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Elements of Symmetry Analysis

In: Symmetry Analysis of Differential Equations with Mathematica®

Author

Listed:
  • Gerd Baumann

    (University of Ulm, Department of Mathematical Physics)

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.

Suggested Citation

  • Gerd Baumann, 2000. "Elements of Symmetry Analysis," Springer Books, in: Symmetry Analysis of Differential Equations with Mathematica®, chapter 2, pages 6-36, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2110-4_2
    DOI: 10.1007/978-1-4612-2110-4_2
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