Definition talk:Divergence Operator

Is there a way of salvaging this page by putting suitable constraints on the conditions, or would it in fact be best to scrap it completely and leave just the Real Cartesian Space version up?

This is what happens when one is mostly self-taught. --prime mover (talk) 18:01, 15 April 2020 (EDT)


 * $\displaystyle \operatorname {div} \mathbf f = \sum_{k \mathop = 1}^n \frac {\partial f_k} {\partial x_k}$ holds only for flat spaces, so it should not be present in the general definition. The problem comes from the definition of standard ordered basis, because this is Cartesian basis in disguise. Relaxing this condition would help the general case. To deal with this properly we need differential geometry and manifold analysis. Or we can hide the details behind a red link. --Julius (talk) 19:08, 15 April 2020 (EDT)


 * Hide whatever details behind a redlink -- because this is all stuff which we will need to cover in due course. Are you able to put this in some sort of order? It would be appreciated. Does a similar consideration apply to gradient and curl? --prime mover (talk) 01:04, 16 April 2020 (EDT)


 * I will do it. As for gradient and curl, they also suffer from the same problems. Check https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates for comparison. --Julius (talk) 06:27, 16 April 2020 (EDT)