Key terms and concepts for sections 14.7-14.8

• The curl of a vector field. Mnemonic: \(\nabla\times\mathbf F\).
• Stokes' theorem:

\[ \oint_{\partial S}\mathbf{F}\cdot\mathrm{d}\mathbf{r} = \iint_S\mathrm{curl}\,\mathbf{F}\cdot\mathbf{n}\,\mathrm d\sigma \]

• Gradient fields have zero curl, and curls have zero divergence:

\[ \mathrm{curl}\,\mathrm{grad}\, f = 0 \quad\quad\quad\quad \mathrm{div}\,\mathrm{curl}\,\mathbf{F} = 0 \]