MTH321(SPRING 2021) (COMPLEX ANALYSIS)

This is an undergraduate course on complex analysis. First class test will be on 26th February 2021.

Quiz dates:


  1. Quiz 1-26/02

  2. Quiz 2:-19/03

  3. Quiz 3-23/04

  4. Quiz 4-11/05 5 pm (Please note a change of date due to semester break).

Class timing:

Tue-5-5.45 pm

Thursday 5-5.45 pm

Friday 3-3.45 pm (live classes)

Office hours

Wednesday 4-5 pm.

Main reference:-

1. Complexanalysis (undergraduate text in mathematics), Joseph Bak and Donald Newmann (Springer).

Other references.

  1. Complex analysis, E. Freitag and R. Bosum, Universitext (Springer).

  2. Function Theory of One Complex Variable: R.E. Greene and S.G. Krantz (2006) AMS

  3. Complex Analysis: L. Alhfors (1979) McGraw Hill

  4. Functions of One Complex Variable I: J.B. Conway
    (1978) GTM Springer

  5. Complex Analysis (Princeton Lectures in Analysis):
    E.M. Stein, R. Shakarchi (2003) Princeton University
    Press

  6. Complex Function Theory: Donald Sarason (2007)
    AMS


Grading :

  1. Mid-Semester Exams-30%

  2. End-Semester Exams-30%.

  3. 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

  1. 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.

.