# Module MA2322: Calculus on Manifolds

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Hilary term 2016-17
**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 PoincarĂ© lemma.

**Module Content**-
- Manifolds in euclidean space,
- Tensors,
- Differential forms,
- Stokes' theorem,
- PoincarĂ© 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%. The supplemental examination paper, if required, will determine 100% of the supplemental module mark.