V. Bitsadze and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

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.

A Primer On Integral Equations Of The First Kind

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Author : G. Milton Wing
language : en
Publisher: SIAM
Release Date : 1991-01-01

A Primer On Integral Equations Of The First Kind written by G. Milton Wing and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.

Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.

A First Course In Integral Equations

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Author : Abdul-Majid Wazwaz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-05-04

A First Course In Integral Equations written by Abdul-Majid Wazwaz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-04 with Mathematics categories.

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.

A First Course In Integral Equations

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Author : Abdul-Majid Wazwaz
language : en
Publisher: World Scientific
Release Date : 1997

A First Course In Integral Equations written by Abdul-Majid Wazwaz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.

The Approximate Solution Of Fredholm Integral Equations Of The First Kind

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Author : I. N. Dombrovskaja
language : en
Publisher:
Release Date : 1966

The Approximate Solution Of Fredholm Integral Equations Of The First Kind written by I. N. Dombrovskaja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Fredholm equations categories.

The instability of the solution of Fredholm integral equations of first kind leads to difficulties if one attempts to obtain approximate solutions by direct numerical procedures such as replacement by a finite algebraic system, or expansion in series. A stable problem is to obtain the best approximation to the solution of the integral equation by an element of some given compact set M. The element of M which satisfies this condition is called a "quasi-solution" of the integral equation. In this paper, a numerical method of approximating the quasi-solution is developed based on solving finite systems of equations in finite-dimensional subsets Mn of M. Convergence of the approximations obtained in this fashion to the quasi-solution is proved.

Introduction To Integral Equations With Applications

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Author : Abdul J. Jerri
language : en
Publisher: John Wiley & Sons
Release Date : 1999-09-03

Introduction To Integral Equations With Applications written by Abdul J. Jerri and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-03 with Mathematics categories.

From the reviews of the First Edition: "Extremely clear, self-contained text . . . offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquées. Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration. Other features include: * A new section on integral equations in higher dimensions. * An improved presentation of the Laplace and Fourier transforms. * A new detailed section for Fredholm integral equations of the first kind. * A new chapter covering the basic higher quadrature numerical integration rules. * A concise introduction to linear and nonlinear integral equations. * Clear examples of singular integral equations and their solutions. * A student's solutions manual available directly from the author.

On Abel Type Integral Equations Of First Kind

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Author : Rudolf Gorenflo
language : en
Publisher:
Release Date : 1993

On Abel Type Integral Equations Of First Kind written by Rudolf Gorenflo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Integral Equations

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Author : Jirō Kondō
language : en
Publisher: Oxford University Press, USA
Release Date : 1991

Integral Equations written by Jirō Kondō and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

Integral equations arise in a very wide variety of mathematical and scientific problems. This textbook is devoted to the study and solution of such equations and it simultaneously provides a unified treatment of the theory together with a description of the range of methods for their solution. Professor Kondo's wide experience in science and engineering ensures that the many applications presented here are both up-to-date and relevant to current problems. Throughout, a wide selection of exercises will help further a student's understanding of the subject as well as give them a familiarity with the most important methods of solution. Consequently, this book will be ideal for final year undergraduates and postgraduates studying integral equations for the first time. All the main classes of integral equations are covered, including Volterra, Fredholm, and nonlinear integral equations. The close relationship with differential equations is also explored in order that students develop an understanding of the relationship between the two classes of equation and their relative merits for solving problems.

Linear Integral Equations

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Author : Raimer Kress
language : en
Publisher: Springer
Release Date : 1989-08-10

Linear Integral Equations written by Raimer Kress and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-10 with Mathematics categories.

I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equa tions of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also in troduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equa tions. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory.

Linear Integral Equations

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Author : Rainer Kress
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Integral Equations written by Rainer Kress and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equa tions of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also in troduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equa tions. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory.