Скачать или смотреть Tensors under general coordinate transformations 1

This is the first lecture in my second series on tensors. Whereas the first series was devoted mostly to scalars vectors and tensors under linear transformation, this series discusses these entities under a general coordinate transformation. This will be especially useful for students of general relativity. Again, in this series of lectures we will focus mainly on "index gymnastics"rather than on the more elegant, but also more abstract differential geometric concepts. This lecture starts with a quick discussion on linear coordinate transformation - this part is essentially a recapitulation of my first series. We then go on to define these quantities under a general coordinate transformation and show the connection between these and the linear coordinate transformation versions.