Curl of a Vector Field
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Curl of a vector field in \(\mathbb{R}^3\)
Previously we defined a divergence of a vector field in \(\mathbb{R}^2\) that measures a local expansion of the field. We then easily extended the formula to \(\mathbb{R}^3\).
Even earlier, we found a formula for calculating a local circulation of a vector field in \(\mathbb{R}^2\). However, there does not seem to be any easy obvious way how to extend that to \(\mathbb{R}^3\). Here we will attempt to do just that: