Spring semester 2010, Topics in Analysis  (Graduate Course)

Exterior Algebra and Partial Differential Equations

In this course we study symmetry of differential equations,  Pfaffian systems and applications to PDE systems.

Material to be covered:

1) Various notions of symmetry of differential equations

2) Noether's theorem on conservation laws

3) First integrals,  examples in classical mechanics,  Frobenius theorem

4) Pfaffian systems,  Cauchy characteristics,  involutivity and prolongation

5) Overdetemined PDE systems

6) Applications and examples: Symmetry algebra for Riemannian 2-manifolds,  

Generalized Newlander-Nirenberg theorem  and more examples if time permits

Text:

Chong-Kyu Han,  Lecture Note,  to be handed out

References:

1) Lie's structural approach to PDE systems, by L. Stormark, Cambridge U. Press, 2000

2) Pfaffian system, k-symplectic systems, by A. Awane and M. Goze,   Kluwer, 2000

3) Selected topics in the geometrical study of differential equations, by N. Kamran,

CBMS Series 96, Amer. Math. Soc. 2000

4) Applications of Lie gorups to differential equations, by P. Olver, Springer, 1993

5)  Exterior differential systems, by R. Bryant, S. S. Chern and others, Springer, 1991

Chong-Kyu Han,  Room 310  Bldg 27