| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential Equations I | MAT231 | 3. Semester | 4 + 0 | 4.0 | 6.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to face |
| Course Coordinator | |
| Instructors | |
| Assistants | |
| Goals | Ensuring the comprehension of the conditions of existence and uniqueness of solutions of differential equation, types of differential equations and solution methods. |
| Course Content | Definition of Differential Equations, Degree in Differential Equations,Differential Equation Solutions, Types of Solutions,Designation of Differential Equation whose General Solution is known,Initial Boundary-Value Problems,Existence and Uniqueness of Solutions,Solution of the First Degree Differential Equations,Differential Equations which can be divided into Variables,Homogenous Differential Equations,Differential Equations which can be Converted into Homogeneous Differential Equations Definitive Differential Equations,Differential Equations which can be Converted into Definitive Differential Equations,Linear Differential Equations, Bernoulli Differential Equation,Riccati Differential Equation Orbits, Envelopes, Equations which can be solved for y and x |
| Learning Outcomes |
- Showing the existence and uniqueness of the solution of a given differential equation. - Designating the type of a given differential equation. - Solving the differential equation problems using a convenient method. - Improving the ability of proving. - Developing new solution methods. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Definition of Differential Equations, Degree in Differential Equations | |
| 2. Week | Differential Equation Solutions, Types of Solutions | |
| 3. Week | Designation of Differential Equation whose General Solution is known | |
| 4. Week | Initial Boundary-Value Problems | |
| 5. Week | Existence and Uniqueness of Solutions | |
| 6. Week | Solution of the First Degree Differential Equations, Differential Equations which can be divided into Variables | |
| 7. Week | Homogenous Differential Equations | |
| 8. Week | MIDTERM EXAM | |
| 9. Week | Differential Equations which can be Converted into Homogeneous Differential Equations | |
| 10. Week | Definitive Differential Equations | |
| 11. Week | Differential Equations which can be Converted into Definitive Differential Equations | |
| 12. Week | Linear Differential Equations, Bernoulli Differential Equation | |
| 13. Week | Riccati Differential Equation | |
| 14. Week | Orbits, Envelopes, Equations which can be solved for y and x |
| • Theory of Differential Equations, E. Hasanov, G. Uzgören, A. Büyükaksoy, Papatya, 2002 |
| • Differential Equations and Applications, M. Aydın, B. Kuryel, G. Gündüz, G. Oturanç, Barış Publication Fakülteler Bookstore, 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 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY4 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY5 | 3 | 3 | 3 | 3 | 3 | 3 | - |
| PY6 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY7 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| PY8 | 3 | 3 | 3 | 3 | 3 | 3 | - |
| PY9 | 4 | 4 | 4 | 4 | 4 | 4 | - |
| PY10 | 3 | 3 | 3 | 3 | 3 | 3 | - |
| 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 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 5 | 1.5 | 7.5 |
| Quiz 1 | 3 | 0.5 | 1.5 |
| Final | 1 | 2 | 2 |
| Total Workload | 153 | ||
| ECTS Credit of the Course | 6.0 | ||
