COURSE UNIT TITLE

: COMPLEX ANALYSIS

DEGREE PROGRAMMES

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 SEÇIL GERGÜN

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 Algebraic and geometric meaning of complex numbers, regions in complex plane
2 Functions of a complex variable, graphs of mappings, limits, continuity
3 Derivatives of functions of a complex variable, the Cauchy-Riemann equations, analytic functions, harmonic functions
4 Elementary functions, exponential function, the logarithmic function and its branches
5 Trigonometric, hyperbolic and inverse trigonometric, inverse hyperbolic functions
6 Smooth paths, contour integrals, antiderivatives, the Cauchy-Goursat Theorem
7 Cauchy's Integral Formula
8 Liouville's Theorem and maximum moduli of functions
9 Series of numbers, power series
10 Taylor series, Laurent series
11 Absolute and uniform convergence of power series, integration and differentiation of power series. The uniqueness of Taylor and Laurent series represantations, analytic continuation
12 The Residue Theorem, isolated singular points, zeros and poles of order m
13 Applications of residues
14 Rouche's Theorem

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


Further Notes About Assessment Methods

1 Midterm Exam
2 Homework
Final Exam

Assessment Criteria

%30 (Midterm examination) + %30 Homework + %50 (Final examination)

Language of Instruction

English

Course Policies and Rules

Exams and evaluations will be carried out in accordance with YÖK Lisansüstü Eğitim ve Öğretim Yönetmeliği and Dokuz Eylül University Lisansüstü Eğitim ve Öğretim Yönetmeliği For details: https://ogrenci.deu.edu.tr/regulations-and-directives/postgraduate-education-and-training-regulation/

Contact Details for the Lecturer(s)

E-posta: secil.gergun@deu.edu.tr
Ofis: B262-1
Tel: +90 232 - 3018595

Office Hours

Monday 11:15-120:00

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 2 16 32
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 192

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.14453433343
LO.24453433343
LO.34453433343
LO.44443433343
LO.54443433343

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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