Analysis 1

Description

Objectifs

The student shall be able to:

    Study the differentiability of a function of several variables and perform a limited (Taylor) expansion

    Perform integral calculations of functions of several variables or over unbounded domains

    Search for extrema of a function of class C1C1 or C2C2

    Study the convergence of a numerical series using bounding and comparison methods

The student shall have understood and be able to explain (main concepts):

    The notion of the differential of a function of several variables, partial derivatives, and their relation to the differential

    The notion of improper integrals, integrals of parameter-dependent functions or of functions of several variables

    The notion of numerical series and the concept of convergence of numerical series

Pré-requis

First-year Linear Algebra: Vector spaces, linear maps, matrices, concept of image and kernel of a linear map.
First-year Analysis Course: Functions, limits, continuity, differentiability in one dimension, linear algebra (vector spaces, linear maps, matrices, vectors).

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…