This thesis is an introductory study of the calculus of variations. We will begin by introducing the field of the calculus of variations, its history and describe the classical problems of the calculus of variations. We will present the solutions to these problems and introduce the mathematical theory needed for their solution. These problems include one of the most famous problems in the calculus of variations, that of finding the brachistochrone curve. After exploring these interesting curves, we will move on to studying geodesics on a variety of surfaces including the cylinder, sphere, torus and cone. In each of these chapters, we work to describe both analytically and geometrically all of the geodesics on these surfaces.
Willert, Jeffrey Alan, "A Study of the Calculus of Variations" (2009). Senior Independent Study Theses. Paper 911.
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2009 Jeffrey Alan Willert