BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| 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. |
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: | 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 |
Learning Outcomes
|
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 |
Course Content
| 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. |
Weekly Detailed Course Contents
| 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 |
Sources
| 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. |
Evaluation System
| 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 | |
ECTS / Workload Table
| 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 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |