Reseña

A course of Functional Analysis with Calculus of Variations introduces fundamental concepts and tools of modern applied mathematics. It introduces topological and metrics spaces before presenting Banach and Hilbert spaces. It continues with the study of the fundamental theorems of Functional Analysis: the uniform boundedness principle, the closed graph theorem, and the theorems of Riesz-Fréchet and Hahn-Banach. With these tools at hand a-not-so-short study of weak topologies is developed to finish Part I. Part II is dedicated to topics of Calculus of Variations taking advantage of what was done in Part I. A good part of Calculus in normed spaces is studied before getting into the classical topics of the Calculus of Variations like the properties of the Euler-Lagrange equation.