Manifolds #10 - Introducing Differential Forms (on R^d)

Notes are on my GitHub! github.com/rorg314/WHYBmaths In this video I introduce differential forms (q-forms) on R^d, for now they are just new and abstract objects that we will realise more what exactly they correspond to in future videos (the dual of vectors). We identify that 0-forms are smooth functions on R^d, and that 1-forms can be constructed by taking the exterior derivative of a 0-form. The exterior derivative of the coordinate functions, dx^\mu, forms the basis of the space of 1-forms (a vector space). I then introduced the anti-symmetric wedge (exterior) product, which acts on a pair of (q,p) forms to give a q+p form. We will use this in the next video to construct a 2-form.