What are basis vectors, one forms, and basis one forms?

[Varnick]

I'm not sure this is the correct forum section for this question, if not, please move me. Essentially, I'm looking for help understanding what basis vectors, one forms, and basis one forms are. I'm fairly sure I get basis vectors, I would describe them as a description of a co-ordinate system, and also function similar to unit vectors. One of the main areas related to this that confuses me is covariance and contravariance, could anyone shed some light on this? Many thanks,

V

 

[quantumdude]

What's your mathematical experience? Do you know elementary linear algebra and calculus?

 

[Varnick]

I'm going into my A2 year (UK education system, just before college for you USers). I've completed work in linear algebra and calculus, and have looked at very basic vector calculus, partial differentiation, matrices, and some tensor analysis (now starting to look at tensor calculus, when my mind isn't exploding). I'm starting to understand what the geometries I listed are mathematically, but not qualitatively. Any help appreciated,

V

 

[quantumdude]

OK, you should be able to handle the following reference with no problem then.

A Geometric Approach to Differential Forms.

It's a free textbook on differential forms aimed at students who have studied multivariable calculus and a little linear algebra.

 

[Varnick]

Thanks, I'll get reading that next week, got to finish a paper for Tuesday.

V