Classical Methods (conclusion of Chap. 2 of Dacorogna 2004 book) Hamilton formulation. From the Euler-Lagrange equation to the Hamilton system. The Hamilton-Jacobi equation. Reference to the fields theories and an application to the Poincaré inequality in 1-d.

Recommended exercises: 2.2.7 + 2.4.1 + 2.5.1 + 2.6.3

Brief revision of the preliminaries of Funcional Analysis: Lebesgue and Sobolev spaces and some of their basic properties. An overview of Convex Analysis in R ⁿ.