MA4060-Complex analysis

• Spherical representation of extended complex plane, Analytic Functions, Harmonic Conjugates, Elementary Functions, Cauchy Theorem and Integral Formula, Homotopic version • Linear fractional transformations, Power Series, Analytic Continuation and Taylor’s theorem, Zeros of Analytic functions, Hurwitz Theorem, Maximum Modulus Theorem.

Judicious redistribution of the topics may be followed in the class. 

Credit distribution (in percentage) is as follows:

1. Assignments  ---  20

2. Minor (Best two out of three) --- 40

3. Find exam ---  40

Textbook:

1. Complex Function Theory  (2nd edition) by Donald E. Sarason. (Primary text)

2. Complex Analysis - An Introduction to the Theory of Analytic Functions of One Complex Variable by Lars V. Ahlfors.

Reference Book:

1. Complex Analysis (Undergraduate text) by Theodore W. Gamelin.

2. Visual Complex Analysis by Tristan Needham.

• Minor exams: 

1. Minor - I  ON 28/08/23

2. Minor - II 18/09/23

3. Minor - III 16/10/23

• Major exam  (FINAL) 25/11/23

Unfinished notes:-

1. Complex numbers and metric topology

2. Cauchy Riemann equations