Differential forms and integration on manifolds
The theory of integration on manifolds is difficult, partly because there is quite a bit of technical machinery involved to set up differential forms. In this video, we begin by giving a brief introduction to multi-linear algebra and in particular, alternating forms so as to define differential forms. We then define integration of differential forms on arbitrary manifolds. We show how the technical algebraic machinery established is precisely what's needed to give a nice theory of integration.