Advanced Complex Analysis

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Complex Analysis, Advanced Analysis, Topology

Course Contents

This course provides candidates with in-depth knowledge on residues and poles, residue theorem, evaluation of improper real integrals and basic theorems, Jordan’s lemma, iImproper integrals involving sines and cosines, definite integrals involving sines and cosines, integration through a branch cut, Cauchy principal value, logarithmic residues, argument principle, Rouche’s theorem, Hurwitz’s theorem, univalent functions and inverse function theorem, conformal mapping and basic theorems, Riemann mapping theorem, linear fractional transformations, Schwarz-Christoffel transformation, analytic continuation and entire analytic function, principle of reflection, Riemann surfaces.

Weekly Schedule

1) Residues and poles, Residue theorem
2) Evaluation of improper real integrals and basic theorems, Jordan’s Lemma
3) Improper integrals involving sines and cosines, Definite integrals involving sines and cosines,
4) Integration through a branch cut, Cauchy principal value
5) Applications of improper real integrals
6) Logarithmic residues, Argument principle
7) Rouche’s theorem, Hurwitz’s theorem, Applications of Rouche’s theorem
8) Midterm examination/Assessment
9) Univalent functions and invers function theorem
10) Conformal mapping and basic theorems
11) Riemann mapping theorem, Linear fractional transformations
12) Applications of linear fractional transformations, Schwarz-Christoffel transformation
13) Analytic continuation and entire function, Principle of reflection
14) Riemann surfaces
15) Riemann surfaces
16) Final examination

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Discussion
3) Drill and Practice
4) Self Study

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	70%
Number Percentage Semester Studies Midterm Examination 1 50% Quiz 1 50%
Contribution of Final Examination to Course Grade	30%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required