Integrated MSc-PhD Program

SYLLABUS

KSM2C03: Complex Analysis

Complex numbers and geometric representation, analytic functions, power series, exponential and logarithmic functions, conformality, Mobius transformations, Complex integration, Cauchy’s theorem, Cauchy’s integral formula including the homotopy version, singularities, Taylor’s theorem, The maximum principle, The residue theorem and applications, Montel’s theorem and Riemann mapping theorem.

Suggested texts:

1. 1. 1. 1. 1. 1. Stein & Shakarchi, Complex Analysis, Princeton University press.
               2. John B. Conway, Functions of one complex variable, second ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978.
               3. Ahlfors L, Complex Analysis.
               4. Lecture notes of Terence Tao for the course 246A offered at UCLA.