Solution
= Solution
In the Cartesian <basis>, writing $F=(F_1,F_2,F_3)$,
$$
\boxed{\nabla\cdot F
+=\partial_iF_i
+=\frac{\partial F_1}{\partial x}
++\frac{\partial F_2}{\partial y}
++\frac{\partial F_3}{\partial z}}
$$
defines the <divergence>, while the <curl> is
$$
\boxed{(\nabla\times F)_i
+=\epsilon_{ijk}\partial_jF_k}.
$$
Equivalently,
$$
\nabla\times F=
+(\partial_yF_3-\partial_zF_2)e_x
++(\partial_zF_1-\partial_xF_3)e_y
++(\partial_xF_2-\partial_yF_1)e_z.
$$