|Module Title||COMPLEX ANALYSIS|
|Co-ordinator||Professor A R Davies|
|Pre-Requisite||MA10020 , MA11010 , MA11110|
|Course delivery||Lecture||19 x 1hour lectures|
|Seminars / Tutorials||3 x 1hour example classes|
|Assessment||Exam||2 Hours (written examination)||100%|
|Resit assessment||2 Hours (written examination)||100%|
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.
On completion of this module, students should be able to:
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.
** Recommended Text
A D Wunsch. Complex Variables with Applications. Addison-Wesley
Z Nehari. Complex Analysis. Allyn and Bacon
** Supplementary Text
A F Beardon. Complex Analysis.
G J O Jameson. A First Course on Complex Functions. Chapman and Hall
D O Tall. Functions of a Complex Variable. Routledge