\begin{definition}[Definition:Divergence Operator/Real Cartesian Space]
Let $\map {\R^n} {x_1, x_2, \ldots, x_n}$ denote the real Cartesian space of $n$ dimensions.
Let $\tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be the standard ordered basis on $\R^n$.
Let $\mathbf f = \tuple {\map {f_1} {\mathbf x}, \map {f_2} {\mathbf x}, \ldots, \map {f_n} {\mathbf x} }: \R^n \to \R^n$ be a vector-valued function on $\R^n$.
Let the partial derivative of $\mathbf f$ with respect to $x_k$ exist for all $f_k$.
The '''divergence of $\mathbf f$''' is defined as:
{{begin-eqn}}
{{eqn | l = \operatorname {div} \mathbf f
      | o = :=
      | r = \nabla \cdot \mathbf f
}}
{{eqn | r = \paren {\sum_{k \mathop = 1}^n \mathbf e_k \dfrac \partial {\partial u_k} } \cdot \mathbf f
      | c = {{Defof|Del Operator}}
}}
{{eqn | r = \sum_{k \mathop = 1}^n \dfrac {\partial f_k} {\partial x_k}
      | c = 
}}
{{end-eqn}}
\end{definition}