This is an undergraduate course on complex analysis. Please read the course template (attachment) for text-books and other important information about the course.
There will be tutorials every Wednesday. There will be short tests on the tutorials of 30 minutes duration starting from 13/01/2016.
The TA for the course Mr. Tathagat mandal. His office A 426.
Office hours
Wednesday 3-4 pm.
Tathagat
Monday 4-5 pm
Grading :
Please note that there will not be any repeat class tests. If you are absent in any of the two class tests then we will use the short test points that are NOT used in the short test performances (1 class test=2 short tests).
First class test will be on 01/02/2016.
Second class test will be on 04/04/2016.
Week 1
04/01/2016: Complex differentiation, Cauchy-Riemann equations.
Course template updated. I have updated main reference and other supplementary references.
06/01/2016: Power series, Exponential and logarithms. Assignment 1 uploaded.
07/01/2016: Tutorial at Madhava Hall (Main building 3rd Floor) at 12 noon.
Week 2
11/01/2016: Holomorphic anti-derivatives, integrations
12/01/2016: Complex line integrals.
13/01/2016: Short test, Tutorial. Assignment 2 uploaded.
Week 3
18/01/2016: Cauchy-Goursat's theorem on triangles.
19/01/2016:Cauchy's integral formula and it's applications. Assignment 3 uploaded.
20/01/2016:Short test, Tutorial.
Week 4
I will be on academic leave this week. I will be attending a conference on "Cohomology of arithmetic groups" at the HCM, Bonn, Germany.
25/01/2016: Tutorial on Cauchy's Theorems by Tathagat Mandal.
26/01/2016: Institute holiday.
27/01/2016: Short test, Tutorial.
Week 5
01/02/2016: Class test 1. Chocolates if you do well in the exams.
02/02/2016: Power series representation of analytic functions.
03/02/2016: Morera's theorem.
05/02/2016: Assignment 4 uploaded.
Week 6
08/02/2016: Schwarz reflection principle.
09/02/2016: Zeros of an analytic function
10/02/2016: Short test, Tutorial.
Week 7
15/02/2016: Singularities.
16/02/2016: Revision.
17/02/2016:Short test, Tutorial.
Week 8
Mid-sem exam.
Week 9
29/02/2016: Tutorial.
01/03/2016:Laurent series expansion.
02/03/2016: Residue theorem.
03/03/2016: Assignment 6 uploaded.
Week 10
07/03/2016: Argument principle and Rouche's theorem.
08/03/2016: Maximum modulus principle and Open mapping theorem.
09/03/2016: Short test, tutorial.
10/03/2016: Assignment 7 uploaded.
Week 11
14/03/2016: Homotopy version of Cauchy's theorem.
15/03/2016: Schwarz lemma.
16/03/2016: Short test, tutorial.
17/03/2016:Assignment 8 uploaded.
Week 12
21/03/2016: Conformal maps.
22/03/2016: Automorphism of unit disc.
23/03/2016:Short test, tutorial. Assignment 9 uploaded
Week 13
28/03/2016: Linear fractional transformations
29/03/2016: Riemann mapping theorem (statement, examples and key steps).
30/03/2016:Short test, tutorial.
01/04/2016: Assignment 10 uploaded.
Week 14
04/04/2016: Class test II
05/04/2016: Sequence and series of complex functions, normal families and Arzela-Ascoli's theorem.
06/04/2016: Montel's theorem and completion of the proof of Riemann mapping theorem.
07/04/2016: Assignment 11 uploaded.
Week 15
11/04/2016: Tutorial: Residue theorem, homotopy version of Cauchy's theorem and conformal maps.
12/04/2016: Tutorial: Rouche's theorem, Maximum modulus principle and Schwarz Lemma.
13/04/2016: Short test, tutorial.
Week 16
End semester examination.