Definition:Divergence Operator/Cartesian 3-Space

Definition
Let $R$ be a region of Cartesian $3$-space $\R^3$.

Let $\map {\mathbf V} {x, y, z}$ be a vector field acting over $R$.

Let $\tuple {i, j, k}$ be the standard ordered basis on $\R^3$.

The divergence of $\mathbf V$ is defined as:

Also see

 * Divergence Operator on Vector Space is Dot Product of Del Operator