Polyanin, AlexanderV. Includes bibliographical references p. ISBN alk. Integral equations—Handbooks, manuals, etc. Aleksandr Vladimirovich II. Reprinted material is quoted withpermission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publishreliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materialsor for the consequences of their use.
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A lotof new exact solutions to linear and nonlinear equations are included. Special attention is paid toequations of general form, which depend on arbitrary functions.
Totally, the number ofequations described is an order of magnitude greater than in any other book available. A number of integral equations are considered which are encountered in various fields ofmechanics and theoretical physics elasticity, plasticity, hydrodynamics, heat and mass transfer,electrodynamics, etc. The second part of the book presents exact, approximate analytical and numerical methodsfor solving linear and nonlinear integral equations.
Apart from the classical methods, some newmethods are also described. Each section provides examples of applications to specific equations. The handbook has no analogs in the world literature and is intended for a wide audienceof researchers, college and university teachers, engineers, and students in the various fields ofmathematics, mechanics, physics, chemistry, and queuing theory.
FOREWORDIntegral equations are encountered in various fields of science and numerous applications inelasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory,electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, medicine, etc. Exact closed-form solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of naturalscience.
Lots of equations of physics, chemistry and biology contain functions or parameters whichare obtained from experiments and hence are not strictly fixed. Therefore, it is expedient to choosethe structure of these functions so that it would be easier to analyze and solve the equation.
As apossible selection criterion, one may adopt the requirement that the model integral equation admit asolution in a closed form. Exact solutions can be used to verify the consistency and estimate errorsof various numerical, asymptotic, and approximate methods. More than integral equations and their solutions are given in the first part of the book Chapters 1—6.
A lot of new exact solutions to linear and nonlinear equations are included. Specialattention is paid to equations of general form, which depend on arbitrary functions. Totally, the number of equationsdescribed in this handbook is an order of magnitude greater than in any other book currentlyavailable.
The second part of the book Chapters 7—14 presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods,some new methods are also described. Some sections may be used by lecturers of collegesand universities as a basis for courses on integral equations and mathematical physics equations forgraduate and postgraduate students. For the convenience of a wide audience with different mathematical backgrounds, the authorstried to do their best, wherever possible, to avoid special terminology.
Therefore, some of the methodsare outlined in a schematic and somewhat simplified manner, with necessary references made tobooks where these methods are considered in more detail.
For some nonlinear equations, onlysolutions of the simplest form are given. The book does not cover two-, three- and multidimensionalintegral equations. The handbook consists of chapters, sections and subsections. Equations and formulas arenumbered separately in each section. The equations within a section are arranged in increasingorder of complexity. The extensive table of contents provides rapid access to the desired equations. The first and second parts of the book, just as many sections, were written so that they could beread independently from each other.
This allows the reader to quickly get to the heart of the matter. We would like to express our deep gratitude to Rolf Sulanke and Alexei Zhurov for fruitfuldiscussions and valuable remarks.
We also appreciate the help of Vladimir Nazaikinskii andAlexander Shtern in translating the second part of this book, and are thankful to Inna Shingareva forher assistance in preparing the camera-ready copy of the book. The authors hope that the handbook will prove helpful for a wide audience of researchers,college and university teachers, engineers, and students in various fields of mathematics, mechanics,physics, chemistry, biology, economics, and engineering sciences. In Chapters 1—11 and 14, in the original integral equations, the independent variable isdenoted by x, the integration variable by t, and the unknown function by y y x.
For a function of one variable f f x , we use the following notation for the derivatives:fx df,dx fxxd2 f,dx2 fxxx d3 f,dx3 fxxxx d4 f,dx4andfx n dn ffor n 5. In some cases, we use the operator notation f x g x , which is defined recursively bydx n n—1 dddf x f x g x f x g x. It is indicated in the beginning of Chapters 1—6 that f f x , g g x , K K x , etc.
The notations Re z and Im z stand, respectively, for the real and the imaginary part of acomplex quantity z. In the first part of the book Chapters 1—6 when referencing a particular equation, we use anotation like 2. To highlight portions of the text, the following symbols are used in the book: indicates important information pertaining to a group of equations Chapters 1—6 ;indicates the literature used in the preparation of the text in specific equations Chapters 1—6 orsections Chapters 7— Polyanin, D.
He receivedhis Ph. Since , A. Professor Polyanin has made important contributions to developingnew exact and approximate analytical methods of the theory of differential equations, mathematical physics, integral equations, engineeringmathematics, nonlinear mechanics, theory of heat and mass transfer,and chemical hydrodynamics.
He obtained exact solutions for several thousands of ordinary differential, partial differential, and integralequations. Hispublications also include more than research papers and three patents. One of his most significantbooks is A.
Polyanin and V. In , A. Alexander V. Manzhirov, D. Manzhirov attended apostgraduate course at the Moscow Institute of Civil Engineering. Hereceived his Ph. Singular Integral Equations. 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.
Multiscale Methods for Fredholm Integral Equations. Authors: Zhongying Chen, Charles A. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Handbook of Integral Equations by Andrei D. Polyanin ,. Alexander V. Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine.
Exact closed-form solutions of in Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine.
Exact closed-form solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science.
Equations of physics, chemistry, and biology contain functions or parameters obtained from experiments - hence, they are not strictly fixed. Therefore, it is expedient to choose the structure of these functions for more easily analyzing and solving the equation. As a possible selection criterion, one may adopt the requirement that the model integral equation admit a solution in a closed form.
Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods. The first part of Handbook of Integral Equations: Contains more than 2, integral equations and their solutions Includes many new exact solutions to linear and nonlinear equations Addresses equations of general form, which depend on arbitrary functions Other equations contain one or more free parameters the book actually deals with families of integral equations ; the reader has the option to fix these parameters.
The second part of the book - chapters 7 through 14 - presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods, the text also describes some new methods. When selecting the material, the authors emphasize practical aspects of the matter, specifically for methods that allow an effective "constructing" of the solution.
Each section provides examples of applicatio Get A Copy. Hardcover , pages. More Details Original Title. Other Editions 5. Friend Reviews.
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