Complex analysis
4 points * First semester * Clayton * Prerequisites: MAP2011, MAT2020
The complex field. Curves in the complex plane. Holomorphic functions. Contour integrals. Cauchy's theorem and its consequences: Cauchy's formulae, Cauchy's inequalities, Liouville's theorem. Singularities, Laurent and Taylor series. Applications: the fundamental theorem of algebra; maximum modulus theorem; the theory of residues; evaluation of real integrals; counting zeros.
Assessment
Examinations (1.5 hours): 73% * Assignments: 27%
Prescribed texts
Stewart I and Tall D Complex analysis CUP, 1983