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| Author | : E. Tournier |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1994-03-03 |
| Genre | : Mathematics |
| ISBN | : 9780521447577 |
Selected papers from the Computer Algebra and Differential Equations meeting held in France in June 1992.
| Author | : Werner M. Seiler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 663 |
| Release | : 2009-10-26 |
| Genre | : Mathematics |
| ISBN | : 3642012876 |
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.
| 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 | : Michael F. Singer |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : |
Teaches computer algebra users about up-to-date research developments in differential equations, with selected papers from CADE 1990, held at Cornell University. Featuring US and European research figures, this book demonstrates scientific computing applications.
| 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 | : Dongming Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 388 |
| Release | : 2005-08-15 |
| Genre | : Mathematics |
| ISBN | : 9783764373689 |
This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
| Author | : Todd Kapitula |
| Publisher | : SIAM |
| Total Pages | : 308 |
| Release | : 2015-11-17 |
| Genre | : Mathematics |
| ISBN | : 1611974097 |
Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system. Ordinary Differential Equations and Linear Algebra: A Systems Approach systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.
| Author | : Johannes Grabmeier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 656 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642558267 |
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 305 |
| Release | : 1998-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971392 |
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.
| Author | : Matthew R. Boelkins |
| Publisher | : Oxford University Press |
| Total Pages | : 573 |
| Release | : 2009-11-05 |
| Genre | : Mathematics |
| ISBN | : 0199736669 |
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. This chapter enables students to quickly learn enough linear algebra to appreciate the structure of solutions to linear differential equations and systems thereof in subsequent study and to apply these ideas regularly. The book offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The following chapter develops the mathematics necessary to solve these problems and explores related topics further. Even in more theoretical developments, we use an example-first style to build intuition and understanding before stating or proving general results. Over 100 figures provide visual demonstration of key ideas; the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and support students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications. Errata sheet available at: www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf
