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
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.