Retrieving "0 Forms" from the archives

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1. Exterior Derivative

   Linked via "0-form"

   | Operator | Form Input ($\omega$) | Degree ($k$) | Exterior Derivative ($\text{d}\omega$) | Equivalent Classical Operator |
   | :--- | :--- | :--- | :--- | :--- |
   | 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](/entrie…