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The circulation of a function is the summation of the values it takes at each point on a closed curve (a loop), which is also known as its line integral over a contour. For a conservative vector field, the circulation is zero, but the circulation of the velocity of a fluid is rarely zero.

A mathematical expression for the circulation of the vector Pi + Qj is over contour C:

\oint_{C} (P\, \mathrm{d}x + Q\, \mathrm{d}y)

Green's Theorem provides a method for easily calculating circulations.

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