Continuous Symmetries Lie Algebras Differential Equations And Computer Algebra
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| Author | : W.-H. Steeb |
| Publisher | : World Scientific |
| Total Pages | : 380 |
| Release | : 1996 |
| Genre | : Science |
| ISBN | : 9789810228910 |
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.
| Author | : Willi-hans Steeb |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 472 |
| Release | : 2007-07-26 |
| Genre | : Science |
| ISBN | : 9813107014 |
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.
| Author | : W.-H. Steeb |
| Publisher | : |
| Total Pages | : |
| Release | : 1996 |
| Genre | : |
| ISBN | : 9789812839787 |
| Author | : Willi-hans Steeb |
| Publisher | : |
| Total Pages | : 472 |
| Release | : 2007 |
| Genre | : |
| ISBN | : 9789812770127 |
| Author | : Peter Ellsworth Hydon |
| Publisher | : Cambridge University Press |
| Total Pages | : 230 |
| Release | : 2000-01-28 |
| Genre | : Mathematics |
| ISBN | : 9780521497862 |
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 | : Decio Levi |
| Publisher | : American Mathematical Society, Centre de Recherches Mathématiques |
| Total Pages | : 520 |
| Release | : 2023-01-23 |
| Genre | : Mathematics |
| ISBN | : 0821843540 |
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.
| Author | : Norbert Euler |
| Publisher | : |
| Total Pages | : 340 |
| Release | : 1992 |
| Genre | : Continuous groups |
| ISBN | : |
| Author | : Fritz Schwarz |
| Publisher | : CRC Press |
| Total Pages | : 446 |
| Release | : 2007-10-02 |
| Genre | : Mathematics |
| ISBN | : 1584888903 |
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 | : Nail H. Ibragimov |
| Publisher | : CRC Press |
| Total Pages | : 554 |
| Release | : 2024-11-01 |
| Genre | : Mathematics |
| ISBN | : 1040294103 |
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.
| Author | : Jaime Gallardo-Alvarado |
| Publisher | : Academic Press |
| Total Pages | : 532 |
| Release | : 2022-06-18 |
| Genre | : Technology & Engineering |
| ISBN | : 0323953476 |
Theory of mechanisms is an applied science of mechanics that studies the relationship between geometry, mobility, topology, and relative motion between rigid bodies connected by geometric forms. Recently, knowledge in kinematics and mechanisms has considerably increased, causing a renovation in the methods of kinematic analysis. With the progress of the algebras of kinematics and the mathematical methods used in the optimal solution of polynomial equations, it has become possible to formulate and elegantly solve problems. Mechanisms: Kinematic Analysis and Applications in Robotics provides an updated approach to kinematic analysis methods and a review of the mobility criteria most used in planar and spatial mechanisms. Applications in the kinematic analysis of robot manipulators complement the material presented in the book, growing in importance when one recognizes that kinematics is a basic area in the control and modeling of robot manipulators. - Presents an organized review of general mathematical methods and classical concepts of the theory of mechanisms - Introduces methods approaching time derivatives of arbitrary vectors employing general approaches based on the vector angular velocity concept introduced by Kane and Levinson - Proposes a strategic approach not only in acceleration analysis but also to jerk analysis in an easy to understand and systematic way - Explains kinematic analysis of serial and parallel manipulators by means of the theory of screws
