Handbook Of Integral Equations
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| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 1143 |
| Release | : 2008-02-12 |
| Genre | : Mathematics |
| ISBN | : 0203881052 |
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 816 |
| Release | : 1998-03-31 |
| Genre | : Mathematics |
| ISBN | : 9780849328763 |
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 2,100 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
| Author | : Alan Jeffrey |
| Publisher | : Elsevier |
| Total Pages | : 449 |
| Release | : 2014-05-19 |
| Genre | : Mathematics |
| ISBN | : 1483295141 |
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse. Special thumb-tab index throughout the book for ease of use Answers are keyed to the type of problem they solve Formulas are provided for problems across the entire spectrum of Mathematics All equations are sent from a computer-checked source code Companion to Gradshteyn: Table of Integrals, Series, and Products, Fifth Edition The following features make the Handbook a Better Value than its Competition: Less expensive More comprehensive Equations are computer-validated with Scientific WorkPlace(tm) and Mathematica(r) Superior quality from one of the most respected names in scientific and technical publishing Offers unique thumb-tab indexing throughout the book which makes finding answers quick and easy
| Author | : Peter J. Collins |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 387 |
| Release | : 2006-08-03 |
| Genre | : Mathematics |
| ISBN | : 0198533829 |
Differential & integral equations involve important mathematical techniques, & as such will be encountered by mathematicians, & physical & social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- & second- order ordinary & partial differential equations.
| Author | : Valentin F. Zaitsev |
| Publisher | : CRC Press |
| Total Pages | : 815 |
| Release | : 2002-10-28 |
| Genre | : Mathematics |
| ISBN | : 1420035339 |
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 800 |
| Release | : 2001-11-28 |
| Genre | : Mathematics |
| ISBN | : 1420035320 |
Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with
| Author | : Prem K. Kythe |
| Publisher | : CRC Press |
| Total Pages | : 622 |
| Release | : 2004-12-20 |
| Genre | : Mathematics |
| ISBN | : 1135437521 |
During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended. The importance of numerical integration in so many areas of science and technology has made a practical, up-to-date reference on this subject long overdue. The Handbook of Computational Methods for Integration discusses quadrature rules for finite and infinite range integrals and their applications in differential and integral equations, Fourier integrals and transforms, Hartley transforms, fast Fourier and Hartley transforms, Laplace transforms and wavelets. The practical, applied perspective of this book makes it unique among the many theoretical books on numerical integration and quadrature. It will be a welcomed addition to the libraries of applied mathematicians, scientists, and engineers in virtually every discipline.
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 1542 |
| Release | : 2006-11-27 |
| Genre | : Mathematics |
| ISBN | : 1420010514 |
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
| Author | : Ram P. Kanwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 327 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 1461207657 |
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 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 date. I wish to thank Professor B.K. Sachdeva who has checked the revised man uscript and has suggested many improvements. Last but not least, I am grateful to the editor and staff of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well. For example, for a ~ s ~ b; a :( t :( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) + ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the function g(s) is the unknown function and all the other functions are known, are integral equations. These functions may be complex-valued functions of the real variables s and t.
| Author | : I.K. Lifanov |
| Publisher | : CRC Press |
| Total Pages | : 416 |
| Release | : 2003-12-29 |
| Genre | : Mathematics |
| ISBN | : 0203402162 |
A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co
