The first part of this course is focussed on the notion of Riemann integral. After introducing the notion of Riemann integrable function, we briefly discuss its basic properties. We next present classical methods for computing integrals (integration by parts, integration by substitution, integration of rational fractions, etc.). Finally, we study the main notions and results on improper integrals, that is, when integrating on a general interval instead of a closed and bounded one.
The second part is dedicated to Taylor's theory of expansion, which gives an approximation of a given function near a given point, as a polynomial, better and better as the degree increases.
The third and final part is devoted to the study of ordinary differential equations, mainly first order linear differential equations and linear systems of ODEs, with a special focus on linear differential equations with constant coefficients.
- Profesor: Bettinelli Jeremie
- Profesor: El Kamel-Meyrigne Melvyn
- Profesor: Fantini Lorenzo
- Profesor: Gierczak-Galle Lucas
- Profesor: Salvi Tony