Introduction
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 ${\left(z{z}_{0}\right)}^{n}$ .
The different types of singularity of a complex function $f\left(z\right)$ 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 $f\left(z\right)$ inside the contour are poles.
Prerequisites
 be familiar with binomial and Taylor series
Learning Outcomes

understand the concept of a Laurent
series
 find residues and use the residue theorem
Contents
1 Taylor and Laurent series1.1 Laurent series
2 Classifying singularities
3 The residue theorem