This is an undergraduate course on complex analysis. First class test will be on 26th February 2021.
Quiz dates:
Quiz 1-26/02
Quiz 2:-19/03
Quiz 3-23/04
Quiz 4-11/05 5 pm (Please note a change of date due to semester break).
Tue-5-5.45 pm
Thursday 5-5.45 pm
Friday 3-3.45 pm (live classes)
Office hours
Wednesday 4-5 pm.
1. Complexanalysis (undergraduate text in mathematics), Joseph Bak and Donald Newmann (Springer).
Complex analysis, E. Freitag and R. Bosum, Universitext (Springer).
Function Theory of One Complex Variable: R.E. Greene and S.G. Krantz (2006) AMS
Complex Analysis: L. Alhfors (1979) McGraw Hill
Functions of One Complex Variable I: J.B. Conway
(1978) GTM Springer
Complex Analysis (Princeton Lectures in Analysis):
E.M. Stein, R. Shakarchi (2003) Princeton University
Press
Complex Function Theory: Donald Sarason (2007)
AMS
Grading :
Mid-Semester Exams-30%
End-Semester Exams-30%.
Class tests (4):-10% (each).
Please note that there will not be any repeat class tests.
Week 1
Complex differentiation, Cauchy-Riemann equations.
Power series, Exponential and logarithms. Assignment 1 uploaded.
Week 2
Holomorphic anti-derivatives, integrations
Complex line integrals.
Tutorial
Week 3
Cauchy-Goursat's theorem on triangles.
Cauchy's integral formula and it's applications.
Week 4
Tutorial on Cauchy's Theorems.
Week 5
Class test 1.
Power series representation of analytic functions.
Morera's theorem.
Week 6
Schwarz reflection principle.
Zeros of an analytic function
Week 7
Singularities.
Revision.
Week 8
Laurent series expansion.
Argument principle and Residue theorem.
Quiz 3
Week 9
Residue theorem and
Rouche's theorem and Maximum modulus principle
Week 10
Teaching break
Week 11
Quiz 4
Open mapping theorem and Maximum modulus principle.
Schwarz lemma.
Week 12
Conformal maps.
Automorphism of unit disc.
Week 13
Tutorial .
Week 14
End-sem exam.
.