Develop computer algebraic skills and calculate symmetry algebras with the included software!
With descriptions of Volumes 2 and 3
Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa
Volume 1, Symmetries, Exact Solutions, and Conservation Laws
Volume 2, Applications in Engineering and Physical Sciences
Volume 3, New Trends in Theoretical Developments and Computa tional Methods
The first part of Volume 1 systematizes the relevant results of Lie and natural generalizations, guides the reader through all group theoretical methods (with a minimum number of theoretical constructions), and introduces the skills necessary to apply the results and methods in Part B to new problems. Part B is devoted to the group classification and characterization of differential equations. It also tabulates their Lie point and contact symmetries, Lie-Bdcklund and nonlocal symmetries, Bdcklund transformations, exact solutions, and conservation laws. Part C addresses numerical considerations.
Volume 1, Symmetries, Exact Solutions, and Conservation Laws
Catalog number 4488WGBA
October 1993, 448 pp., ISBN: 0-8493-4488-3
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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 leading world experts in the field, this up-to-date source book covers topics such as Lie-Bdcklund, 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.
Minimum of 2.5 MB of RAM (4 MB is recommended), 3.25" disk drive.
Volume 3 - New Trends in Theore tical Developments and Computational Methods
Catalog number 9419WGBA
October 1995, 560 pp., 3.25" diskette, ISBN: 0-8493-9419-8
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Volume 2 is divided into three parts. Part A focuses on relevant definitions, main algorithms, group classification schemes for partial differential equations, and multifaceted possibilities offered by Lie group theoretic philosophy. Part B tabulates symmetry groups and solutions for linear equations of mathematical physics, classical field theory, viscous and non-Newtonian fluids, boundary layer problems, Earth sciences, elasticity, plasticity, plasma theory, and nonlinear optics and acoustics. The last part offers an English translation of Sophus Lie's fundamental paper on the group classification and invariant solutions of linear second-order equations with two independent variables.
Volume 2, Applications in Engin eering and Physical Sciences
Catalog number 2864WGBA
November 1994, 576 pp., ISBN: 0-8493-2864-0
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Catalog 4442WCRX
Differential Equations and Group Methods for Scientists and Engineers by Hill
Catalog 7373WCRX
Computational Mathematics in Engineering and Applied Science by Schiesser