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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.