Module MA2322: Calculus on Manifolds
- Credit weighting (ECTS)
- 5 credits
- Semester/term taught
- Hilary term 2018-19
- Contact Hours
- 11 weeks, 3 lectures including tutorials per week
- Lecturer
- Prof Jan Manschot
- Learning Outcomes
- On successful completion of this module, students will be able to:
- proof theorems about manifolds in euclidean space,
- proof 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, proof 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.
- Module Prerequisite
- Analysis in several real variables (MA2321)
Required reading:
J. R. Munkres, "Analysis on Manifolds", Westview Press (1991)
- Assessment Detail
-
This module will be examined in a 2-hour examination in Trinity term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session, with the examination counting for the remaining 90%.