The Calculus of Variations: An Introduction

Abstract

If $\mathcal{E}$ is a normed vector space composed of mappings, for example, the space of continuous real-valued functions defined on a compact interval, then we refer to a real-valued mapping F defined on a subset S of $\mathcal{E}$ as a functional. The calculus of variations is concerned with the search for extrema of functionals. In general, the set S is determined, at least partially, by constraints on the mappings and the functional F is defined by an integral. The elements of S are often said to be F-admissible(or admissible if there is no possible confusion).