More mathematically, nabla (∇, ∇ in

HTML) is a

3D vector that is composed of the three

partial derivatives, this means :

( ∂/∂x, ∂/∂y, ∂/∂z)

It can be used to represent a number of vector operations on

scalar fields or

vector fields.

For instance,

**grad** F = ( ∂F/∂x, ∂F/∂y, ∂F/∂z) =( ∂/∂x, ∂/∂y, ∂/∂z)F=**∇** F

**curl F**= **∇** × **F** //not demonstrated because of the formatting limitations of E2

- div
**F**=∂F_{x}/∂x,∂F_{y}/∂y,∂F_{z}/∂z =( ∂/∂x, ∂/∂y, ∂/∂z).(F_{x},F_{y},F_{z})=**∇** . **F**

- Δ F=( ∂
^{2}F/∂x^{2}, ∂^{2}F/∂y^{2}, ∂^{2}F/∂z^{2}) = ( ∂/∂x, ∂/∂y, ∂/∂z).( ∂/∂x, ∂/∂y, ∂/∂z)F = div **grad** F= ∇^{2}F.

That pretty much sums it up, two vector field, two scalar fields, two applied on scalar fields, two applied on vector fields.