**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.

- 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.

# | 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 |