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
Integration of forms on surfaces/manifolds, Poincare lemma, general Stokes theorem.
Analysis in several real variables (MA2321)
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..