Teacher(s)
Language
French
Prerequisites
This course supposes acquired the notions of mathematics developed in the courses LEPL1101 and LEPL1102.
Main themes
Functions of several real variables. Continuity and differentiability. Optimization problems, vector analysis and integral theorems. Linear differential equations. Modelling of simple problems.
Aims
At the end of this learning unit, the student is able to :  
1 
At the end of the course the students will be able to

Content
 Linear constantcoefficient ordinary differential equations of any order, Cauchy problem
 Scalar and vectorvalued real functions of several variables, topology, continuity
 Differentiability, partial and directional derivatives, chain rule, tangent plane, gradient and Jacobian matrix
 Higher order partial derivatives and Taylor polynomial
 Unconstrained and constrained extrema, Lagrange multipliers
 Multiple integrals and changes of variables
 Line and surface integrals, circulation and flux of a vector field
 Notion of boundary and Stokestype theorems
Teaching methods
Lectures in a large auditorium, supervised exercise (APE) and problem (APP) sessions in small groups, possibly online exercises.
Evaluation methods
Students will be evaluated with an individual written exam, based on the abovementioned learning outcomes.
Online resources
Bibliography
 Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.
Teaching materials
 Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.
Faculty or entity