I am teaching complex analysis (MA 224) during the Jan-April 2023 semester.
Course details:
Class timings: Mondays, Wednesdays, Fridays, 10-11:00 am.
Office hours: tba
Team code: xk3u17o
Brief description
The main topics and results that we will be covering in this course are
Holomorphic functions Analytic functions, Power series
Meromorphic functions, Residue formula, Singularities, Complex Logarithms
Entire functions, Picard's theorem, Weierstrass infinite products, Hadamard's factorization theorem
Conformal maps, Schwarz Lemma, Riemann mapping theorem.
If time permits, we will discuss the Prime Number Theorem.
Grading
There will be a homework assignment every other week. The lowest homework score is dropped.
Homework: 50%
Midterm exam: 20%
Final exam 30%
Prerequisites
MA 221 (Analysis I: Real Anaysis)
Some familiarity with the following topics will be expected:
Limits, continuous functions, differentable functions, radius of convergence, integration, open sets and exponential, trigonometric, logarithmic functions.
(see Chapter 1 of Stein and Shakarchi)
References
The main reference textbook for this course will be
Complex Analysis by Stein and Shakarchi
We intend to cover the following chapters
Chapter 1: Preliminaries to Complex Analysis
Chapter 2: Cauchy's theorem and its applications
Chapter 3: Meromorphic functions and the logarithm
Chapter 5: Entire functions
Chapter 8: Conformal mappings
If time permits, we will cover Chapter 7 (
The Zeta function and the Prime-Number Theorem).
Here are other references that you may also consult:
Functions of one complex variable by Conway
Complex analysis by Ahlfors
Complex analysis by Gamelin
Introduction to Complex Analysis by Shabat
Miscellaneous:
There will be no backup exams. The exams will not be rescheduled. No late homework will be accepted. Instead, the lowest homework score will be dropped.
Emails: If you would like to send me an email about this course, please write MA 224 in the subject. If you would like to discuss mathematics, I encourage you to come to my office hours, rather than discuss it over email.
Discussions: You are encouraged to discuss homework questions and the course content on the discussion forum on MS Teams. If you have a mathematical question, I will redirect you to the discussion forum and ask you to post it here so that it may benefit everyone.
Ethics: Obtaining external help (for e.g. seeking solutions on the internet, requesting
solutions on external forums, discussing with students not in this course, etc) will be considered plagiarism. On the other hand, you are encouraged to discuss with other students in this course. Please read the IISC student ethics guide. I will expect you to be ethical.
