MAA105 - Integral and Differential Calculus (2022-2023)

Integrals and differential calculus (MAA105) develops students's skills in crucial analytical tools, in particular integration. 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: Taylor expansions (a tool for function approximation) and differential equations, which are required to understand basic physical problems (trajectories, populations, etc.).



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.