 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/4/a/i/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

\oint_{C} f (z) d z = 2 πi z_{k} inside C \sum 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.

 New to topics? Read the docs here!