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
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- 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)
- Recommended Reading
J.R. Munkres, 'Analysis on Manifolds', Westview Press (1991)
- Assessment Detail
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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.