Course Archives    Theoretical Statistics and Mathematics Unit

Course: Complex Analysis Time: Currently not offered Level: Postgraduate

Syllabus Past Exams Syllabus: A review of basic Complex Analysis: Cauchy-Riemann equations, Cauchy theorem and estimates. power series expansions, maximum modulus principle, Classification of singularities and calculus of residues. Normal families, Arzela theorem. Product developments, functions with prescribed zeroes and poles, Hadamard theorem. Conformal mappings, the Riemann mapping theorem, the linear fractional transformations. Depending on time available, some of the following topics may be done : (i) Subharmonic functions, the Dirichlet problem and Green functions. (ii) An introduction to elliptic functions. (iii) Introduction to functions of several complex variables. Suggested Texts : 1. L. V. Ahlfors, Complex analysis. An introduction to the theory of analytic functions of one complex variable, McGraw-Hill (1978). 2. J. B. Conway, Functions of one complex variable, GTM (159), Springer- Verlag (1995). 3. W. Rudin, Real and complex analysis, McGraw-Hill (1987). 4. R. Narasimhan and Y. Nievergelt, Complex Analysis in One Variable, Birkhauser (2001). Evaluation: Midterm Exam 30 marks Assignment 20 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 10.pdf 12.pdf 14.pdf 16.pdf 18.pdf 20.pdf Solution 10.pdf 12.pdf 14.pdf Semestral 06.pdf 10.pdf 12.pdf 16.pdf 18.pdf Supplementary and Back Paper 06.pdf 10.pdf 16.pdf 18.pdf Top of the page

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