Cauchy's theorem Cauchy's integral formula. Liouville's theorem for entire functions. Maximum modulus theorem. Fundamental theorem of algebra. Formula for coefficients in complex Taylor series.
Analytic functions are infinitely differentiable.
Calculus of residues. Definitions of pole of order m, simple pole, removable singularity, essential singularity, residue. Cauchy's residue theorem. Postgraduate Module Catalogue Information set up and maintained by Geoff Lidster .