1-forms. Line Integrals. Degree
In this video, we introduce the simplest type of integration on manifolds, the analogues of line integrals. We define 1-forms, which are the objects to be integrated in this case. These are dual to the notion of vector fields. We finish off the video by looking at an interesting 1-form on the circle which is intimately related to the notion of degree in topology. This is the first of many examples of the interesting connection between differential forms and topology.