Advanced Mathematics : 1/ Vectorial Analysis 2/ Topology.

Objectives

At the end of this module, students should be able to :
1/ Vectorial Analysis :
- give pararametric  representations of curves or surfaces and to calculate their geometric characteristics (tangent line or plane, normal vector(s), curvature, torsion),- calculate integrals of scalar or vector fields on such submanifolds,- apply the various versions of the Stokes theorem.
2/ Topology :- handle open sets, closed sets, closures, interiors, boundaries in metric spaces,- apply basic properties of complete spaces,- apply basic properties of  compact spaces,- apply basic properties of  connected spaces.
In vectorial analysis, students  should be able to perform differential and integral calculations involving functions of several variables. In topology, students should be able to develop a rigorous reasoning.

Needed prerequisite

Mathematics 1
Mathematics 2
Analysis and Algebra
Analyse and Signal

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...