lepl1105  2018-2019  Louvain-la-Neuve

5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Glineur François; Keunings Roland; SOMEBODY;
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  Express metric notions in Rn using the language of general topology.  Study limits, continuity, directional derivatives and differentiability for functions of several variables. Apply Taylor polynomial in order to approximate a function. Locate and identify free extrema of a function; locate extrema under constraints of a function using the technique of Lagrange multipliers. Calculating multiple integrals possibly using a change of variables. Calculate line integrals, surface integrals, the flow of a vector field along a curve and the flow of a vector field through a surface possibly using Stokes type theorems. Apply the resolving method for linear differential equations with constant coefficients of order n. Analyse and write rigorously statements and demonstrations on the mathematical content specified below, and illustrate them with examples and counter-examples.

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
• Scalar and vector-valued real functions of several variables, topology, limit and continuity
• Differentiability, partial and directional derivatives, 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 Stokes-type 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 above-mentioned objectives. Results from continuous assessment may also be taken into account for the final grade.
Online resources
Bibliography
• Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.
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
BTCI

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

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Engineering

Bachelor in Engineering : Architecture