MATH-437 / 5 crédits

Enseignant: Stra Federico

Langue: Anglais


Summary

Introduction to classical Calculus of Variations and a selection of modern techniques.

Content

Keywords

calculus of variations, optimization, minimization, Euler-Lagrange equations, first variation, direct method, Lagrangian, functional analysis, Sobolev spaces, minimal surfaces, convexity, existence, uniqueness, regularity.

Learning Prerequisites

Required courses

  • MATH-200: Analysis III
  • MATH-205: Analysis IV
  • MATH-303: Measure and integration

Recommended courses

  • MATH-301: Ordinary differential equations
  • MATH-302: Functional analysis I
  • MATH-305: Sobolev spaces and elliptic equations

Important concepts to start the course

The students are required to have sufficient knowledge on real analysis and measure theory. Having taken a course on functional analysis or Sobolev spaces will be an advantage.

Learning Outcomes

By the end of the course, the student must be able to:

  • Illustrate historically important optimization problems
  • Model geometrical and/or physical problems in the form of optimization
  • Analyze the existence and uniqueness of minimizers of optimization problems
  • Investigate the regularity properties of minimizers

Teaching methods

Lectures + exercises.

Assessment methods

Oral exam.

Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.

Supervision

Assistants Yes
Forum No

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

Main reference:

  • Introduction to the Calculus of Variations, B. Dacorogna

Other useful resources:

  • Direct Methods in the Calculus of Variations, E. Giusti
  • Introduction to the Modern Calculus of Variations, F. Rindler
  • Functional Analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis
  • Partial Differential Equations, L. C. Evans

Ressources en bibliothèque

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Calculus of variations
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Calculus of variations
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Calculus of variations
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22