Laurent Series

Find the Laurent series about all singular points of {see attachment} Thanks.

Mapping (Quarter-Plane; Half-Line)

Find the image of the quarter-plane {see attachment} under the mapping {see attachment}. Show graphs (shaded regions) in the w-plane and identify the images of the half-lines {see attachment}.

Computing an Integral Using Residues

Use residue theory to compute the integral: (see attachment)

Classifying Isolated Singularities

Classify all the isolated singularities of the following functions (classify as removable, pole of order m, or essential). Explain the reasoning for each classification. *See attachment for functions*

Laurent Series

Find a Laurent series which converges for ... {see attachment for complete question}