Complex Analysis

Code: MA547 | L-T-P-C: 3-1-0-8

Review of complex numbers; Analytic functions, harmonic functions, elementary functions, branches of multiple-valued functions, conformal mappings; Complex integration, Cauchy's integral theorem, Cauchy's integral formula, theorems of Morera and Liouville, maximum-modulus theorem; Power series, Taylor's theorem and analytic continuation, zeros of analytic functions, open mapping theorem; Singularities, Laurent's theorem, Casorati-Weierstrass theorem, argument principle, Rouche's theorem, residue theorem and its applications in evaluating real integrals.

Texts:

1. R.V. Churchill and J.W. Brown, Complex Variables and Applications, 5th edition, McGraw Hill, 1990.
2. J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, 3rd edition, Narosa, 1998.

References:

1. L. V. Ahlfors, Complex Analysis, 3rd Edn., McGraw Hill, 1979.
2. J. E. Marsden and M. J. Hoffman, Basic complex analysis, 3rd Edn., W. H. Freeman, 1999.
3. D. Sarason, Complex function theory, 2nd Edn., Hindustan book agency, 2007.
4. J.B. Conway, Functions of One Complex Variable, 2nd Edn., Narosa, 1973.