Recent Advances in Integral Equations
Recent Advances in Integral Equations

Author: Francisco Bulnes

Publisher: BoD – Books on Demand

Published: 2019-07-24

Total Pages: 102

ISBN-13: 183880658X

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Integral equations are functional equations in which an unknown function appears under an integral sign. This can involve aspects of function theory and their integral transforms when the unknown function appears with a functional non-degenerated kernel under the integral sign. The close relation between differential and integral equations does that in some functional analysis, and function theory problems may be formulated either way. This book establishes the fundamentals of integral equations and considers some deep research aspects on integral equations of first and second kind, operator theory applied to integral equations, methods to solve some nonlinear integral equations, and singular integral equations, among other things. This is the first volume on this theme, hoping that other volumes of this important functional analysis theme and operator theory to formal functional equations will be realized in the future.

Integral Equations and Their Applications
Integral Equations and Their Applications

Author: Matiur Rahman

Publisher: WIT Press

Published: 2007

Total Pages: 385

ISBN-13: 1845641019

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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.

Integral Equations
Integral Equations

Author: F. G. Tricomi

Publisher: Courier Corporation

Published: 2012-04-27

Total Pages: 256

ISBN-13: 0486158306

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Authoritative, well-written treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography.

Linear Integral Equations
Linear Integral Equations

Author: Rainer Kress

Publisher: Springer Science & Business Media

Published: 2013-12-04

Total Pages: 427

ISBN-13: 1461495938

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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)

A Course on Integral Equations
A Course on Integral Equations

Author: A. C. Pipkin

Publisher: Springer Science & Business Media

Published: 1991-09-12

Total Pages: 302

ISBN-13: 9780387975573

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This book is based on a one semester course for graduate students in physical sciences and applied mathemat- ics. Not detailed mathematical background is needed but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is problem-solving rather than theorem proving, the main requirement is that the student should be willing to work out a large number of specific examples. The course is divided about equally into three parts, where the first part is mostly theoretical and the remaining two parts emphasize on problem solving.

The Classical Theory of Integral Equations
The Classical Theory of Integral Equations

Author: Stephen M. Zemyan

Publisher: Springer Science & Business Media

Published: 2012-07-10

Total Pages: 350

ISBN-13: 0817683496

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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.

Integral Equations
Integral Equations

Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 181

ISBN-13: 048615212X

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This text begins with simple examples of a variety of integral equations and the methods of their solution, and progresses to become gradually more abstract and encompass discussions of Hilbert space. 1977 edition.

Techniques of Functional Analysis for Differential and Integral Equations
Techniques of Functional Analysis for Differential and Integral Equations

Author: Paul Sacks

Publisher: Academic Press

Published: 2017-05-16

Total Pages: 322

ISBN-13: 0128114576

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Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Linear and Nonlinear Integral Equations
Linear and Nonlinear Integral Equations

Author: Abdul-Majid Wazwaz

Publisher: Springer Science & Business Media

Published: 2011-11-24

Total Pages: 639

ISBN-13: 3642214495

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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 integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.