MA 4060: Complex Analysis
Class timings:
Monday: 11:00 am to 11:55 am
Wednesday: 10:00 am to 10:55 am
Thursday: 09:00 am to 09:55 am
Examination and Grades:
The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.
Syllabus:
Spherical representation of extended complex plane, Analytic Functions, Harmonic Conjugates, Elementary Functions, Cauchy Theorem and Integral Formula, Homotopic version
Linear fractional transformations, Power Series, Analytic Continuation and Taylor's theorem, Zeros of Analytic functions, Hurwitz Theorem, Maximum Modulus Theorem, Laurent's Theorem, Classification of singularities
Residue theorem and applications, Argument Principle, Theorem of Rouche, Schwarz-Christoffel Transformation.
References:
- T.W. Gamelin, Complex analysis. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2001.
- J.W. Brown, R.V. Churchill, Complex Variables, McGraw Hill, 8th Edition, 2010.
- L. Ahlfors, Complex analysis, Mc Graw Hill, 1979.
- J. B. Conway, Functions of one Complex Variables, Springer, 2nd Edition, 1978.
- A.R. Shastri, Basic Complex Analysis of one variable, Mc Millan, New Delhi, 2011.
- S. Kumaresan. A Pathway to Complex Analysis. Techno World, 2021.