The Calculus of Residues

The residue theorem

Let be analytic in a simply connected domain except a finite number of isolated singularities . Let be a closed counter clockwise contour in that encloses all . Then:

We often make use of Jordan’s Lemma when calculating an integral along a half circle when .

We do various stuff like keyhole contours and rectangular contours. Can’t be bothered to put examples here. Look in notes.