Pre-Quantum Electrodynamics

\begin{align} {\boldsymbol \nabla} \times {\bf v} &= \left| \begin{array}{ccc} \hat{\bf x} & \hat{\bf y} & \hat{\bf z} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ v_x & v_y & v_z \end{array} \right| \nonumber \\ &= \hat{\bf x} \left(\frac{\partial v_z}{\partial y} - \frac{\partial v_y}{\partial z} \right) + \hat{\bf y} \left(\frac{\partial v_x}{\partial z} - \frac{\partial v_z}{\partial x} \right) + \hat{\bf z} \left(\frac{\partial v_y}{\partial x} - \frac{\partial v_x}{\partial y} \right) \label{Gr(1.41)} \end{align}