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MAU23206 Calculus on manifolds

Module Code MAU23206
Module Title Calculus on manifolds
Semester taught Semester 2
ECTS Credits 5
Module Lecturer Prof. Florian Naef
Module Prerequisites MAU23203 Analysis in several real variables

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 2.
  • Continuous assessment contributes 10% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Prove theorems about manifolds in Euclidean space.
  • Prove 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, prove 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

Recommended Reading

  • Analysis on manifolds by James Munkres.