Introduction to partial differential equations

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.

Content

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Learning Prerequisites

Required courses

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

Resources

Virtual desktop infrastructure (VDI)

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

Ressources en bibliothèque

• Partial Differential Equations / Fritz John
• Elliptic Partial Differential Equations of Second Order / David Gilbarg & Niel S. Trudinger
• Partial Differential Equations / Lawrence C. Evans
• Functional Analysis, Sobolev Spaces and Partial Differential Equation / Haïm Brézis

Notes/Handbook

Lecture notes available on the webpage

Moodle Link

• https://go.epfl.ch/MATH-305

Prerequisite for

• Master courses on theory of PDEs: Equations aux dérivées partielles d'évolution, Calculus of variations, Optimal Transport, Dispersive PDEs, Theory of stochastic calculus, Nonlinear Schrödinger equations, Distributions and interpolation spaces; Introduction to general relativity; Introduction to stochastic PDEs
• 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;