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 in a 2-hour examination in Trinity term.