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 | Spring | 3 | 0 | 3 | 9 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
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: | 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 |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | % 0 | |
Presentation | 1 | % 20 |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 1 | % 30 |
Preliminary Jury | % 0 | |
Final | 1 | % 50 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
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 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 1 | 40 | 40 |
Project | 0 | 0 | 0 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 20 | 20 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 28 | 28 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |