/sci/ - Science & Math

Could someone please explain vector fields in polar coordinates to me? Every explanation so far has used engineering notation, and I feel I don't grasp it well enough to change notation, which is a bad sign.

I understand vector fields in Cartesian coordinates well enough, but the unit vectors depending on our angle seems strange to me, and I'm not even sure how you would express that without resorting to engineering notation, but of course it must be possible.