| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Complex Analysis II | MAT332 | 6. Semester | 2 + 2 | 3.0 | 6.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Assoc. Prof. Dr. Tuba TUNÇ |
| Instructors |
Tuba TUNÇ |
| Assistants | |
| 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. |
| Learning Outcomes |
- The students gain primary informations about the mathematics |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Cauchy Integral Theorem and Cauchy Integral Formula | |
| 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 | |
| 6. Week | Taylor Series | |
| 7. Week | Laurent Series | |
| 8. Week | Mid-term Exam | |
| 9. Week | Residue Theorem | |
| 10. Week | The applicaitons of Residue Theorem to Improper Integrals. | |
| 11. Week | Logarithmic Derivative Results | |
| 12. Week | Argument Principle, Rouche Theorem | |
| 13. Week | Argument Principle, Rouche's Theorem | |
| 14. Week | Argument Principle, Rouche's Theorem |
| 1.R.V. Churchill, Complex Variable and Applications, McGraw-Hill , Inc. |
| 2.Ali Dönmez, Karmaşık Fonksiyonlar Kuramı, Dicle Üni., 19853) |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 4 | 0 | - |
| PY2 | 5 | 0 | - |
| PY3 | 4 | 0 | - |
| PY4 | 4 | 4 | 60 |
| PY5 | 1 | 0 | - |
| PY6 | 1 | 0 | - |
| PY7 | 5 | 0 | - |
| PY8 | 5 | 0 | - |
| PY9 | 2 | 0 | - |
| PY10 | 3 | 0 | - |
| PY11 | 1 | 0 | - |
| PY12 | 4 | 0 | - |
| PY13 | 3 | 0 | - |
| PY14 | 3 | 0 | - |
| PY15 | 1 | 0 | - |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 4 | 56 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 2 | 28 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 2 | 28 |
| Practice End-Of-Term | 14 | 1 | 14 |
| Total Workload | 158 | ||
| ECTS Credit of the Course | 6.0 | ||
