
Green's Theorem
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Mathematics/Calculus
Green's TheoremTheorem 1. Let $C$ be a piecewise smooth, simple closed curve enclosing a region $R$ in the plane. Let $\mathbf{F}(x, y) = \langle M(x, y), N(x, y) \rangle$ be a vector field with $M$ and $N$ having continuous first partial derivatives in an open region containing $R$. Then the counterclockwise circulation of $\mathbf{F}$ around $C$ equals the double integral of $(\nabla \times \m..