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.

 

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.

Références

Cours de calcul différentiel, H. Cartan
Mathématiques de deuxième année MP, cours et exercices, C. Deschamps, A. Warusfel
Cours de Mathématiques, tome2, Analyse, J. Lelong-Ferrand, JM Arnaudiès
Analyse II, calcul différentiel et équations différentielles, L. Schwartz