Rapor Tarihi: 13.04.2026 06:02
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Complex Analysis II | MAT306 | Turkish | Compulsory | 6. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Doç. Dr. Tuba TUNÇ |
| Instructor(s) | |
| Goals | To give the integral and some results of integral in the complex plane. |
| Course Content | Cauchy Integral theorem, Cauchy derivative formulas, Simply connected regions, Cauchy Inequality, Lioville Theorem, Fundamental theorem of algebra, Morera theorem, Mean value theorem, Sequences and series; Taylor and Laurent series; Residue theorem and its applications, Argument principal and Rouche theorem. |
| # | Öğrenme Kazanımı |
| 1 | Identifies different types of curves in the complex plane and represents them parametrically |
| 2 | Computes the definite integral of a complex-valued function and demonstrates knowledge of its fundamental properties. |
| 3 | Evaluates the line integral of a given complex-valued function and is familiar with the properties of line integrals. |
| 4 | Knows the Cauchy integral and differentiation formulas and uses these methods to evaluate special types of integrals. |
| 5 | Understands the fundamental concepts of complex-valued sequences and analyzes their convergence. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Cauchy Integral Theorem and Cauchy Integral Formula | |
| 1. Week | Curves and Their Parametric Representations | Preparation, After Class Study, Research, Interview |
| 2. Week | Simply Connected Domains | |
| 3. Week | Cauchy's Inequality, Lioville Theorem, Fundemantal Theorem of Algebra | |
| 4. Week | Morera’s Theorem, Mean-Value Theorem | |
| 5. Week | Sequences and Series | |
| 9. Week | Residue Theorem | |
| 10. Week | The applicaitons of Residue Theorem to Improper Integrals. |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 |
| PY2 | 5 | 5 | 5 | 5 | 5 |
| PY3 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 4 | 4 | 4 | 4 | 4 |
| PY5 | 1 | 1 | 1 | 1 | 1 |
| PY6 | 1 | 1 | 1 | 1 | 1 |
| PY7 | 5 | 5 | 5 | 5 | 5 |
| PY8 | 5 | 5 | 5 | 5 | 5 |
| PY9 | 2 | 2 | 2 | 2 | 2 |
| PY10 | 3 | 3 | 3 | 3 | 3 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Homework | 14 | 2 | 28 | |
| Homework Preparation | 14 | 1 | 14 | |
| Final | 1 | 2 | 2 | |
| Practice | 14 | 1 | 14 | |
| Practice End-Of-Term | 14 | 1 | 14 | |
| Total Workload | 130 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
