The Theory of Exterior Differential Systems and it’s Applications

Abstract

We used exterior algebra to study partial differential equations geometrically, and explained how to rephrase any system of partial differential equations as an exterior differential system (EDS). Our strategy is to find orthogonal coordinates corresponding to a prescribed metric system. Our study emphasizes finding and interpreting differential invariants to enable one to use the same techniques in other settings. Also we studied physical applications of exterior algebra in conservation laws and find the relation between exact and balance conservation laws which lead to generation of physical fields from closed exterior forms (conservative objects). Finally we studied sets of periodic orbits of Billiards on bounded domains, and we gave another proof of the Rychlik’s Theorem using EDS . III