Course Archives    Theoretical Statistics and Mathematics Unit
Course: Complex Analysis
Time: Currently not offered
Level: Postgraduate
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).

Top of the page

Past Exams
10.pdf 12.pdf 14.pdf 16.pdf 18.pdf
10.pdf 12.pdf 14.pdf
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

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]