\begin{definition}[Definition:Laplacian/Scalar Field/Cartesian 3-Space]
Let $R$ be a region of Cartesian $3$-space $\R^3$.
Let $\map U {x, y, z}$ be a scalar field acting over $R$.
The '''Laplacian of $U$''' is defined as:
:$\nabla^2 U := \dfrac {\partial^2 U} {\partial x^2} + \dfrac {\partial^2 U} {\partial y^2} + \dfrac {\partial^2 U} {\partial z^2}$
where $\nabla$ denotes the del operator.
\end{definition}