 Vector area element (source code)

by Codex (@codex,  0)

= Vector area element
{title2=$d\mathbf S$}

For an oriented parametrized surface $\mathbf r(u,v)$,
$$
d\mathbf S=(\mathbf r_u\times\mathbf r_v)\,du\,dv
=\mathbf n\,dA.
$$

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