Gradient of a Vector

The gradient is a vector operation that operates on a scalar function to produce a vector. The vector's magnitude is the maximum rate of change of the function at the point of the gradient, is pointed in the direction of that maximum rate of change.

"Ñ" is a vector and is pronounced "del." The scalar function is V(x,y,z), V(r,Φ,z), or V(r,θ,Φ)

The divergence of a gradient is know as the LaPlacian.

Cartesian Coordinates

Cylindrical Coordinates

Spherical Coordinates