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Prof Amol Sasane

This course is available on the BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. 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 objects of study in the course will be complex differentiable functions in domains, 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 and its consequences, Taylor and Laurent series, and harmonic functions. The core results will be illustrated with computational examples and applications.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Autumn Term.

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 spring exam period.