Dr Amol Sasane

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Solid grounding in mathematics, especially analysis, in particular MA203 Real Analysis.

The course will cover the fundamental concepts and methods in complex analysis. The basic object of study in the course will be a complex differentiable function in a region, and the far-reaching consequences of the notion complex differentiability will be dealt with in the course. The specific topics that will be covered are: the geometry of complex numbers, complex differentiation, Cauchy-Riemann equations, Cauchy's integral theorem, Cauchy's integral formula, Taylor series. We continue by covering: Liouville's Theorem, Maximum Modulus Theorem, Rouche's Theorem. We also give a brief introduction to Laurent Series and use of the Residue Theorem. The core results will be illustrated with computational examples and applications.

22 hours of lectures and 10 hours of classes in the LT.

Written answers to set problems will be expected on a weekly basis.

(1) S.D. Fisher. Complex Variables. Corrected reprint of the second (1990) edition, Dover Publications, Inc., Mineola, NY, 1999.

(2) J.E. Marsden and M.J. Hoffman. Basic Complex Analysis. Second edition, W. H. Freeman and Company, New York, 1987.

(3) D.O. Tall. Functions of a Complex Variable. Routledge and Kegan Paul, London, 1985

Exam (100%, duration: 2 hours) in the main exam period.