# Tensor calculus> definition of contravariants

Hello Big minds,

In the book of Arfken [Math Meth for Physicists] p 134 he defined contravariant tensor...my question is about a_ij he defined them first as cosines of an angle of basis then he suddenly replaced them by differential notation...why is that?

cosines are not mention in this article as well:
http://en.wikipedia.org/wiki/Covariant_transformation

please note that I newly "ride on my horse" through tensor analysis!

best regards

Abolaban

## Answers and Replies

Orodruin
Staff Emeritus
Homework Helper
Gold Member
General coordinate transformations are not necessarily rotations. When you deal with Cartesian tensors, you will only come across rotations and so your transformations will contain sines and cosines. However, the general case is more ... well ... general.

When you refer to pages in Arfken, please also state the edition - there are now seven of them ...

that was from Arfken's book 6th ed

Orodruin
Staff Emeritus