MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT6016 | Selected Topics in Analysis | Fall Spring |
3 | 0 | 3 | 8 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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: | To provide engineering and technical applications for the students who have a background on complex analysis, To give the basic definitions of the theory of functions, Varieties of convergence of theory of functions and algebraic structures of power series, To give applications of Cauchy theory, Laurent and Fourier series |
The students who have succeeded in this course; 1) To Recognize the number fields and toplogical concepts 2) To define differentiable and analytical functions 3) To explain the conformal mappings 4) To comment on pointwise, uniform, locally uniform and compact convergence 5) To define Laurent and Fourier series 6) To apply Residue theorem |
Elements of the theory of functions (number fields, topological concepts, fundamentals, convergent sequences and series, continuous functions), the differential calculus (differentiable and analytic functions), analyticity and conformality, function theory, convergence varieties, power series (analytical and algebraic structures), Cauchy theory, Laurent and Fourier series, Residue evaluation. |
Week | Subject | Related Preparation |
1) | Complex numbers and concepts of complex functions | |
2) | Number fields, toplogical concepts | |
3) | convergent sequences and series, continuous functions | |
4) | Analyticity and conformality | |
5) | Convergence types (pointwise, uniform, locally uniform, compact convergence) | |
6) | Algebraic structure and analiticity of power series | |
7) | Cauchy Theory | |
8) | Applications of Cauchy theory | |
9) | Conformal mappings | |
10) | Applications of harmonic functions | |
11) | Laurent and Fourier series | |
12) | Applications of Laurent series | |
13) | Residue calculation | |
14) | Residue calculation |
Course Notes / Textbooks: | Başarır, Metin; “Kompleks Değişkenli Fonksiyonlar Teorisi”, Sakarya Kitabevi, 2002, Sakarya. |
References: | Başkan, Turgut; “Kompleks Fonksiyonlar Teorisi”,Uludağ Üni.Yay., 1996, Bursa. Paliouras, John D.; “Complex variables for scientist and engineers”, Macmillan, 1990, New York. Bak, Joseph, Donald J.Newman; Complex Analysis, Springer-Verlag, 1982. |
Semester Requirements | Number of Activities | Level of Contribution |
Presentation | 1 | % 20 |
Midterms | 1 | % 30 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 1 | 40 | 40 |
Midterms | 1 | 20 | 20 |
Final | 1 | 28 | 28 |
Total Workload | 200 |
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. | 5 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 5 |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 5 |
4) | Ability to make individual and team work on issues related to working and social life. | 3 |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 4 |
6) | Ability to use mathematical knowledge in technology. | |
7) | To apply mathematical principles to real world problems. | 4 |
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. | 5 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
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. | 4 |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. | 4 |