Aims

This course aims at developing the following
skills: mastery of the language, rigor in the analysis of a
proposition, search for relevant examples, precision in the
expression and understanding of the various methods of proofs.
More precisely, it deals with the mathematical aspects of the
notions of continuity, convergence, derivative and integral. It
aims at developing the basic methods of explicit resolution of
differential equations and it offers an outlook towards fields of
applications. This first course in mathematical analysis presents
the basic notions and results with rigor and intuition :
convergence, continuity, derivative, integral. The lectures will
also contain an introduction to explicit solutions for
differential equations and openings to various applications
fields.

Main themes

This first part covers basic notions in elementary analysis such as the Real Number System, Elementary Sey Theory, Limit, Continuity, Derivative for real functions. It covers both the concepts, its properties and fundamental results such as the Intermediate Value Theorem, Weierstrass Theorem, Rolle's Theorem and the Mean Value Theorem.

Content and teaching methods

The course will contain three parts : synthesis of the
basic tools from secondary school, one variable calculus, ordinary
differential equations

Other credits in programs