MATH-305 / 5 crédits

Enseignant: Nobile Fabio

Langue: Anglais

## Summary

This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs.

Analysis I-IV

## Recommended courses

Measure and Integration; Functional Analysis I

## Learning Outcomes

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

• Classify different types of PDEs
• Define different notions of solutions
• Analyze the properties of solutions of PDEs
• Prove existence and regularity results of solutions of elliptic PDEs

## Transversal skills

• Use a work methodology appropriate to the task.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking

## Teaching methods

Ex cathedra lectures, exercises in classroom

## 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

No

## Bibliography

• David Gilbarg, Niel S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 2nd edition, 2001.
• Lawrence C. Evans. Partial Differential Equations, AMS-Graduate Studies in Mathematics, 2nd edition, 2010.
• Haïm Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011
• Fritz John, Partial Differential Equations, Springer-Verlag, 4th edition, 1982

## Notes/Handbook

Lecture notes available on the webpage

## Prerequisite for

• Master courses on theory of PDEs: Equations aux dérivées partielles d'évolution, Calculus of variations, Optimal Transport, Dispersive PDEs, Théorie du calcul stochastique, Distributions and interpolation spaces;
• Bachelor / Master courses on numerical approximation of PDEs: Numerical Approximation of PDEs; Numerical methods for conservation laws; Computational finance; Numerical integration of stochastic differential equations; Numerics for fluids, structures & electromagnetics;

## Dans les plans d'études

• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Introduction to partial differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 MAB111 9-10 10-11 MAB111 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mardi, 8h - 10h: Cours MAB111

Mardi, 10h - 12h: Exercice, TP MAB111