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 .
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