Linear Integral Equations

by Rainer Kress

Publisher: Springer Berlin Heidelberg in Berlin, Heidelberg

Written in English
Cover of: Linear Integral Equations | Rainer Kress
Published: Pages: 299 Downloads: 139
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Subjects:

  • Mathematics,
  • Global analysis (Mathematics)

About the Edition

Up till now there has been no text on integral equations adequately combining theory, applications and numerical methods: this book sets out to cover each of these areas with the same weighting. The first part provides the basic Riesz-Fredholm theory for equations of the second kind with compact operators in dual systems, including all functional analytic concepts necessary. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace equation and the heat equation as one of the main historical sources for the development of integral equations, and also introduces Cauchy type singular integral equations. The third part describes the fundamental ideas for the numerical solutions of integral equations. In the final part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. So that the book is accessible not only to mathematicians but also to physicists and egineers, it is kept as self-contained as possible, requiring only a solid foundation in differential and integral calculus and, for some parts in complex function theory. Some background in functional analysis will be helpful, but the basic concepts needed are reviewed or developed within the book: the reader must of course be willing to accept the modern functional analytic language for describing the theory and the numerical solution of integral equations.

Edition Notes

Statementby Rainer Kress
SeriesApplied Mathematical Sciences -- 82, Applied Mathematical Sciences -- 82
Classifications
LC ClassificationsQA299.6-433
The Physical Object
Format[electronic resource] /
Pagination1 online resource (xi, 299p. 1 illus.)
Number of Pages299
ID Numbers
Open LibraryOL27071307M
ISBN 103642971482, 3642971466
ISBN 109783642971488, 9783642971464
OCLC/WorldCa851370127

Analysis of linear integral equations. New York, McGraw-Hill [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Linear integral equations. [Ram P Kanwal] -- Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Its treatment of boundary value problems and an extended and up-to-date bibliography will also make the book useful to research workers in many applied More than integral equations and their solutions are given in the first part of the book (Chapters 1–6). A lot of new e xact solutions to linear and nonlinear equations are :// 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

Ordinary Differential Equations. This note covers the following topics related to Ordinary Differential Equations: Linear Constant-Coefficient, Damped Oscillator, Forced Oscillations, Series Solutions, Trigonometry via ODE's, Green's Functions, Separation of Variables, Circuits, Simultaneous Equations, Simultaneous ODE's, Legendre's Equation, Asymptotic :// Additional Physical Format: Online version: Mikhlin, S.G. (Solomon Grigorʹevich), Linear integral equations. Delhi, Hindustan Pub. Corp.,   "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, ) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a :// Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra

Ordinary differential equations an elementary text book with an introduction to Lie's theory of the group of one parameter. This elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for the beginner in Differential Equations, or, perhaps, for the student of Technology who will not make a specialty of pure The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy Kovalevsky ://?id=VWLvAgAAQBAJ. Get this book in print. Linear Integral Equations (x Kn{x Lemma limit linear integral equation linearly independent Mathematical Analysis Neumann's problem nirx normalized orthogonal system notation obtain odd function orthogonality theorem parameter permanently convergent power series proof prove the following real and continuous Ri Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral ://

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"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, ) "This is a good introductory text book on linear integral equations. "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, ) "This is a good introductory text book on linear integral equations. › Mathematics › Analysis. Linear Integral Equations: Theory and Technique is an 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 ://   Linear Integral Equations book.

Read reviews from world’s largest community for readers. Derived from the author's lectures at Leningrad University, this Linear Integral Equations book. Read 3 reviews from the world's largest community for readers. Many physical problems that are usually solved by differen In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me.

Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this :// Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Linear Integral Equations book I offers a comprehensive and systematic treatment of linear integral equations of the first and second :// The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations.

Discover the world's research 17+ million members   The book deals with linear integral equations, that is, equations involving an unknown function which appears under an integral sign.

Such equations occur widely in diverse areas of applied mathematics and physics. They offer a powerful technique for solving a variety of practical problems. One obvious reason for using   aim of this book is to offer practical treatment of linear and nonlinear inte-gral equations emphasizing the need to problem solving rather than theorem proving.

The book was developed as a result of many years of experiences in teach-ing integral equations and conducting research work in this field. The author   This book resulted from the author's fascination with the mathematical beauty of integral equations.

It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same :// Linear integral equations is a small, useful text which is easy to follow and has examples and problems with solutions.

It covers Fredholm theory and Schmidt-Hilbert methods with a chapter on application for each. It should be easy to follow for someone with an elementary differential equations  › Books › Science & Math › Mathematics. Significant new material has been added in Chapters 6 and 8.

For instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real line. Also, there is a section on integral equations with a logarithmic kernel. The bibliography at the end of the book has been exteded and brought up to ://   Denoting the unknown function by φwe consider linear integral equations which involve an integral of the form K(x,s)φ(s)ds or K(x,s)φ(s)ds a x ∫ a b ∫ The type with integration over a fixed interval is called a Fredholm equation, while if the upper limit is x, a variable, it is a Volterra equation.

The other fundamental division of these ~rac/MT/Integral - Buy Linear Integral Equations book online at best prices in India on Read Linear Integral Equations book reviews & author details and more at   Up till now there has been no text on integral equations adequately combining theory, applications and numerical methods: this book sets out to cover each of these areas with the same weighting.

The first part provides the basic Riesz-Fredholm theory for equations of the second kind with compact operators in dual systems, including all functional analytic concepts :// 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  › Mathematics › Analysis. In this page volume, the author presents the reader with a number of methods for solving linear integral equations, which are often discussed within the context of Fredholm integrals using matrix, integral transforms (e.g.

Fourier and Laplace transforms, pp), successive-approximation techniques (pp), and partial differential equations (pp) › Books › Science & Math › Mathematics. Linear Integral Equations: Theory and Technique is an 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 ://   Linear and Nonlinear Integral Equations - Books.

Information > Mathematical Books > Integral Equations. Books on Integral Equations. Agarwal, R. P., O'Regan, D., and This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications.

Indeed, many more examples have been added throughout the text. Significant new material has been added in Chapters 6 and 8. For instance, in Chapter 8 we have included  › Birkhäuser › Mathematics. Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts.

Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce  › Mathematics › Analysis.

In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me. Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book.

As in  › Mathematics › Analysis. Linear Integral Equations (Applied Mathematical Sciences) (Vol 82) 2nd Edition by Raimer Kress (Author) out of 5 stars 1 rating. ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book  › Books › Science & Math › Mathematics.

springer, 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  › Home › Catalog.

This uncorrected soft cover reprint of the second edition places the emphasis on applications and presents a variety of techniques with extensive ally published inLinear Integral Equations is ideal as a text for a beginning graduate level course.

Its treatment of boundary value problems also makes the book useful to This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering.

The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of  › Birkhäuser › Mathematics.

Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts.

Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me.

Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book. As in the first edition, the main motivation is to present the fundamental theory of integral equations, some ?id=R3BIOfKssQ4C.

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 ://. "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, ) "This is a good introductory text book on linear integral equations. › Books › Engineering & Transportation › Engineering."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, ) "This is a good introductory text book on   Theory of linear Volterra integral equations A linear Volterra integral equation (VIE) of the second kind is a functional equation of the form u(t) = g(t) + Zt 0 K(t,s)u(s)ds, t ∈ I:= [0,T]. Here, g(t) and K(t,s) are given functions, and u(t) is an unknown function.

The function K(t,s) is called the kernel of the VIE. A linear VIE of the ~hbrunner/harbin10/