Differential Geometry

Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

Doel vak

The student understands how to read and write in the language of
coordinate free analysis and geometry.
She can reproduce the most important arguments and constructions in
differential geometry.
She can apply these to compute on concrete geometric objects
The student can translate between geometric intuition and mathematical

Inhoud vak

This course is an introduction to the theory of manifolds. Apart from
giving the most relevant definitions from differential geometry
(manifolds, vector bundles and differential forms), we make short
excursions to Riemannian geometry (Riemannian metrics), dynamical
systems (flows of vector fields), as well as to algebraic topology
(fundamental group and de Rham cohomology). More precisely, the subject
list includes:

- Submanifolds, manifolds, tangent vectors
- Smooth maps (between manifolds),
- Vector fields and their flows, Lie bracket, Lie groups
- Vector bundles, tangent bundles, tensor products, sections
- Riemannian metrics, distances on Riemannian manifolds
- Differential forms, pullbacks, exterior derivative
- Stokes’ Theorem and De Rham cohomology
- Fundamental group and outlook towards algebraic topology


Lectures (2 hours per week) and exercise classes (2 hours per week)


Homework (makes up for 30% of the final grade), written final exam
(70%). A grade of 5/10 is required for the final exam to pass the

Vereiste voorkennis

Single Variable and Multi Variable Calculus, Mathematical Analysis,
Linear Algebra.


Lee, Introduction to smooth manifolds, Springer


3W, 3W-B

Overige informatie

Lecture notes will be made available in addition to the book.

Aanbevolen voorkennis


Algemene informatie

Vakcode X_400631
Studiepunten 6 EC
Periode P1+2
Vakniveau 400
Onderwijstaal Engels
Faculteit Faculteit der Bètawetenschappen
Vakcoördinator dr. O. Fabert
Examinator dr. O. Fabert
Docenten dr. O. Fabert

Praktische informatie

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Werkvormen Werkcollege, Hoorcollege

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