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Module MA2322: Calculus on Manifolds

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2012-13
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
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.
 
Module Prerequisite
Analysis in several real variables (MA2321)
Assessment Detail
This module will be examined jointly with MA2321 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. However there will be separate results for MA2321 and MA2322..