Changes

where <math>\hat x</math>, <math>\hat y</math>, and <math>\hat z</math> are the unit basis vectors.

where <math>\hat x</math>, <math>\hat y</math>, and <math>\hat z</math> are the unit basis vectors.

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the cross product notation makes sense.  This is also useful for remembering how to calculate a curl.

If one thinks of <math>\nabla</math> as being a fictional vector field with components <math>(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z})</math>, one can sort of see that the [[cross product]] notation makes sense.  This is also useful for remembering how to calculate a curl.

The curl is a true vector field operation&mdash;the result is independent of the coordinate system that is used.

The curl is a true vector field operation&mdash;the result is independent of the coordinate system that is used.

The curl operation has an intrinsic "handedness" to it.  Any physical phenomenon described by the curl operation (for example, magnetic fields), involves some kind of "right-hand rule."

The curl operation has an intrinsic "handedness" to it.  Any physical phenomenon described by the curl operation (for example, [[magnetic field]]s), involves some kind of "[[right-hand rule]]."

The curl is an extremely important operation in physics, mathematics, and engineering.  It is perhaps most famous for its appearance in [[Maxwell's Equations]].

The curl is an extremely important operation in physics, mathematics, and engineering.  It is perhaps most famous for its appearance in [[Maxwell's Equations]].

==References==

==References==

{{reflist}}

{{reflist}}

[[Category:Calculus]]

[[Category:Calculus]]

[[Category:Physics]]

[[Category:Physics]]