Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course Learn the basics concepts in complex variables and complex-variable functions and to be able to work with their derivatives, contour integration, and to learn some applications of these.
Course Content Complex numbers, complex functions, continuity, differentiation, power series, logarithms, branch cuts, singularities, complex integration, Cauchy's theorem and its consequences, indefinite integral, Taylor series, Laurent series, applications of contour integration.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Fatih Erman
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Complex Variables and Applications, J.W.Brown & R.V.Churchill.
Complex Analysis, J. M. Howie, Springer

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Exams and Exam Preparations 1 199 199
Total Work Load   Number of ECTS Credits 8 235

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To use derivative and Cauchy Riemann equations.
2 To apply the line integrals and the Cauchy s integral theorem.
3 To evaluate Cauchy s integral formula for analytic functions.
4 To use Taylor and Laurent series.
5 To evaluate integrals with the residue theorem.
6 To use elementary functions for mapping various curves and regions.

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Basic concepts in analysis revisited
2 Complex Numbers, motivation, basic properties, completeness property.
3 Continuity of Complex Functions
4 Differentiation, Cauchy-Riemann equations, holomorphic functions, Goursat's Lemma,
5 Power Series, radius of convergence, examples for some complex elementary functions.
6 Logarithms, cuts and branch points, types of singularities.
7 Complex Integration
8 Complex integration, uniform convergence.
9 Cauchy's Theorem
10 Cauchy's integral formula, Morera's theorem, fundamental theorem of algebra, Liouville's theorem,
11 Indefinite Integral theorem, Taylor Series
12 Applications of Residues.
13 Laurent series, residue theorem.
14 Applications of Contour Integration.

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 2 2 3
C2 2 2 3
C3 2 2 3
C4 1 2 3
C5 2 2 3 3
C6 2 3 3 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant