Complex Analysis

Code: MA1610H | L-T-P-C: 3-1-0-4

Complex numbers and elementary properties; Complex functions - limits, continuity and differentiation, Cauchy-Riemann equations, analytic and harmonic functions, elementary analytic functions, anti-derivatives and line (contour) integrals, Cauchy-Goursat theorem, Cauchy's integral formula, Morera's theorem, Liouville's theorem, Fundamental theorem of algebra, Maximum modulus principle; Power series, Taylor series, zeros of analytic functions, singularities and Laurent series, Rouche's theorem and argument principle, residues, Cauchy's Residue theorem,  Applications of Residues; Conformal mappings, Mobius transformations.

Texts:

• J. W. Brown and R. V. Churchill, Complex Variables and Applications, Seventh Edition, McGraw Hill, 2004.

 

References:

• J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, Third Edition, Narosa,1998.
• S. Ponnusamy, Foundation of Complex Analysis, Narosa, 2011.