These lectures were given in the SIAM Special Topics Seminar for Fall 2020 to graduate students at the University of Delaware.
These lectures are based on Chapter 4 of Differential Topology by Victor Guillemin and Alan Pollack.
Motivation for a rigorous theory of differential forms and what properties a differential form should have.
(video 61 min)
The alternating tensor, the wedge product and the exterior algebra.
(video 60 min) (video 32 min)
Differential forms on manifolds (a rushed introduction)
(video 47 minutes)