Course Archives Theoretical Statistics and Mathematics Unit | ||||||||||||||||||
Course: Complex Analysis Time: Currently not offered Level: Postgraduate |
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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:
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Midterm
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[ Semester Schedule ][ SMU ] [Indian Statistical Institute] |