MATH-322 / 5 crédits
Enseignant: Cossarini Marcos
Differentiable manifolds are a certain class of 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.
- topological and differentiable manifolds
- vector bundles
- tangent space and tangent bundle
- vector fields, integral curves
- differential forms, tensors, exterior derivative
- orientation, integration of differential forms
- Stokes's theorem (and applications)
differentiable manifold, tangent space, vector field, differential form, Stokes
Espaces métriques et topologique, Topologie, Analyse III et IV
Important concepts to start the course
Topological spaces, multivariate calculus (implicit function theorem etc.)
By the end of the course, the student must be able to:
- Define and understand the key concepts (differentiable structure, (co)tangent bundle etc.)
- Use these concepts to solve problems
- Prove the main theorems (Stokes etc.)
- Continue to work through difficulties or initial failure to find optimal solutions.
- Demonstrate a capacity for creativity.
- Access and evaluate appropriate sources of information.
- Demonstrate the capacity for critical thinking
- Assess one's own level of skill acquisition, and plan their on-going learning goals.
2h lectures + 2h exercises
Expected student activities
Attend classes and solve exercises, revise course content / read appropriate literature to understand key concepts.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Introduction to differentiable manifolds
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines