Partial Differential Equations (PDE) and Applications

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Program Overview

This master's degree offers advanced training in functional analysis, PDE theory, and numerical methods, with applications to fields such as fluid mechanics, electromagnetism, quantitative finance, and materials science.

Students acquire theoretical and practical skills to tackle complex problems related to linear and nonlinear PDEs.

Teaching Language : English- French

Curriculum Highlights

Core Courses

The program is structured into several fundamental blocks:

1- Core Curriculum

 i-Advanced Functional Analysis: Sobolev spaces, compact operators, fundamental theorems.

ii-Theory of linear PDEs: Variational methods, distributions, regularity of solutions.

iii-Numerical methods for PDEs: Finite elements, finite differences, error analysis.

iv-Calculus of variations and optimisation: Variational problems and applications to PDEs.

V- Applications and Modelling

VI-PDEs in physics and engineering: Fluid mechanics (Navier-Stokes equations), electromagnetism (Maxwell).

V-DEs in Biology and Ecology: Diffusion-Reaction Models, Wave Propagation in Living Media.

Advanced Topics

In the second year, specialised courses and research topics are offered:

I-Nonlinear PDEs: Viscosity Solutions, Viscosity Schemes, Entropic Methods.

II-Fractional Laplacian and Nonlocal Operators: Applications in Mechanics of Heterogeneous Media.

III-Boundary Value Problems and Fine Regularity: De Giorgi, Nash, and Moser Techniques.

VI-Optimal Control and applications.

VII-PDEs of hyperbolic type.

Career Opportunities

1- Academic Research: PhD in Mathematical Analysis, Mathematical Physics, or Scientific Computing.

2- Industry and Engineering: Numerical Modeling in Fluid Mechanics, Image Processing, and Biomathematics.

3- Finance and Insurance: Stochastic Calculus and Option Pricing.

4- Data Science & AI: Applications of PDEs in Machine Learning.

- Conclusion

The Master's in PDEs and Applications is a demanding and exciting program, combining theoretical rigour with modern applications. It prepares students for both research and the professional world.

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Admissions Information

Applicants must meet the following requirements:

·        Academic Background:

o   A bachelor's degree in mathematics, applied mathematics, physics, engineering, or a related field.

o   A strong foundation in analysis, linear algebra, and differential equations.

·        Minimum GPA Requirement:

o   minimum average for the licence degree 15/20 (or equivalent) is required.

·        Prerequisite Knowledge:

o   Prior coursework in real and functional analysis, PDEs, and numerical methods is recommended.

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