Elements of Symmetry Analysis

Gerd Baumann
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Gerd Baumann: University of Ulm, Department of Mathematical Physics

Chapter 2 in Symmetry Analysis of Differential Equations with Mathematica®, 2000, pp 6-36 from Springer

Abstract: Abstract At the beginning we will introduce some basic concepts which will be important throughout the whole book. First, we define the general properties of a group. These group properties are extended to Lie groups in the next step. The related Lie algebra connected with the Lie group is then introduced. We also introduce the notion of a vector field which is closely related to Lie algebras. We present all these highly abstract terms in connection with Mathematica. Different examples serve to vitalize the mathematical expressions. This chapter serves also to describe the first steps in Mathematica and introduce its notation. The elementary representation of mathematical expressions in Mathematica provides the connection between mathematics and computer algebra.

Keywords: Structure Constant; Symmetry Analysis; Function Rotation; Infinitesimal Symmetry; Infinite Dimensional Vector Space (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2110-4_2

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DOI: 10.1007/978-1-4612-2110-4_2

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