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Elementary Lie Group Analysis And Ordinary Differential Equations

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Elementary Lie Group Analysis and Ordinary Differential Equations

Elementary Lie Group Analysis and Ordinary Differential Equations Book
Author : N. H. Ibragimov,Nailʹ Khaĭrullovich Ibragimov
Publisher : John Wiley & Sons
Release : 1999-05-04
ISBN : 0987650XXX
File Size : 55,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.

Elementary Lie Group Analysis and Ordinary Differential Equations

Elementary Lie Group Analysis and Ordinary Differential Equations Book
Author : Nailʹ Khaĭrullovich Ibragimov
Publisher : Unknown
Release : 1999
ISBN : 0987650XXX
File Size : 52,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Download Elementary Lie Group Analysis and Ordinary Differential Equations book written by Nailʹ Khaĭrullovich Ibragimov and published by with total hardcover pages 347 . Available in PDF, EPUB, and Kindle, read book directly with any devices anywhere and anytime.

Symmetry Analysis of Differential Equations

Symmetry Analysis of Differential Equations Book
Author : Daniel J. Arrigo
Publisher : John Wiley & Sons
Release : 2015-01-07
ISBN : 1118721446
File Size : 34,9 Mb
Language : En, Es, Fr and De

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Book Summary :

A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.

Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations Book
Author : Peter J. Olver
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1468402749
File Size : 28,8 Mb
Language : En, Es, Fr and De

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Book Summary :

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Algorithmic Lie Theory for Solving Ordinary Differential Equations

Algorithmic Lie Theory for Solving Ordinary Differential Equations Book
Author : Fritz Schwarz
Publisher : CRC Press
Release : 2007-10-02
ISBN : 9781584888901
File Size : 36,8 Mb
Language : En, Es, Fr and De

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Book Summary :

Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble

Applications of Lie Group Analysis in Geophysical Fluid Dynamics

Applications of Lie Group Analysis in Geophysical Fluid Dynamics Book
Author : Nail? Kha?rullovich Ibragimov,R. N. Ibragimov
Publisher : World Scientific
Release : 2011
ISBN : 9814340464
File Size : 26,5 Mb
Language : En, Es, Fr and De

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Book Summary :

Quickly learn essential inventor tools and techniques This full-color Autodesk Official Press guide will help you quickly learn the powerful manufacturing software′s core features and functions. Thom Tremblay, an Autodesk Certified Instructor, uses concise, straightforward explanations and real-world, hands-on exercises to help you become productive with Inventor. Full-color screenshots illustrate tutorial steps, and chapters conclude with a related and more open-ended project to further reinforce the chapter′s lessons. Based on the very real-world task of designing tools and a toolbox to house them, the book demonstrates creating 2D drawings from 3D data, modeling parts, combining parts into assemblies, annotating drawings, using advanced assembly tools, working with sheet metal, presenting designs, and more. Full-color screenshots illustrate the steps, and additional files are available for download so you can compare your results with those of professionals. You′ll also get information to help you prepare for the Inventor certification exams. Introduces new users to the software with real-world projects, hands-on tutorials, and full-color illustrations Begins each chapter with a quick discussion of concepts and learning goals and then moves into approachable, hands-on exercises Covers the interface and foundational concepts, modeling parts, combining them into assemblies building with the frame generator, using weldments Includes material to help you prepare for the Inventor certification exams Autodesk Inventor 2014 Essentials provides the information you need to quickly become proficient with the powerful 3D mechanical design software.

Symmetries of Integro Differential Equations

Symmetries of Integro Differential Equations Book
Author : Sergey V. Meleshko,Yurii N. Grigoriev,N. Kh. Ibragimov,Vladimir F. Kovalev
Publisher : Springer Science & Business Media
Release : 2010-07-12
ISBN : 9048137969
File Size : 21,9 Mb
Language : En, Es, Fr and De

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Book Summary :

This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.

Handbook of Ordinary Differential Equations

Handbook of Ordinary Differential Equations Book
Author : Andrei D. Polyanin,Valentin F. Zaitsev
Publisher : CRC Press
Release : 2017-11-15
ISBN : 1351643916
File Size : 27,6 Mb
Language : En, Es, Fr and De

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Book Summary :

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.