I am trying to clarify terms in order to help me figure out what I'd like to study.
I understand that $p$-forms and $p$-vectors are used with things like wedge products, exterior algebras, and a bunch of other concepts I don't understand that seem to fall under the label of "exterior" or "geometric". For instance, the exterior derivative. Yet I also understand there is something called "tensor calculus" which is supposed to be the tensor analog of vector calculus.
Are these two genres of mathematical objects different? They both seem to involve tensors and calculus so I am confused since a concept like exterior derivative seems to involve both tensors and calculus and yet I don't see it called "tensor calculus."
Thanks!