Module Identifier MX31510  
Academic Year 2003/2004  
Co-ordinator Professor Russell Davies  
Semester Semester 2  
Pre-Requisite MA10020 , MA11010 , MA11110  
Mutually Exclusive MA21510  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, students should be able to:

Brief description

Complex analysis is the study of complex valued functions of a complex variable. It is, on the one hand, a fruitful area of pure mathematics exhibiting many elegant and surprising results, while, on the other, the theory has numerous applications in many branches of mathematics and engineering. The important role of complex variables in applied mathematics, for instance, is partly due to the use of the theory of residues in the evaluation of certain real integrals and the application of conformal mapping in hydrodynamics and problems in potential theory.


The aim of the module is to study the theoretical foundations of complex variable theory and to develop skills in the application of this theory to particular problems. These skills are a necessary prerequisite to the study of some topics in other modules in the department.


1. Revision of the Elementary Properties of Complex Numbers.
2. Cauchy-Riemann Equations. Analytic functions. Necessary and sufficient conditions for a function to be analytic.
3. Contour Integration. The fundamental theorem of integration.
4. Cauchy's theorem. Cauchy's integral formula, including the general version.
5. Taylor series.
6. Laurent series.
7. Theory of residues.

Reading Lists

** Recommended Text
A D Wunsch (1994) Complex Variables with Applications 2nd. Addison-Wesley 0201122995
Z Nehari (1961) Introduction to Complex Analysis Allyn and Bacon
** Supplementary Text
A F Beardon (1979) Complex Analysis Wiley 0471996726
G J O Jameson (1979) A First Course on Complex Functions Chapman and Hall 0412097109
D O Tall Functions of a Complex Variable Routledge 0710086555


This module is at CQFW Level 6