| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential Equations II | MAT232 | 4. Semester | 4 + 0 | 4.0 | 6.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator | |
| Instructors | |
| Assistants | |
| Goals | To learn fundamental definitions, theorems and solution methods of higher order differential equations |
| Course Content | Higher Order Differential Equations Basic Definitions and Theorems, Homogeneous Solutions of Linear Differantial Equations with Constant Coefficients, Non-homogeneous Linear Differential Equations with Constant Coefficients Custom, Solution Finding Methods: Consecutive Integral Method, Inverse Operators Method, Method of Variation of Constants, Method of Undetermined Coefficients, Solutions of Linear Differantial Equations of Higher Order with Variable Coefficients, Cauchy-Euler differential equation, Legendre's Differantial Equation , Order Reduction Method, MIDTERM EXAM, Solutions with Power Series, Legendre and Bessel Differantial Equations, Differantial Equations, Definition and Properties of Laplace Transform, Solutions of Differential Equations by Laplace Transform, Applications of Differential Equations and Related Presentations |
| Learning Outcomes |
- Learning methods of solution for high-order differential equations. - Making the physical application on differential equations. - Learning the Legendre and Bessel's differential equations. - Applying the Cauchy-Euler differential equation problems. - Making solutions with power series. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Higher Order Differential Equations Basic Definitions and Theorems | |
| 2. Week | Homogeneous Solutions of Linear Differantial Equations with Constant Coefficients | |
| 3. Week | Non-homogeneous Linear Differential Equations with Constant Coefficients Custom Solution Finding Methods: Consecutive Integral Method, Inverse Operators Method | |
| 4. Week | Method of Variation of Constants, Method of Undetermined Coefficients | |
| 5. Week | Solutions of Linear Differantial Equations of Higher Order with Variable Coefficients | |
| 6. Week | Cauchy-Euler differential equation | |
| 7. Week | Legendre's Differantial Equation , Order Reduction Method | |
| 8. Week | MIDTERM EXAM | |
| 9. Week | Solutions with Power Series | |
| 10. Week | Legendre and Bessel Differantial Equations | |
| 11. Week | Differantial Equations | |
| 12. Week | Definition and Properties of Laplace Transform | |
| 13. Week | Solutions of Differential Equations by Laplace Transform | |
| 14. Week | Applications of Differential Equations and Related Presentations |
| • Diferansiyel Denklemler Teorisi, E. Hasanov, G. Uzgören, A. Büyükaksoy, Papatya, 2002 |
| • Diferansiyel Denklemler ve Uygulamaları, M. Aydın, B. Kuryel, G. Gündüz, G. Oturanç, Barış Yayınları Fakülteler Kitabevi, 2001 |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | Measurement Method |
|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY2 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY3 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY4 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY5 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY6 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY7 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY8 | 3 | 3 | 3 | 3 | 3 | 3 | - |
| PY9 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY10 | 2 | 2 | 2 | 2 | 2 | 2 | - |
| 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 |
| Preparation, After Class Study | 14 | 2 | 28 |
| Research | 14 | 2 | 28 |
| Other Activities | 14 | 3 | 42 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 2 | 1 | 2 |
| Homework 2 | 2 | 1 | 2 |
| Final | 1 | 2 | 2 |
| Total Workload | 162 | ||
| ECTS Credit of the Course | 6.0 | ||
