Tensor Calculus

[Eli]

"Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:[2]

In our subject of differential geometry, where you talk about manifolds, one difficulty is that the geometry is described by coordinates, but the coordinates do not have meaning. They are allowed to undergo a transformation. And in order to handle this kind of situation, an important tool is the so-called tensor analysis, or Ricci calculus, which was new to mathematicians. In mathematics you have a function, you write down the function, you calculate, or you add, or you multiply, or you can differentiate. You have something very concrete. In geometry, the geometric situation is described by numbers, but you can change your numbers arbitrarily. So to handle this, you need the Ricci calculus." - See the source.

Here is a video series on Tensor Calculus:

[Admin]

Here is another video series on Tensor Calculus: