Subject Code: MA5L007 Subject Name:  Complex Analysis L-T-P: 3-0-0 Credit: 3
Pre-requisite(s): Real Analysis (MA5L002)
Polar representation and roots of complex numbers; Spherical representation of extended complex plane; Elementary properties and examples of analytic functions: The exponential, Trigonometric functions,  Mobius transformations, Cross ratio; Complex  integration: Power series representation of analytic functions, Zeros of analytic functions,  Cauchy theorem and integral formula,  The index of a point with respect to a closed curve, the general form of Cauchy’s theorem;  Open Mapping Theorem;  Classification of singularities: Residue theorem and applications;  The Argument Principle; The Maximum modulus Principle;  Schwarz’s lemma; Phragmen-Lindelof theorem.
Text Books:
  1. Conway  J.B.  Functions of One Complex Variable,Narosa, New Delhi
  2. Ahlfors L. V. Complex Analysis, McGraw Hill
Reference Books:
  1.  Gamelin T.W. Complex Analysis, Springer International Edition
  2. Churchill  R.V.  and Brown  J.W. Complex Variables and Applications, McGraw Hill
  3. Rudin W.  Real and complex analysis,  McGraw-Hill Book Co