Differential and Integral Calculus

Objective

This course has two objectives. The first is to familiarise students with the tools of integral calculus, which will be heavily used later in studying probability. The second is to introduce the concepts of differential calculus that will be required in the second-semester optimisation course.

Assessment:

The overall grade for the course will be the average of the continuous assessment (“contrôle continu”, CC) grade (50%) and the written final exam (50%).

The continuous assessment grade is made up of three elements, each graded out of twenty points: (i) the mid-term grade, (ii) the grade for attendance at amphitheater/tutorial sessions, whose attendance is mandatory, and (iii) the grade for participation in amphitheater/tutorial sessions. The CC grade is calculated as follows: 50% of the mid-term grade + 25% of the attendance grade + 25% of the maximum between the participation grade and the mid-term grade.

The attendance grade is calculated according to the scale available on the school's intranet.

Planning

1. Integral calculus -Reminders about the Riemann integral, the multiple integral and changes of variable.
2. Derivatives -Reminders, definitions and properties, operations on derivatives, differential calculus in econometrics.
3. Applications of the concept of derivatives -Taylor formulae, convex functions, quasi-convex functions, homogeneous functions, implicit functions.
4. Differential equations -General remarks: Lipschitz case, linear equations, systems of linear differential equations, linear equations of order p.

References

Cours de calcul différentiel, H. Cartan
Mathématiques de deuxième année MP, cours et exercices, C. Deschamps, A. Warusfel
Cours de Mathématiques, tome 2, Analyse, J. Lelong-Ferrand, JM Arnaudiès
Analyse II, calcul différentiel et équations différentielles, L. Schwartz