Definition:Gradient Operator/Geometrical Representation

Definition
Let $R$ be a region of space.

Let $F$ be a scalar field acting over $R$.

The gradient of $F$ at a point $A$ in $R$ is defined as:


 * $\grad F = \dfrac {\partial F} {\partial n} \mathbf {\hat n}$

where:
 * $\mathbf {\hat n}$ denotes the unit normal to the equal surface $S$ of $F$ at $A$
 * $n$ is the magnitude of the normal vector to $S$ at $A$.

Also see

 * Justification for Geometrical Representation of Gradient Operator