A Brief Survey of the History of the Calculus of Variations and its Applications

Details A Brief Survey of the History of the Calculus of Variations and its Applications A Brief Survey of the History of the Calculus of Variations and its Applications

2004-02-23

arxiv.org/abs/math/0402357v1

Mathematics

History and Overview

26 pages, no figures

Scientific paper

In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for developments in the mathematical theory. From the 18th century onwards, the task of establishing a rigourous framework of the calculus of variations is studied, culminating in Hilbert's work on the Dirichlet problem and the development of optimal control theory. Finally, we make a brief tour of some applications of the theory to diverse problems.

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