Del Operator

The del operator operates on a scalar to produce a vector. Compare the ∇ operation to taking the time derivative. Where δ/δt means to take the derivative with respect to time and introduces a s^-1 component to the units of the result, the ∇ operation means to take the derivative with respect to distance (in 3 dimensions) and introduces a m^-1 component to the units of the result. ∇ terms may be called space derivatives and an equation which contains the ∇ operator may be called a vector differential equation. In other words ∇A is how fast A changes as you move through space.

In rectangular coordinates

In cylindrical coordinates

In spherical coordinates

See also: Divergence, Laplacian.