| 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 |
| MAT4051 | Advanced Complex Analysis | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
| Course Objectives: | To study advanced studies and applications in the theory of functions of a complex variable. |
|
The students who have succeeded in this course; Grap residue theorem and its applications in evaluation of reel integrals Explain general principles of theory of conformal mappings. Grab Laplace and Fourier Transforms. |
| Concept of Residue, Residue Theorem. Applications of Residue Theorem to Real Integrals. Argument Principle, Rouche and Hurwitz Theorems. Infınıte Products, Weierstrass Formula. Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula. Concept of Analytic Continuity, Analytic Continuity of an Analytic Function. Weierstrass Method of Analytic Continuity. General Principle of Conformal Mappings. Riemann Mapping Theorem. Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula. Functions Denoted by Cauchy Kernel. Regularity of an Integral Depending on a Parameter. Laplace Transform. Fourier Transform. |
| Week | Subject | Related Preparation | |
| 1) | Concept of Residue, Residue Theorem. | ||
| 2) | Applications of Residue Theorem to Real Integrals. | ||
| 3) | Argument Principle, Rouche and Hurwitz Theorems. | ||
| 4) | Infınıte Products, Weierstrass Formula. | ||
| 5) | Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula. | ||
| 6) | Concept of Analytic Continuity, Analytic Continuity of an Analytic Function. | ||
| 7) | Weierstrass Method of Analytic Continuity. | ||
| 8) | General Principle of Conformal Mappings. | ||
| 9) | Riemann Mapping Theorem. | ||
| 10) | Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula. | ||
| 11) | Functions Denoted by Cauchy Kernel. | ||
| 12) | Regularity of an Integral Depending on a Parameter. | ||
| 13) | Laplace Transform. | ||
| 14) | Fourier Transform. | ||
| Course Notes: | A.I. Markushevich “Theory of Functions of a Complex Variable” Ruel V. Churchill, James Ward Brown, “Complex variables and applications” |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 16 | % 0 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 7 | % 10 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 50 |
| 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 | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 7 | 2 | 14 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 10 | 20 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 21 | 21 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |