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Module MA2322: Calculus on Manifolds
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Hilary term 2014-15
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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Prof. David Simms
- Learning Outcomes
- On successful completion of this module, students will be able to:
- Establish the properties of the exterior algebra (wedge product) of a finite dimensional real vector space;
- Establish the properties of the Hodge star operator for a finite dimensional oriented real vector space with a non-degenerate symmetric scaler product;
- Establish the properties of the differential of a differential form;
- Prove the Poincare lemma;
- Prove Stokes' theorem for a manifold with boundry
- Module Content
- Integration of forms on surfaces/manifolds, Poincare lemma, general Stokes theorem.
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- Module Prerequisite
- Analysis in several real variables (MA2321)
- Assessment Detail
- This module will be examined in a 2-hour examination in Trinity term.