Understanding Coordinate Transforms: Partial Derivatives

[Storm Butler]

Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives i just don't get the whole thought process behind it. I came across this while reading about covariant and contrivariant vectors. If anyone can help clear up how this works i would really appreciate it. Also if i need to be more specific about what i mean or if you would like to see an example of what I am talking about just ask and i would be happy to post it up.

 

[tiny-tim]

Hi Storm Butler!

Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives …

We don't use partial derivatives for the transformation itself, we can only use them for a very local transformation, or for transforming the d part in an integral: ∫∫∫dx dy dz = ∫∫∫ (jacobian) da db dc.

see http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant" for some details.