# Module MA2322: Calculus on Manifolds

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Hilary term 2015-16
**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)

**Recommended 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.