An introduction to exterior differential systems

Abstract

An exterior differential system is by definition a partial differential equation for submanifolds formulated in the language of differential forms. In this introduction we construct the contact systems on several kinds of jet bundles in order to reduce general partial differential equations to exterior differential systems. Moreover we discuss the algebraic properties of the Spencer cohomology associated to an exterior differential system and sketch a proof of the theorem of Cartan-Kähler about the analytical solutions to an analytical exterior differential system. © 2014 Springer International Publishing Switzerland.