Integral Equations A Reference Text
Download Integral Equations A Reference Text full books in PDF, epub, and Kindle. Read online free Integral Equations A Reference Text ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Zabreyko |
Publisher | : Springer |
Total Pages | : 472 |
Release | : 1975-01-09 |
Genre | : Mathematics |
ISBN | : |
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 | : P. P. Zabrejko |
Publisher | : |
Total Pages | : 0 |
Release | : 1975 |
Genre | : |
ISBN | : |
Author | : Rainer Kress |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2013-12-04 |
Genre | : Mathematics |
ISBN | : 1461495938 |
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 | : C. Corduneanu |
Publisher | : |
Total Pages | : 366 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780521340502 |
The purpose of this book is threefold: to be used for graduate courses on integral equations; to be a reference for researchers; and to describe methods of application of the theory. The author emphasizes the role of Volterra equations as a unifying tool in the study of functional equations, and investigates the relation between abstract Volterra equations and other types of functional-differential equations.
Author | : Dr Jitendra Singh |
Publisher | : Dr. Jitendra Singh |
Total Pages | : 138 |
Release | : 2024-10-02 |
Genre | : Education |
ISBN | : |
This book is part of the P-17 series designed specifically for the CSIR NET (JRF) in Mathematical Sciences and other competitive mathematics examinations. Integral equations play a crucial role in various fields, including applied mathematics, physics, and engineering. This text aims to provide a comprehensive introduction to integral equations, offering both theoretical insights and practical problem-solving techniques. Chapter 1 lays the groundwork by differentiating between Fredholm and Volterra integral equations and clarifying the distinctions between first- and second-kind integral equations. Understanding these foundational concepts is essential for tackling more complex topics. In Chapter 2, we explore several methods for solving integral equations, including the resolvent kernel method and the Neumann series approach. These techniques provide powerful tools for both analytical and numerical solutions. Chapter 3 delves into separable kernels, showcasing their significance in solving integral equations and their applications in mathematical physics and engineering contexts. Chapter 4 addresses eigenvalue problems, connecting characteristic numbers and eigenfunctions to the well-established Sturm-Liouville theory, which is pivotal in understanding the spectral properties of differential operators. Finally, Chapter 5 discusses the resolvent kernel, detailing its theory and applications in solving integral equations effectively. This book aims to equip students and researchers with the knowledge and skills necessary to navigate the complexities of integral equations, fostering a deeper appreciation for their applications in both pure and applied mathematics.
Author | : N. I. Muskhelishvili |
Publisher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2013-02-19 |
Genre | : Mathematics |
ISBN | : 0486145069 |
DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div
Author | : Matiur Rahman |
Publisher | : WIT Press |
Total Pages | : 385 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 1845641019 |
The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Author | : Petr Petrovich Zabreiko |
Publisher | : |
Total Pages | : 443 |
Release | : 1975 |
Genre | : |
ISBN | : |
Author | : N.I. Muskhelishvili |
Publisher | : Springer Science & Business Media |
Total Pages | : 453 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400999941 |
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.
Author | : L. M. Delves |
Publisher | : CUP Archive |
Total Pages | : 392 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780521357968 |
This textbook provides a readable account of techniques for numerical solutions.