Elementary Lie Group Analysis And Ordinary Differential Equations
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Elementary Lie Group Analysis And Ordinary Differential Equations
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Author : Nailʹ Khaĭrullovich Ibragimov
language : en
Publisher:
Release Date : 1999
Elementary Lie Group Analysis And Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential equations categories.
Elementary Lie Group Analysis And Ordinary Differential Equations
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Author : Nailʹ Khaĭrullovich Ibragimov
language : en
Publisher: Wiley-Blackwell
Release Date : 1999-05-04
Elementary Lie Group Analysis And Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and has been published by Wiley-Blackwell this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-04 with Mathematics categories.
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.
Group Analysis Of Differential Equations
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Author : L. V. Ovsiannikov
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Group Analysis Of Differential Equations written by L. V. Ovsiannikov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
Applications Of Lie Groups To Differential Equations
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Author : Peter J. Olver
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Lie Groups To Differential Equations written by Peter J. Olver and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Symmetry Methods For Differential Equations
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Author : Peter E. Hydon
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Symmetry Methods For Differential Equations written by Peter E. Hydon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and integrating factors.
Stratified Lie Groups And Potential Theory For Their Sub Laplacians
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Author : Andrea Bonfiglioli
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-24
Stratified Lie Groups And Potential Theory For Their Sub Laplacians written by Andrea Bonfiglioli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-24 with Mathematics categories.
This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
Handbook Of Ordinary Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2017-11-15
Handbook Of Ordinary Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
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.
Practical Course In Differential Equations And Mathematical Modelling A Classical And New Methods Nonlinear Mathematical Models Symmetry And Invariance Principles
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Author : Nail H Ibragimov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-11-19
Practical Course In Differential Equations And Mathematical Modelling A Classical And New Methods Nonlinear Mathematical Models Symmetry And Invariance Principles written by Nail H Ibragimov and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-19 with Mathematics categories.
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
Symmetries And Applications Of Differential Equations
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2021-12-14
Symmetries And Applications Of Differential Equations written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939–2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.