An exterior differential system (EDS) is a system of equations of defined on a manifold involving exterior differentials forms. In this talk, we'll introduce differential forms and differential ideals and describe how to construct an EDS. We'll see a couple of theorems (probably without proof) on the existence of solutions to EDS. One reason that EDS are useful is that every PDE can be rephrased as an EDS and the tools of exterior algebra give a coordinate-free way to analyze the PDE/EDS
Exterior Differential Systems