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Continuous Symmetries Lie Algebras And Differential Equations
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Book Synopsis Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra by : W-H Steeb
Download or read book Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra written by W-H Steeb and published by World Scientific Publishing Company. This book was released on 1996-09-30 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It is suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics. The book provides an application-orientated text that is reasonably self-contained. A large number of worked examples have been included to help readers working independently of a teacher. The advance of algebraic computation has made it possible to write programs for the tedious calculations in this research field, and thus the book also makes a survey of computer algebra packages.
Book Synopsis Continuous Symmetries, Lie Algebras and Differential Equations by : Norbert Euler
Download or read book Continuous Symmetries, Lie Algebras and Differential Equations written by Norbert Euler and published by . This book was released on 1992 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra by : W.-H. Steeb
Download or read book Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra written by W.-H. Steeb and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition). by : Willi-hans Steeb
Download or read book Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition). written by Willi-hans Steeb and published by . This book was released on 2007 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra by : W.-H. Steeb
Download or read book Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra written by W.-H. Steeb and published by World Scientific. This book was released on 1996 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It is suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics.The book provides an application-orientated text that is reasonably self-contained. A large number of worked examples have been included to help readers working independently of a teacher. The advance of algebraic computation has made it possible to write programs for the tedious calculations in this research field, and thus the book also makes a survey of computer algebra packages.
Book Synopsis Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition) by : Willi-hans Steeb
Download or read book Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition) written by Willi-hans Steeb and published by World Scientific Publishing Company. This book was released on 2007-07-26 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory.Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation.Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painlevé equations.
Book Synopsis Transformation Groups and Lie Algebras by : Nail H Ibragimov
Download or read book Transformation Groups and Lie Algebras written by Nail H Ibragimov and published by World Scientific Publishing Company. This book was released on 2013-05-20 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Book Synopsis Symmetry Methods for Differential Equations by : Peter Ellsworth Hydon
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.
Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
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.
Book Synopsis Lie Group Mathematics by : Edited by: Kisak
Download or read book Lie Group Mathematics written by Edited by: Kisak and published by CreateSpace. This book was released on 2015-07-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. Lie groups provide a natural framework for analyzing the continuous symmetries of differential equations in much the same way as permutation groups are used in Galois theory for analyzing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.
Book Synopsis Lie Groups: Quantization (Volume 2) by : Thomas Fleming
Download or read book Lie Groups: Quantization (Volume 2) written by Thomas Fleming and published by States Academic Press. This book was released on 2021-11-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A group is a collection of symmetries of any object, and each group is the symmetries of some object. Lie groups are groups whose elements are organized continuously and smoothly, making them differentiable manifolds. This is in contrast to discrete groups, where the elements are separated. A Lie group is a continuous group whose elements are described by several real parameters. As such, they provide a natural model for the concept of continuous symmetry, such as rotational symmetry in three dimensions. The real motivation for introducing Lie groups was to model the continuous symmetries of differential equations. They are extensively used in various parts of contemporary mathematics and physics. Lie groups also play a huge role in modern geometry on many different levels. This book outlines the processes and applications of Lie groups in detail. It covers some existent theories and innovative concepts revolving around this field. With state-of-the-art inputs by acclaimed experts of this field, this book targets students and professionals.
Book Synopsis Lie Symmetry Analysis of Fractional Differential Equations by : Mir Sajjad Hashemi
Download or read book Lie Symmetry Analysis of Fractional Differential Equations written by Mir Sajjad Hashemi and published by CRC Press. This book was released on 2020-07-09 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
Author :Decio Levi Publisher :American Mathematical Society, Centre de Recherches Mathématiques ISBN 13 :0821843540 Total Pages :520 pages Book Rating :4.8/5 (218 download)
Book Synopsis Continuous Symmetries and Integrability of Discrete Equations by : Decio Levi
Download or read book Continuous Symmetries and Integrability of Discrete Equations written by Decio Levi and published by American Mathematical Society, Centre de Recherches Mathématiques. This book was released on 2023-01-23 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
Book Synopsis Differential Equations by : Hans Stephani
Download or read book Differential Equations written by Hans Stephani and published by Cambridge University Press. This book was released on 1989 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and application of the solution to differential equations using symmetries, a technique of great value in mathematics and the physical sciences. It will apply to graduate students in physics, applied mathematics, and engineering.
Download or read book Dynamical Symmetry written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical Symmetry by : Carl Wulfman
Download or read book Dynamical Symmetry written by Carl Wulfman and published by World Scientific. This book was released on 2011 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Book Synopsis Applications of Lie Groups to Difference Equations by : Vladimir Dorodnitsyn
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
