\begin{definition}[Definition:Laplacian/Scalar Field]
Let $\R^n$ denote the real Cartesian space of $n$ dimensions.
Let $\map U {x_1, x_2, \ldots, x_n}$ be a scalar field over $\R^n$.
Let the partial derivatives of $U$ exist throughout $\R^n$.
The '''Laplacian of $U$''' is defined as:
:$\ds \nabla^2 U := \sum_{k \mathop = 1}^n \dfrac {\partial^2 U} {\partial {x_k}^2}$
\end{definition}