# Gradient of a Vector Function in Other Co-ordinate Systems

1. Feb 25, 2010

### DylanB

1. The problem statement, all variables and given/known data
I am trying to figure out how to take the gradient of a vector function in polar and spherical co-ordinates.

2. Relevant equations

3. The attempt at a solution
I am aware of how the gradient of a vector function in cartesian co-ords looks, simply the second order tensor

$$(\boldsymol{\nabla}\mathbf F)_{ij} = \frac{\partial F_i(\boldsymbol x)}{\partial x_j}$$

I am having trouble extending this idea to polar and spherical co-ords. The del operator is easy enough to derive in different co-ordinates but finding the second order tensor I am having difficulties.

Last edited: Feb 25, 2010
2. Apr 8, 2010

### jca

Any luck figuring out how to take a gradient of a vector field in spherical coordinates? I am also stumped on this and would appreciate any insight you have. Thanks!