Surface gradient

In the vector analysis of the surface gradient denotes a differential operator similar to the gradient. Here, the gradient along a surface is formed.

Definition

For a surface in a scalar field of the surface gradient is defined as

Here, the unit normal vector to the designated area. Thus, the surface gradient represents the ordinary gradient without the normal to the surface proportion dar. It is therefore tangent to the surface. The surface gradient can also be interpreted as an orthogonal projection of the gradient on the surface.