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Subsection A.6.1 2-Forms

Definition A.6.1 2-form.

\begin{equation*} (dx \wedge dy)(\mathbf{v}_1, \mathbf{v}_2) = dx(\mathbf{v}_1)dy(\mathbf{v}_2) - dx(\mathbf{v}_2)dy(\mathbf{v}_1) \end{equation*}

Note A.6.2.

For this definition, we assume \(\mathbf{v}_1\) and \(\mathbf{v}_1\) are both 2D vectors.