COURSE UNIT TITLE

: COMPLEX CALCULUS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3050 COMPLEX CALCULUS COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR SEÇIL GERGÜN

Offered to

Mathematics (Evening)
Mathematics

Course Objective

The aim of this lecture is to learn complex numbers, differential and integral calculus for functions of a complex variable and conformal mappings with applications.

Learning Outcomes of the Course Unit

1   Wil be able to apply the algebraic and geometric properties of complex numbers
2   Wil be able to describe and use an analytic function and the elementary functions
3   Wil be able to apply the Cauchy-Goursat theorem and Cauchy's integral Formula
4   Wil be able to find Taylor or Laurent expansions and analytic continuation of a function.
5   Will be able to apply Residue theorem.
6   Will be able to make transformations by elementary functions and conformal mapping.

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, graph of mappings, limits, continuity, differentiability..
3 The Chauchy-Riemann equations, analytic functions, harmonic functions.
4 Elementary function, exponential, The logarithmic functions and its branches.
5 Trigonometric, hyperbolic and inverse trigonometric and hyperbolic functions.
6 Smooth paths, contour integrals, antiderivatives, the Cauchy-Goursat theorem.
7 Cauchy integral formula, Liouvile's theorem and maximum moduli of functions.
8 Midterm exam.
9 Convergence of a series, Taylor series, Laurent series.
10 Absolute and uniform convergence of power series, integration, differentiation of power series. The uniqueness of Taylor and Laurent series representiation, analytic continuation..
11 The residue theorem, isolated singular points, zeros and poles of order m.
12 Applications of residues. Rouche's theorem.
13 Mapping by elementary functions, linear fractional mapping, exponential and logarithmic mapping.
14 Conformal mapping.

Recomended or Required Reading

Textbook(s): Complex Variables and Apllications, J. W. Brown, R. V. Churchill, McGraw-Hill Internatinal Editions
Supplementary Book(s): 1.Complex Variables, M. J. Ablolowitz, A. S. Fokas, Cambrige Texts.
2.Complex Variables, M. R. Spiegel, Schaum's Outlines.
References:Complex Analysis, J. Bak, D. J. Newman, Springer
Materials: Presentiations

Planned Learning Activities and Teaching Methods

Lecture notes, presentiations, solving problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 0.60


*** 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

To be announced.

Contact Details for the Lecturer(s)

e-mail: murat.altunbulak@deu.edu.tr
Office: (232) 3018592
e-mail: melda.duman@deu.edu.tr
Office: (232) 3018583

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 12 5 60
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Final 1 2,5 3
Midterm 1 2,5 3
TOTAL WORKLOAD (hours) 168

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15535
LO.25435
LO.3543532
LO.4543432
LO.55434
LO.65434

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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