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, Laurent’s Theorem, Classification of singularities • Residue theorem and applications, Argument Principle, Theorem of Rouche, Schwarz-Christoffel Transformation. 

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