Retrieving "2 Forms" from the archives

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1. Exterior Derivative

   Linked via "2-form"

   | Gradient | Function $f$ (0-form) | $k=0$ | $\text{d}f = \frac{\partial f}{\partial x} dx \wedge dy \wedge dz$ (after cyclic permutation) | $\text{grad} f$ |
   | Curl | Vector field $\mathbf{V}$ (via its dual 1-form) | $k=1$ | $\text{d}\omega$ | $\text{curl} \mathbf{V}$ |
   | Divergence | Vector field $\mathbf{V}$ (via its dual 2-form) | $k=2$ | $\text{d}\alpha$ | $\text{div} \mathbf{V}$ (with a sign convention) |
   Note that the standard identification of [divergence](/entries/diver…