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Symbolic tensor analysis in Mathematica 8


Hello,

Recently I begun to use Mathematica. For now I'm trying to learn to
use it properly.
The first tasks I would like to play with, are vector and tensor
analysis.
The question is:
For simplicity I would like to have vector definition:

v={v1,v2,v3} or v={vx,vy,vz}

where 1,2,3 or x,y,z are subscripts or superscripts. How do I achieve
that? When I write something like that I get the recursion which I do
not want. And the other thing is: how do I tell Mathematica that for
example vx is a function of x,y,z to get something like:

vx=f(x,y,z), vy=g(x,y,z), vz=h(x,y,z)

to describe vector field. But during derivations I may not know
formulas for f,g,h. But when counting the derivative I would like to
get

Dv/dx={f'(x,y,z),g'(x,y,z),h'(x,y,z)}
and so on.

Thanks in advance and
Best regards,
Misery



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