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 3054 COMPLEX CALCULUS COMPULSORY 4 0 0 6

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR SEÇIL GERGÜN

Offered to

Mathematics

Course Objective

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

Learning Outcomes of the Course Unit

1   will be able to apply the algebraic and geometric properties of complex numbers
2   will be able to describe and use an analytic function and the elementary functions
3   will be able to apply the Cauchy-Goursat Theorem and Cauchy's Integral Formula
4   will 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

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 + Midterm Exam
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

Textbooks:
1. Mathews, J. H., Howell, R. W., Complex Analysis for Mathematics and Engineering, Jons and Barlett Publishers, 2006
Supplementary Books:
2. Brown, J. W., Churchill, R. V., Complex Variables and Applications, McGraw Hill Editions, 2014
3. Ablowitz, M. J., Fokas, A. S., Complex Variables: Introduction and Applications, Cambridge Texts, 2005
4. Spiegel, M.R., Complex Variables, Schaum's Outline, 2009
5. Bak, J., Newman, D. J., Complex Analysis, Springer, 2010
6. Gamelin, T. W., Complex Analysis, Springer, 2001
7. Needham, T., Visual Complex Analysis, Oxford University Press, 1997
References:
Materials: Presentations

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, 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

Midterm, Final

Language of Instruction

English

Course Policies and Rules

To be announced

Contact Details for the Lecturer(s)

E-mail: secil.gergun@deu.edu.tr
Office: 0 232 3018606

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 20 20
Preparation for final exam 1 25 25
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 144

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
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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