Differential Geometry

Differential Geometry

This course is an introduction to differential geometry, in which I provide a very simple introduction and general information, mostly without proofs, as the course is intended for undergraduate mathematics students and master's students who are not specializing in geometry (in my case, these are students in the third year of their Bachelor's degree in Analysis and the second year of their Master's degree in Functional Analysis).

The continuation of this course is in the second-year Master's program, first semester, entitled: Analysis on Manifolds

Chapter II: Differential Calculus

This chapter is devoted to the concept of differential calculus, as a reminder and continuation of the differential calculus course from analysis 4, in which we find the three main lines:

• The differential 

• Local Inversion Theorem

• Implicit Function Theorem

Géométrie Différentielle chapitre 02 : Calcul différentiel.pdf 

Chapter IV: Differential Forms

In this chapter we give:

• Tensor algebra

• A reminder about multilinear and alternating multilinear forms

• Differential Forms and their Properties.   

Géométrie Différentielle chapitre 04 Formes différentielles.pdf 

• L3.Control TD 2024-2025.pdf 

• L3.Exam + Corr 2024-2025.pdf 

 exam retake questions

• L3.Rattrapage 2022-2023.pdf

• L3.Rattrapage 2020-2021.pdf

• L3.Rattrapage 2019-2020.pdf

• L3.Rattrapage 2017-2018.pdf

• L3.Rattrapage 2016-2017.pdf