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Author: G. Milton Wing Publisher: SIAM ISBN: 0898712637 Category : Mathematics Languages : en Pages : 141
Book Description
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.
Author: G. Milton Wing Publisher: SIAM ISBN: 0898712637 Category : Mathematics Languages : en Pages : 141
Book Description
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.
Author: George Milton Wing Publisher: SIAM ISBN: 9781611971675 Category : Integral equations Languages : en Pages : 149
Book Description
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. The book emphasizes understanding, while deliberately avoiding special methods of highly limited application. Special features: all problems illustrate important topics covered in the text; the subject is explained using a fairly non-rigorous approach to introduce any mathematics not commonly understood by the intended audience; designed for self-study, but can also be used as a text.
Author: A. V. Bitsadze Publisher: World Scientific ISBN: 9789810222635 Category : Mathematics Languages : en Pages : 286
Book Description
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: Abdul-Majid Wazwaz Publisher: World Scientific ISBN: 9789810231019 Category : Mathematics Languages : en Pages : 228
Book Description
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.
Author: Abdul-majid Wazwaz Publisher: World Scientific Publishing Company ISBN: 9814675148 Category : Mathematics Languages : en Pages : 327
Book Description
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.
Author: Jirō Kondō Publisher: Oxford University Press, USA ISBN: Category : Mathematics Languages : en Pages : 484
Book Description
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.
Author: Abdul J. Jerri Publisher: John Wiley & Sons ISBN: 9780471317340 Category : Mathematics Languages : en Pages : 458
Book Description
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.
Author: Prem Kythe Publisher: Springer Science & Business Media ISBN: 1461201012 Category : Mathematics Languages : en Pages : 525
Book Description
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 problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.
Author: I. G. Petrovskii Publisher: Courier Corporation ISBN: 9780486697567 Category : Mathematics Languages : en Pages : 142
Book Description
Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Author: G. Milton Wing
Author: G. Milton Wing
Author: George Milton Wing
Author: A. V. Bitsadze
Author: Abdul-Majid Wazwaz
Author: Abdul-majid Wazwaz
Author: Jirō Kondō
Author: Abdul J. Jerri
Author: Maxime Bôcher
Author: Prem Kythe
Author: I. G. Petrovskii