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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.