### MA 205 – Complex Analysis

**Session:** 2018-19

**Instructor:** Bata Krishna Das

**Course Content:**

Definitions and properties of analytic functions, Cauchy Riemann equations, harmonic functions, Power series and their properties, Elementary functions, Cauchy’s theorem and it’s applications, Taylor series and Laurent expansion, Residues and the Cauchy residue formula, Evaluation of improper integrals, Conformal mappings, Inversion of Laplace transforms

**Prerequisite:** MA 105

**Feedback on the lectures:**

The lectures were a bit dull in terms of flair, but the professor answered all the doubts by the students. Attendance was not compulsory, nor did the professor enforce it.

**Feedback on Assignments/Tutorials:**

Tutorials were not too challenging, but were important. Many students ended up not attending the tutorials, but doing this course without attending tutorials is hard, which also might explain the low grade cutoffs. They are short and don’t require more than simple turning up for the tutorial (and maybe spending at most an hour later reviewing material) – so be sure to take these seriously.

The quiz was not challenging. It had a couple of straightforward questions just to test that you knew the material.

The midsem had 5 questions of 7 marks each, and some of these depended on a good insight into the problem – thus, you need to be alert to try out different theorems that you’ve learnt and keep trying to apply them to the setting. If you had actually gone through all the material, 4 out of 5 problems were direct applications. One was a functional equation that depended on the insight that depended on some nice inequality argument, and the only subpart which required thinking beyond the material. So, keep looking out for the easy questions.

This was a half-semester course, so there were only 2 exams.

**Difficulty (on a scale of 1-5 with 5 being very tough):** 3

**Textbooks/References:** R.V. Churchill and J.W. Brown, Complex variables and applications

**Comments:**

Don’t take this course too lightly and leave it for the last weekend – keep up with the pace of the class. Otherwise, this is a difficult course to handle – especially, in sem 3 where the midsem of this course might clash with some other courses. So, be prepared and be on top of the material being covered.

Reviewed by - **Shubham Anand Jain**