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 .
The different types of singularity of a complex function 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 inside the contour are poles.
- be familiar with binomial and Taylor series
understand the concept of a Laurent
- find residues and use the residue theorem
1.1 Laurent series
2 Classifying singularities
3 The residue theorem