Solution
= Solution
Let $f$ be <meromorphic> on and inside a positively oriented simple closed <contour> $C$, with finitely many isolated poles $z_k$ inside and none on $C$. The <residue theorem> states
$$
\boxed{\oint_C f(z)\,dz=2\pi i\sum_{z_k\text{ inside }C}\operatorname{Res}_{z=z_k}f(z).}
$$
The positive orientation is counterclockwise. A clockwise contour reverses the sign, and the <residue> is the coefficient of $(z-z_k)^{-1}$ in the local <Laurent series>.