Definition:Divergence Operator/Cartesian 3-Space

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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 $R$.


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

\(\ds \operatorname {div} \mathbf V\) \(:=\) \(\ds \nabla \cdot \mathbf V\)
\(\ds \) \(=\) \(\ds \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}\) Definition of Dot Product


Also see

  • Results about the divergence operator can be found here.


Sources