Cálculo variacional: uma breve introdução e aplicações

Abstract

The aim of this end-of-course work is to present a brief introduction to variational calculus and its applications. In this way, the development consists of recalling concepts of normed vector spaces, metric spaces and differential and integral calculus. Subsequently, these concepts will be refined for the study of functionals, where concepts about the Fréchet and Gâteaux derivatives, as well as the Euler equation, will inevitably arise. Finally, we will discuss sufficient conditions for extrema.