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
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {IV}$: The Operator $\nabla$ and its Uses: $3 a$. The Operation $\nabla \cdot \mathbf V$
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: The Gradient: $22.30$