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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6070 COMPLEX ANALYSIS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR MURAT ALTUNBULAK

Offered to

Mathematics (English) Mathematics (English)

Course Objective

This course aims to present the classical theory of function of complex variables.

Learning Outcomes of the Course Unit

1   will be able to use metric spaces and topology of complex numbers. 2   will be able to identify analytic functions. 3   will be able to use complex integration. 4   will be able to understand singularities and residues. 5   will be able to use maximum modulus theorem.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Preliminaries. The Complex Number System 2 Metric Spaces and the Topology of C. 3 Analytic Functions. 4 Complex Integration. 5 Zeros of Analytic Functions. 6 Cauchy's Theorem. 7 Open Mapping Theorem. 8 Midterm Exam 9 Singularities and Residues. 10 Maximum Modulus Theorem. 11 Topology of Space of Functions. 12 Riemann Mapping Theorem. 13 Weierstrass Factorization Theorem. 14 The Gamma Function. Riemann Zeta Function.

Recomended or Required Reading

Textbook(s): John B. Conway, Functions of one complex variable, Springer-Verlag, Graduate Texts in Math vol 11, 1978. Supplementary Book(s): S. Lang Complex Analysis. Springer, 1993.

Planned Learning Activities and Teaching Methods

Lecture Notes Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Office: B-220 (Math. Dept.) Phone: (30)1 85 92

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 5 65 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 4 8 32 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 192

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 4 4 5 3 4 3 3 3 4 3 LO.2 4 4 5 3 4 3 3 3 4 3 LO.3 4 4 5 3 4 3 3 3 4 3 LO.4 4 4 4 3 4 3 3 3 4 3 LO.5 4 4 4 3 4 3 3 3 4 3