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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.
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,
College 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.
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-B lund, 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 the modern group analysis and addresses
issues to both beginners and experienced researchers in the
application of Lie group methods.
This book is based on the experience of teaching the subject by the
author in Russia, France, South Africa and Sweden. The author
provides students and teachers with an easy to follow textbook
spanning a variety of topics on tensors, Riemannian geometry and
geometric approach to partial differential equations. Application
of approximate transformation groups to the equations of general
relativity in the de Sitter space simplifies the subject
significantly.
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-BAcklund,
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.
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-B?cklund,
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 the modern group analysis and
addresses issues to both beginners and experienced researchers in
the application of Lie group methods.
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