CRC Handbook of Lie Group Analysis of Differential Equations

Author: Nail H. Ibragimov

Publisher: CRC Press

ISBN: 9780849394195

Category: Mathematics

Page: 560

View: 5889

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Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
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Handbook of Nonlinear Partial Differential Equations

Author: Andrei D. Polyanin,Valentin F. Zaitsev

Publisher: CRC Press

ISBN: 1135440816

Category: Mathematics

Page: 840

View: 1419

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The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
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Handbook of Differential Equations: Ordinary Differential Equations

Author: A. Canada,P. Drabek,A. Fonda

Publisher: Elsevier

ISBN: 9780080463810

Category: Mathematics

Page: 752

View: 9533

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This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
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Handbook of Differential Equations

Author: Daniel Zwillinger

Publisher: Gulf Professional Publishing

ISBN: 9780127843964

Category: Mathematics

Page: 801

View: 434

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This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. * For nearly every technique, the book and CD-ROM provide: * The types of equations to which the method is applicable * The idea behind the method * The procedure for carrying out the method * At least one simple example of the method * Any cautions that should be exercised * Notes for more advanced users * References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
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Handbook of Differential Equations: Evolutionary Equations

Author: C.M. Dafermos,Eduard Feireisl

Publisher: Elsevier

ISBN: 9780080461380

Category: Mathematics

Page: 676

View: 5457

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The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
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Handbook of Differential Equations: Ordinary Differential Equations

Author: Flaviano Battelli,Michal Fečkan

Publisher: Elsevier

ISBN: 9780080559469

Category: Mathematics

Page: 400

View: 3522

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This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. * Covers a variety of problems in ordinary differential equations * Pure mathematical and real-world applications * Written for mathematicians and scientists of many related fields
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Handbook of First-Order Partial Differential Equations

Author: Andrei D. Polyanin,Valentin F. Zaitsev,Alain Moussiaux

Publisher: CRC Press

ISBN: 9780415272674

Category: Mathematics

Page: 520

View: 1775

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This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding types of differential equations are outlined and specific examples are considered. It presents equations and their applications, including differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. This handbook is an essential reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences.
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Handbook of Differential Equations: Stationary Partial Differential Equations

Author: Michel Chipot

Publisher: Elsevier

ISBN: 9780080560595

Category: Mathematics

Page: 624

View: 1704

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This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems. * Collection of self-contained, state-of-the-art surveys * Written by well-known experts in the field * Informs and updates on all the latest developments
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Handbook of Linear Partial Differential Equations for Engineers and Scientists

Author: Andrei D. Polyanin

Publisher: CRC Press

ISBN: 1420035320

Category: Mathematics

Page: 800

View: 9122

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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 constant and variable coefficients New exact solutions to linear equations and boundary value problems Equations and problems of general form that depend on arbitrary functions Formulas for constructing solutions to nonhomogeneous boundary value problems Second- and higher-order equations and boundary value problems An introductory section outlines the basic definitions, equations, problems, and methods of mathematical physics. It also provides useful formulas for expressing solutions to boundary value problems of general form in terms of the Green's function. Two supplements at the end of the book furnish more tools and information: Supplement A lists the properties of common special functions, including the gamma, Bessel, degenerate hypergeometric, and Mathieu functions, and Supplement B describes the methods of generalized and functional separation of variables for nonlinear partial differential equations.
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Handbook of Exact Solutions for Ordinary Differential Equations

Author: Valentin F. Zaitsev,Andrei D. Polyanin

Publisher: CRC Press

ISBN: 1420035339

Category: Mathematics

Page: 816

View: 3976

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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 handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including: An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations The addition of solutions to more than 1200 nonlinear equations An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily Expansion of the supplement on special functions This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.
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