Applications Of Lies Theory Of Ordinary And Partial Differential Equations

Author : L Dresner
Publisher : CRC Press
ISBN 13 : 9781420050783
Total Pages : 242 pages
Book Rating : 4.88/5 ( download)

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Download or read book Applications of Lie's Theory of Ordinary and Partial Differential Equations written by L Dresner and published by CRC Press. This book was released on 1998-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 1468402749
Total Pages : 524 pages
Book Rating : 4.42/5 ( download)

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Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Abraham Cohen
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.89/5 ( download)

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Download or read book An Introduction to the Lie Theory of One-parameter Groups written by Abraham Cohen and published by . This book was released on 1911 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : E. C. Zachmanoglou
Publisher : Courier Corporation
ISBN 13 : 048613217X
Total Pages : 432 pages
Book Rating : 4.74/5 ( download)

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Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Author : Fritz Schwarz
Publisher : CRC Press
ISBN 13 : 9781584888901
Total Pages : 448 pages
Book Rating : 4.03/5 ( download)

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Download or read book Algorithmic Lie Theory for Solving Ordinary Differential Equations written by Fritz Schwarz and published by CRC Press. This book was released on 2007-10-02 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Vladimir Dorodnitsyn
Publisher : CRC Press
ISBN 13 : 9781420083101
Total Pages : 344 pages
Book Rating : 4.04/5 ( download)

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Download or read book Applications of Lie Groups to Difference Equations written by Vladimir Dorodnitsyn and published by CRC Press. This book was released on 2010-12-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods

Author : Peter Ellsworth Hydon
Publisher : Cambridge University Press
ISBN 13 : 9780521497862
Total Pages : 230 pages
Book Rating : 4.68/5 ( download)

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Download or read book Symmetry Methods for Differential Equations written by Peter Ellsworth Hydon and published by Cambridge University Press. This book was released on 2000-01-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.

Author : Nailʹ Khaĭrullovich Ibragimov
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.22/5 ( download)

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Download or read book Elementary Lie Group Analysis and Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and published by John Wiley & Sons. This book was released on 1999-05-04 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Abraham Cohen
Publisher : Forgotten Books
ISBN 13 : 9781331128397
Total Pages : 260 pages
Book Rating : 4.90/5 ( download)

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Download or read book An Introduction to the Lie Theory of One-Parameter Groups written by Abraham Cohen and published by Forgotten Books. This book was released on 2015-06-24 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from An Introduction to the Lie Theory of One-Parameter Groups: With Applications to the Solution of Differential Equations The object of this book is to present in an elementary manner, in English, an introduction to Lie's theory of one-parameter groups, with special reference to its application to the solution of differential equations invariant under such groups. The treatment is sufficiently elementary to be appreciated, under proper supervision, by undergraduates in their senior year as well as by graduates during their first year of study. While a knowledge of the elementary theory of differential equations is not absolutely essential for understanding the subject matter of this book, frequent references being made to places where necessary information can be obtained, it would seem preferable to approach for the first time the problem of classifying and solving differential equations by direct, even if miscellaneous, methods to doing so by the elegant general methods of Lie; and this book is intended primarily for those who have some acquaintance with the elementary theory. To such persons it should prove of great interest and undoubted practical value. An attempt has been made throughout the work to emphasize the role played by the Lie theory in unifying the elementary theory of differential equations, by bringing under a relatively small number of heads the various known classes of differential equations invariant under continuous groups, and the methods for their solution. Special attention may be called to the lists of invariant differential equations and applications in §§ 19, 28, 30; while the two tables in the appendix include most of the ordinary differential equations likely to be met. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Michael Shearer
Publisher : Princeton University Press
ISBN 13 : 0691161291
Total Pages : 286 pages
Book Rating : 4.97/5 ( download)

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Download or read book Partial Differential Equations written by Michael Shearer and published by Princeton University Press. This book was released on 2015-03-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors