Relativity Prelim #1 - Vectors and the coordinate basis скачать в хорошем качестве

Relativity Prelim #1 - Vectors and the coordinate basis

Notes are on my GitHub! github.com/rorg314/WHYBmaths These videos aim to cover some of the preliminary notions we will need to use quite heavily in our study of special and general relativity. These videos are in no way a substitute for other videos on my channel, where I have covered these topics in much greater depth, but these should hopefully serve as a brief overview / review of the main concepts. Here I introduce the concept of a vector, and how we realise it concretely as a linear combination of basis vectors. We realise that every coordinate system comes naturally equipped with a basis, the coordinate basis, obtained from the coordinate derivatives in each coordinate direction. We therefore see that vectors should now be understood as linear differential operators that act on functions, producing the tangent to that function. After we have introduced 1-forms we will see how we can connect this notion of a vector with the gradient operator you may be familiar with from vector calculus.