MTL506: Complex Analysis

4 Credits (3-1-0)

Field of complex numbers, complex plane, polar representation, stereographic projection.

Analytic functions, Cauchy-Riemann equation, harmonic conjugates, power series, MÖbius transforms.

Contour integrals, power series representation of an analytic function, zeros of an analytic function, Liouville’s theorem and applications.

Index of a closed curve, Cauchy’s theorem, Cauchy integral formula, Open mapping theorem, Goursat’s theorem.

Isolated singularities, Laurent Series, Residue theorem and application to real integrals. Meromorphic functions, Argument principle and Rouche’s theorem.

Maximum modulus principle and Schwarz’s Lemma.