Taylor’s series for functions of a real variable is generalised here to the Laurent series for a function of a complex variable, which includes terms of the form ( z z 0 ) n .

The different types of singularity of a complex function f ( z ) are discussed and the definition of a residue at a pole is given. The residue theorem is used to evaluate contour integrals where the only singularities of f ( z ) inside the contour are poles.


Learning Outcomes

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