Level: Ms.C.

Course Syllabus:

1. Geometric foundations
2. Lie groups
3. Representation theory
4. Jets and contact transformations
5. Differential invariants
6. Symmetries of differential equations
7. Symmetries of variational problems
 

Texts:

· Olver, P.J., Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, New York, 1995.
· Olver, P.J., Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York, 1993.
· Bluman, G.W., and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
· Bluman, G.W. and Anco, S.C., Symmetry and Integration Methods for Differential Equations, Second Edition, Springer-Verlag, New York, 2002.
· Stephani, H., Differential Equations: Their Solutions Using Symmetries, Cambridge Univ. Press, Cambridge, 1989.
· Hydon, P.E., Symmetry Methods for Differential Equations: A Beginner's Guide, Cambridge Univ. Press, Cambridge, 2000.
 

Power Points:

1. Introduction
2. Geometric foundations
3. Lie groups
4. Representation theory
5. Jets and contact transformations
6. Differential invariants
7. Symmetries of differential equations
8. Symmetries of variational problems