| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Advanced Differential Equations II | MAT529 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Prof. Dr. HÜSEYİN BUDAK |
| Instructors |
İlhame AMİRALİ |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Relations between differential equation and singular point; Singular points; Singular point for single-valued functions; Singular point for multiple-valued functions; Seperated singular point; Relations between linear differential equations and their solutions and singular point; Ordinary points; Smooth singular points; Fucks types of equations; Study on singular point’s around; Removing singularities by changing independent and dependent variable; Relation between nonlinear differential equations and their solutions and singular point; Classification of special type second order nonlinear differential equations; First order Binom equations |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Relations between Differential equation and singular point | |
| 2. Week | Aykırı noktalar | |
| 3. Week | Tek değerli fonksiyonlar için aykırı noktalar | |
| 4. Week | Singular point for multiple-valued functions | |
| 5. Week | Seperated singular point | |
| 6. Week | Relations between linear differential equations and their solutions and singular point | |
| 7. Week | Ordinary point | |
| 8. Week | Midterm | |
| 9. Week | Uniform singular point, Fukcs types of equations | |
| 10. Week | Study on Singular Point’s around | |
| 11. Week | Removing singularities by changing independent variable | |
| 12. Week | Relation between nonlinear differential equations and their solutions and singular point | |
| 13. Week | Classification of special type second order nonlinear differential equations | |
| 14. Week | First order binom equations |
| Sheply L. Ross, Differential Equations, New York, Wiley 1984. |
| 2. C. Henry Edwards and David E. Penny, Translated by Ömer Akın, Differential Equations and Boundary Value Problems, Ankara, 2006. |
| Program Requirements | Contribution Level | Measurement Method |
|---|---|---|
| PY1 | 4 | 60 |
| PY2 | 4 | 40 |
| PY3 | 3 | 40 |
| PY4 | 4 | 60 |
| PY5 | 3 | 40 |
| PY6 | 5 | 40 |
| PY7 | 4 | 60 |
| PY8 | 4 | 40 |
| PY9 | 4 | 60 |
| PY10 | 4 | 60 |
| 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 | 3 | 42 |
| Research | 14 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 1 | 2 | 2 |
| Quiz 2 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 8 | 48 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 198 | ||
| ECTS Credit of the Course | 8.0 | ||
