# Analysis of multivariate functions

lbir1211  2019-2020  Louvain-la-Neuve

Analysis of multivariate functions
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Hanert Emmanuel;
Language
French
Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Content
The following topics will be covered:
• Functions of two variables and space geometry
• Limits and continuity of functions of two variables
• Partial derivatives and tangent plane
• Gradient vector and applications of partial derivatives
• Extreme values of functions of two or three variables and Lagrange multipliers
• Multiple integration on regular domains and Riemann sums
• Multiple integration on arbitrary domaines
• Vector analysis (line integrals of scalar and vector fields, Green and Stokes's theorem, ...)
• Introduction to Fourier calculus
• Introduction to partial differential equations
Teaching methods
There will be one two-hour lecture and one two-hour practical session per week.
Evaluation methods
The course assessement is based entirely on a written exam.
Other information
The course does not use any particular support which would have to be paid and deemed obligatory. Any paid books that may be recommended are optional.
Online resources
Bibliography
Ouvrages de référence et outils de travail : Ce cours se base uniquement le deuxième volume du livre de référence « Analyse, concepts et contextes :  Fonctions de plusieurs variables » de James Steward, 3ème édition, de boeck. Ce livre est disponible à la DUC. Une version électronique est également disponible sur le site suivant (après identification) : http://accesnoto.deboecksuperieur.com/notobib. Des documents complémentaires seront également mis à disposition sur le site Moodle du cours.
Faculty or entity
AGRO

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Bioengineering
5