Computer Algebra and Differential Equations
Computer Algebra and Differential Equations

Author: E. Tournier

Publisher:

Published: 1989

Total Pages: 240

ISBN-13:

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Ordinary differential equations have been studied by mathematicians for many years and the standard techniques have been either by series expansions or by numerical methods. Computer algebra has introduced an alternative means of treating differential equations and solving them more readily.**This volume assembles contributions from leading mathematicians in this growing field of computer algebra.

Involution
Involution

Author: Werner M. Seiler

Publisher: Springer Science & Business Media

Published: 2009-10-26

Total Pages: 663

ISBN-13: 3642012876

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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.

Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra
Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra

Author: W.-H. Steeb

Publisher: World Scientific

Published: 1996

Total Pages: 380

ISBN-13: 9789810228910

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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.

Ordinary Differential Equations and Linear Algebra
Ordinary Differential Equations and Linear Algebra

Author: Todd Kapitula

Publisher: SIAM

Published: 2015-11-17

Total Pages: 308

ISBN-13: 1611974097

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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.

Perturbation Methods, Bifurcation Theory and Computer Algebra
Perturbation Methods, Bifurcation Theory and Computer Algebra

Author: Richard H. Rand

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 254

ISBN-13: 1461210607

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Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.

Computer Algebra in Quantum Field Theory
Computer Algebra in Quantum Field Theory

Author: Carsten Schneider

Publisher: Springer Science & Business Media

Published: 2013-10-05

Total Pages: 422

ISBN-13: 3709116163

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The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Introduction to Linear Algebra and Differential Equations
Introduction to Linear Algebra and Differential Equations

Author: John W. Dettman

Publisher: Courier Corporation

Published: 2012-10-05

Total Pages: 442

ISBN-13: 0486158314

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Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Some Tapas of Computer Algebra
Some Tapas of Computer Algebra

Author: Arjeh M. Cohen

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 365

ISBN-13: 3662038919

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This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

The Center and Cyclicity Problems
The Center and Cyclicity Problems

Author: Valery Romanovski

Publisher: Springer Science & Business Media

Published: 2009-04-29

Total Pages: 336

ISBN-13: 0817647279

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Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.