Infinitesimal calculus MOC

Curl

The curl of a vector field is a measurement of the field’s tendency of a field to twist. It is given by

where is the nabla operator (sometimes called ). The formula for curl is actually derived by an infinitesimal circulation integral. Let be filled disc at with normal and area . Then curl is given by

Properties

• If everywhere, then is a Conservative vector field.
• Conversely, for any continuous, smooth , (this is easy to prove by Clairaut’s theorem).

Practice problems

These practice problems are for both curl and Divergence.

• 2016. Calculus, p. 1149 (§16.5 exercises)

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