Course

MATH-437: Calculus of variations

Summary

Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet energy, p-energy, etc).

Lectures

Instructor

Alexandre Perozim De Faveri

Official source

https://edu.epfl.ch/coursebook/en/calculus-of-variations-MATH-437

Moodle Page

http://go.epfl.ch/MATH-437

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Summary

Lectures

Instructor

Alexandre Perozim De Faveri

Official source

https://edu.epfl.ch/coursebook/en/calculus-of-variations-MATH-437

Moodle Page

http://go.epfl.ch/MATH-437

About this result

Lectures in this course (12)

Legendre Transform

Explores the Legendre transform, duality in convex analysis, and optimization problems.

Euler-Lagrange Equation

Explores the classical methods for solving optimization problems, emphasizing the Euler-Lagrange equation and its variants.

Lagrange Multiplier and DuBois-Reymond Equation

Explores Lagrange multiplier method and DuBois-Reymond equation in optimization.

Hamiltonian Formulation and Equivalence with Euler-Lagrange

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

Hamilton-Jacobi Equation: Exact Fields

Explores the Hamilton-Jacobi equation, optimal control, and Bellman principle in exact fields.

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