Pre-Quantum Electrodynamics

\begin{align} {\boldsymbol \nabla} \cdot {\bf v} &= \left( \hat{\bf x} \frac{\partial}{\partial x} + \hat{\bf y} \frac{\partial}{\partial y} + \hat{\bf z} \frac{\partial}{\partial z} \right) \cdot \left(v_x ~\hat{\bf x} + v_y ~\hat{\bf y} + v_z ~\hat{\bf z} \right) \nonumber \\ &= \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z}. \label{Gr(1.40)} \end{align}