Analysis
Fall 2026 and Spring 2027
Teacher: Virginie Ehrlacher (ENPC)
Relevant topics: Normed vector spaces, Banach spaces, Hilbert spaces, measure theory and integration, Lebesgue spaces, Fourier series, distribution theory, Fourier transform
Theoretical and exercise sessions (42h)

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Partial differential equations: variational approaches
Spring 2026
Teacher: Frédéric Legoll (ENPC)
Relevant topics: Lax-Milgram theorem, variational formulation of PDEs
Theoretical and exercise sessions (6h)

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Introduction to partial differential equations and to finite differences method
Spring 2024, Spring 2025, Spring 2026
Teacher: Sonia Fliss (ENSTA)
Relevant topics: linear and nonlinear hyperbolic PDEs in 1D, method of characteristics, finite differences method, CFL condition, stability, consistency, convergence
Exercise and computer sessions (12h)

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Dynamical systems: analysis and stability
Fall 2024
Teacher: Frédéric Jean (ENSTA)
Relevant topics: differential calculus, linear and nonlinear dynamical systems, theory of ODEs, phase portrait, equilibria, stability
Exercise sessions (13h)