Cylindrical coordinates are often given as so that is azimuthal in the same sense as spherical polar, and so that is differentiated from . However, many other similar conventions are used. For example, or or are not uncommon. We will use in this review to avoid as much confusion as possible with spherical polar coordinates.

- Vectors:
But

**Note Well:**is now a function of ! Similarly:with a function of the angle that defines the direction of . Specifically:

- Unit vectors (relative to Cartesian
:
- Direct Length
- Directed Area
- Volume Element
- Gradient:
- Divergence;
The divergence is constructed by the same argument that proves the
divergence theorem in a general curvilinear coordinate system given
above.
- Curl
The curl is evaluated in exactly the same way from the expression above,
but it ends up being much more complex:
- Laplacian
The Laplacian follows by applying the divergence rule to the gradient
rule and simplifying: