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Module MAU23206: Calculus on Manifolds

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2019-20
Contact Hours
11 weeks, 3 lectures including tutorials per week
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

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, with the examination counting for the remaining 90%.”Re-assessments if required will consist of 100% exam.