Lecture Format and Access to Resources. Lectures will be held on Microsoft Teams. All the resources related to the course (recordings of the lectures, notes, assignments, etc.) will be posted on the MA 224 team page. If you wish to attend this course, please add yourself to the MA 224 team using the team link/code available on the IISc intranet bulletin board.
Instructor. Purvi Gupta (purvigupta(at)iisc(dot)ac(dot)in)
Tutor/TA. Pritam Ganguly (pritamg(at)iisc(dot)ac(dot)in)

Lectures. MWF 2:00 - 3:00 pm.
Tutorials. M 6:00 - 7:00 pm (first session: Mar. 08).
Office hours. TBA.

Course Description. This course will be an introduction to complex analysis in one variable. We will cover the standard topics (listed below) for a course at this level. If time permits, we will cover one or two topics in addition to the ones listed below.

Basic properties of complex numbers. Complex differentiation, holomorphicity and the Cauchy—Riemann equations. Complex integration, Cauchy’s theorem and integral formula, power series representability, and Liouville’s theorem. Simply connected domains. Isolated singularities, residues, and the argument principle. The open mapping theorem, the maximum modulus principle and Rouché’s theorem. Conformal mappings, Schwarz’s lemma, automorphisms of the disc and the complex plane. Normal families and Montel’s theorem. The Riemann mapping theorem.

Suggested References.
  • L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979.
  • J. B. Conway, Functions of One Complex Variable, Springer-Verlag, 1978.
  • For more practice problems: Complex Analysis by T. W. Gamelin and/or Complex Analysis by E. M. Stein and R. Shakarchi.

Evaluation Scheme.
Course Calendar. Typically, I will update the calendar twice a week --- on Saturdays (to update the upcoming week's plan), and on Wednesdays (to post assignments).

# Date (Day) Topics Assignment Tracker
1. 22/02 (M) Basic properties of the complex plane
2. 24/02 (W) Topological properties of the plane; C-linearity Assignment 1
3. 26/02 (F) Holomorphicity and analyticity
4. 01/03 (M) Examples of holomorphic functions
5. 03/03 (W) Examples (contd.) and conformality Assignment 2 will be posted.
6. 05/03 (F) Complex Integration