MAU23206/MAU33206 Calculus on manifolds
| Module Code | MAU23206/MAU33206 |
|---|---|
| Module Title | Calculus on manifolds |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Florian Naef |
| Module Prerequisites | MAU23203 Analysis in several real variables |
Assessment Details for MAU23206
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Assessment Details for MAU33206
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 10% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Prove theorems about manifolds in Euclidean space.
- Prove theorems about differential forms and perform calculations with them.
- Carry out integration on manifolds in Euclidean space.
- Explain the relation between scalar, vector, tensor fields and differential forms.
- Explain, prove and apply Stokes' theorem for differential forms.
- Explain and apply the Poincaré lemma.
Module Content
- Manifolds in Euclidean space
- Tensors
- Differential forms
- Stokes' theorem
- Poincaré lemma
Recommended Reading
- Analysis on manifolds by James Munkres.