Course content

This course deals with the study of differential forms and vector analysis on manifolds. It will develop de Rham theory as a tool to study the topology of manifolds. The topics to be studied are: Manifolds, tangent spaces, exterior algebras and differential forms (local and global), de Rham cohomology, orientation, integration and Stokes's theorem, and applications.

Learning outcome

1. Knowledge. The student has knowledge of fundamental concepts and methods concerning differential forms, de Rham cohomology and integration on manifolds.

2. Skills. The student is able to apply his or her knowledge of de Rham theory to formulate and solve problems of a topological nature.

Learning methods and activities

The course will be given in autumn in years of odd numbers.

Recommended previous knowledge

It is a big advantage to have taken at least one of the courses TMA4190 Introduction to Topology and TMA4192 Differential Topology, but it is not strictly necessary. Some knowledge of analysis beyond basic calculus is an advantage.

Course materials

Will be announced at the start of the course.

Credit reductions