APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5008 Complex Analysis Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ERSİN ÖZUĞURLU
Recommended Optional Program Components: None
Course Objectives: Learn basic results of the function theory of one complex variable, practice of conformal mappings and its applications

Learning Outcomes

The students who have succeeded in this course;
Construct conformal mappings
Relate suitable contours to evaluate integrals and series
In advanced complex analysis, to learn and apply the main theorems and definitions.

Course Content

Classification of singularities. Residues. Argument principle. The maximum modulus theorem. Space of meromorphic functions. Ricmann mapping theorem. Weierstrass product theorem. Gamma function. Ricmann Zeta function. Theorem of Mittag-Leffer. Ricmann surfaces and analytic continuation. Harmonic functions.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Approximation theorems and Runge theorem
2) The Riemann mapping theorem
3) Conformal mappings:survey
4) Schwarz-Christoffel formula
5) Principle of reflection
6) Conformal mappings using reflection principle
7) Evaluation of definite integrals using special domains
8) Summation of series
9) Harmonic functions
10) Dirichlet problem
11) Weierstrass factorization theorem
12) Blaschke products
13) Mittag-Leffler expansion theorem
14) Mittag-Leffler expansion theorem

Sources

Course Notes / Textbooks: 1.Gilman J.P., Kra I., Rodriguez R.E. Complex analysis. In the spirit of Lipman Bers. (Springer, 2007) (ISBN 9780387747149) 2.Freitag E., Busam R. Complex analysis (2ed., Springer, 2009)(ISBN 3540939822)3.K.Kodaira. Complex analysis. Cambridge University Press, 2007.
References: .

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 7 % 30
Presentation 1 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Presentations / Seminar 1 40 40
Homework Assignments 7 14 98
Final 1 20 20
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.