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Visualizing Behaviors in Differential Geometries using Mathematica

Gerald Thomas
Organization: Milwaukee School of Engineering

Wolfram Technology Conference 2014
Conference location

Champaign, Illinois, USA

Differential geometries require partial differential equations to provide geodesic behaviors. Physical models such as Einsteins theory of relativity are examples. My interest has been using differential geometry in the social sciences; in particular to gain insight into the causal behavior of decision processes. The difficulty in all of these endeavors is to see a picture of the behaviors that are consequences of the differential geometry. This talk will apply Mathematica solutions of limit cycles and limit surfaces and their relationship to harmonic solutions and chaotic behaviors. It will then proceed with model solutions using Mathematica of more complicated differential geometry possibilities that have applications to gravitational theories and decision theories. We find that the NDSolve and Manipulate functionality can be used to great advantage in order to "see" the behaviors in these geometries. There are many applications of these visualizations, such as teaching possibilities in Electro-Magnetism courses.

*Wolfram Technology

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Visualizing behaviors in differential geometries using Mathematica final 10232014 jerry thomas.nb (3.9 MB) - Mathematica Notebook