Prerequisite: MAA102

Integral and differential calculus

(MAA105) develops students’ skills in

two crucial analytical tools: Integration

and Differential Equations. The approach

to Integration employed in this course

is Riemann’s integral, a foundational

mathematics theory. This course also

introduces students to two important

and related topics covered in the Bachelor

program: differential equations which

is required to understand basic physical

problems (trajectories, populations, etc.),

and geometry through the study of parametrized

curves.

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 the basic properties of such functions. Next we present the classical methods for computing integrals (integration by parts, integration by substitution, integration of rational fractions, elementary abelian integrals…) Finally, we study the main notions and results on improper integrals.

The second part is dedicated 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.

The third part is devoted to the study of plane parametric curves. We will see their fundamental properties and how to sketch a plane curve. We will cover parametric curves in Cartesian coordinates and in polar coordinates.

- Teaching coordinator: Etienne Bellin
- Teaching coordinator: Jeremie Bettinelli
- Teaching coordinator: Francesco Morabito
- Teaching coordinator: Léo Vivion