Date of Award

8-1-2014

Degree Name

Master of Science

Department

Mathematics

First Advisor

Kocik, Jerzy

Abstract

This thesis explores the algebraic and geometric structure of the Legendre transform and its application in various field of mathematics and physics. Specifically linear transformation as a mathematical process and motivating it in terms related to phenomena in mathematics and physics. The Legendre transform provides a change of variables to express equations of the motion or other physical relationships in terms of most convenient dynamical quantities for a given experiment or theoretical analysis. In classical mechanics the Legendre transform generates the Hamiltonian function of a system from the Lagrangian function or vice versa. In thermodynamics the Legendre transform allows thermodynamic relationships to be written in terms of alternative sets of independent variables. Here we review the properties of Legendre transform and why it is so important in mathematics and physics.

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