Level: Ms.C.

Course Syllabus:

· Equivalence of Coframes
· Formulation of Equivalence Problems
· Cartan's Equivalence Method
· Involution
· Prolongation of Equivalence Problems
· Differential Systems
· Frobenius' Theorem
· The Cartan-Khler Existence Theorem
 

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:

8. Equivalence of Coframes
9. Formulation of Equivalence Problems
10. Cartan's Equivalence Method
11. Involution
12. Prolongation of Equivalence Problems
13. Differential Systems
14. Frobenius' Theorem
15. The Cartan-Khler Existence Theorem