Editing Operator (mathematics) (section)

=== Fundamental analysis operators on scalar and vector fields ===
{{Main|Vector calculus|Vector field|Scalar field|Gradient|Divergence|Curl (mathematics)|l6=Curl}}

Three operators are key to [[vector calculus]]:
* Grad ([[gradient]]), (with operator symbol [[del|<math>\nabla </math>]]) assigns a vector at every point in a scalar field that points in the direction of greatest rate of change of that field and whose norm measures the absolute value of that greatest rate of change.
* Div ([[divergence]]), (with operator symbol [[del#Divergence|<math>{\nabla \cdot} </math>]]) is a vector operator that measures a vector field's divergence from or convergence towards a given point.
* [[curl (mathematics)|Curl]], (with operator symbol [[del#Curl|<math>\nabla \!\times </math>]]) is a vector operator that measures a vector field's curling (winding around, rotating around) trend about a given point.

As an extension of vector calculus operators to physics, engineering and tensor spaces, grad, div and curl operators also are often associated with [[tensor calculus]] as well as vector calculus.<ref name=Schey-2005>{{cite book |first=H.M. |last=Schey |year=2005 |title=Div, Grad, Curl, and All That |location=New York, NY |publisher=W.W. Norton |isbn=0-393-92516-1}}</ref>