Teaching
You can find details for all the courses that I teach on the Université Virtuelle. For those of you not enrolled as a student at the ULB, but who still want to laugh at my French, written course material is available below, but be warned this may not be the most up-to-date available.
Calcul Différentiel et Intégral
This course, taught jointly with Denis Bonheure, is an introduction to real analysis. It is divided into two parts, taught in the first and second quadrimestres.
In the first quadrimester we start from an axiomatic definition of the real numbers (as a complete ordered field) and consider convergence of sequences and series of real numbers. We then move on to real-valued functions of a single real variable. We investigate continuous functions, differentiable functions and integrable functions (in the sense of Riemann), culminating in the fundamental theorem of calculus. We close the first part of the course with applications to ordinary differential equations.
In the second quadrimester we move on to functions of many variables. We study continuous and differentiable functions and the implicit function theorem, including applications to optimisation modulo constraints and Lagrange multipliers. We then consider integrals of functions of many variables (in the sense of Riemann). We finish with vector analysis in three-dimensional space and the theorems of Gauss and Stokes.