Fiches de cours 2018-2019

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Introduction to differentiable manifolds

MATH-322

Enseignant(s) :

Kiesenhofer Anna

Langue:

English

Summary

Differentiable manifolds are (certain) topological spaces which, in a way we will make precise, locally resemble R^n. We introduce the key concepts of this subject, such as vector fields, differential forms, integration of differential forms etc.

Content

Keywords

differentiable manifold, tangent space, vector field, differential form, Stokes

Learning Prerequisites

Required courses

 Espaces métriques et topologique, Topologie, Analyse III et IV

 

Important concepts to start the course

Topological spaces, multivariate calculus (implicit function theorem etc.)

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

2h lectures + 2h exercises

Expected student activities

Attend classes and solve exercises, revise course content / read appropriate literature to understand key concepts.

Assessment methods

Written exam.

Resources

Bibliography

John M. Lee: Introduction to Smooth Manifolds (e-book:
https://link.springer.com/book/10.1007%2F978-1-4419-9982-5)

Ressources en bibliothèque

Dans les plans d'études

    • Semestre
       Automne
    • Forme de l'examen
       Ecrit
    • Crédits
      5
    • Matière examinée
      Introduction to differentiable manifolds
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9 MAA330   
9-10    
10-11 MAA330   
11-12    
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand