Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

8-2016

Committee Chair or Co-Chairs

Jeff Knisley

Committee Members

Ariel Cintron-Arias, Robert Gardner

Abstract

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.

Document Type

Thesis - Open Access

Copyright

Copyright by Robert Whitinger