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 |
MAT5008 | Complex Analysis | Fall | 3 | 0 | 3 | 12 |
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: | Learn basic results of the function theory of one complex variable, practice of conformal mappings and its applications |
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. |
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. |
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 |
Course Notes: | 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: | . |
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 | 7 | % 30 |
Presentation | 1 | % 30 |
Project | % 0 | |
Seminar | % 0 | |
Midterms | % 0 | |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
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 | 0 | 0 | 0 |
Presentations / Seminar | 1 | 40 | 40 |
Project | 0 | 0 | 0 |
Homework Assignments | 7 | 14 | 98 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 0 | 0 | 0 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 20 | 20 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |