\begin{definition}[Definition:Gradient Operator/Geometrical Representation]
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 $A$.
\end{definition}