MAT 616E - Intro.to the Lie Gr. An. of D.E.

Course Objectives

1. To introduce Lie theory of differential equations,
2. To introduce the necessary basic concepts of one parameter Lie groups of transformations
and Lie algebras,
3. To show how group transformations are used to construct solutions and how to find group
transformations leaving second order ordinary differential equations invariant,
4. To introduce the connection between conservation laws and the invariance of differential
equations under Lie groups of transformations,
5. The concept of Lie groups of transformations is to generalize further to include nonlocal
symmetries of differential equations.

Course Description

Lie theory of differential equations, one parameter transformation groups, integration of second order ordinary differential equations, group classification of second order ordinary differential equations, invariant solutions, generalizations, Lie-Backlund transformation groups, Noether type conservation theorems, nonlocal symmetry generators via Backlund transformations.