| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Differential Equations | BM221 | Turkish | Compulsory | 3. Semester | 4 + 0 | 4.0 | 4.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Face to face education |
| Course Coordinator | Dr. Öğr. Üyesi Barış KANTOĞLU |
| Instructor(s) | Dr. Öğr. Üyesi Barış KANTOĞLU (Güz) |
| Goals | Matematiksel düşünceyi geliştirmek. Matematik, Fizik ve mühendislikte karşılaşılan diferansiyel denklem problemlerini çözebilmek. |
| Course Content | Diferansiyel denklemlerin temel kavramları ve çeşitli mühendislik alanlarında uygulamaları. Birinci mertebeden diferansiyel denklemlerin sınıflandırılması, Birinci mertebeden değişkenlerine ayrılabilir diferansiyel denklemler. Homojen diferansiyel denklemler. Homojen türe dönüştürülebilen diferansiyel denklemler. Tam diferansiyel denklemler. Tam diferansiyel türe dönüştürülebilen diferansiyel denklemler. Birinci mertebeden lineer diferansiyel denklemlerin mühendislik uygulamaları ve çözümler teorisi. Bernoulli diferansiyel denklemi. Riccati diferansiyel denklemi. Yüksek dereceden diferansiyel denklemler. Clairaut diferansiyel denklemi. Lagrange diferansiyel denklemi. İkinci mertebeden diferansiyel denklemler. İkinci mertebeden lineer diferansiyel denklemler. |
| # | Öğrenme Kazanımı |
| 1 | Diferansiyel denklemi tanımlar |
| 2 | Değişkenlerine ayrılabilen, homojen, lineer, tam diferansiyel denklem çeşitlerini çözer |
| 3 | Bernoulli ve Riccati diferansiyel denklemlerini çözer |
| 4 | İkinci ve daha yüksek mertebeden sabit katsayılı lineer diferansiyel denklemleri çözer |
| 5 | Yüksek dereceden diferansiyel denklemleri çözer. |
| 6 | Parametrelerin değişimi yöntemini bilir. |
| 7 | Değişken katsayılı diferansiyel denklemleri tanımlar |
| 8 | Bazı değişken katsayılı diferansiyel denklemleri çözer |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Basic concepts and classification of differential equations | Class Hours Practice Interview Presentation (Preparation) |
| 2. Week | Introduction to first order differential equations, differential equations that can be divided into variables | Class Hours Presentation (Preparation) Practice Interview |
| 3. Week | Linear Differential Equations | Interview Practice Presentation (Preparation) Class Hours |
| 4. Week | Homogeneous Differential Equations | Class Hours Interview Practice Presentation (Preparation) |
| 5. Week | Exact Differential Equations | Interview Class Hours Presentation (Preparation) Practice |
| 6. Week | Fully Differential Equation Convertible Differential Equations | Class Hours Interview Practice Presentation (Preparation) |
| 7. Week | Bernoulli and Riccati Differential Equations | Interview Presentation (Preparation) Practice Class Hours |
| 8. Week | Bernoulli and Riccati Differential Equations | |
| 9. Week | Engineering applications and solutions theory of first order differential equations. | Interview Presentation (Preparation) Practice Class Hours |
| 10. Week | High order differential equations, Lagrange and Clairaut differential equations | Practice Presentation (Preparation) Class Hours Interview |
| 11. Week | Introduction to higher order differential equations, differential equations with constant coefficients | Interview Class Hours Presentation (Preparation) Practice |
| 12. Week | Differential equations with variable coefficients | Class Hours Interview Presentation (Preparation) Practice |
| 13. Week | Differential equations with variable coefficients | Interview Presentation (Preparation) Practice Class Hours |
| 14. Week | Method of variation of parameters | Practice Class Hours Presentation (Preparation) Interview |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge of mathematics, science and related engineering disciplines; Ability to use theoretical and applied knowledge in these fields in complex engineering problems | ✔ | |||||
| 2 | Ability to identify, define, formulate and solve complex engineering problems; for this purpose, the ability to select and apply appropriate analysis and modeling methods | ✔ | |||||
| 2 | Ability to identify, define, formulate and solve complex engineering problems; for this purpose, the ability to select and apply appropriate analysis and modeling methods | ✔ | |||||
| 3 | Knowledge and awareness about the management, control, development and security/reliability of Information Technologies | ✔ | |||||
| 4 | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; for this purpose, the ability to apply modern design methods | ✔ | |||||
| 5 | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself | ✔ | |||||
| 6 | Ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics | ✔ | |||||
| 7 | Ability to work effectively in disciplinary and multi-disciplinary teams; individual study skills | ✔ | |||||
| 8 | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; Ability to use information technologies effectively | ✔ | |||||
| 9 | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions | ✔ | |||||
| 10 | Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | DK8 |
|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 4 | 4 | 4 | 4 | 4 | 2 | 3 | 4 |
| PY3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY5 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY6 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY7 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY9 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY10 | 3 | 3 | 3 | 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 | 1 | 1.5 | 1.5 |
| Final | 1 | 1.5 | 1.5 | |
| Practice End-Of-Term | 11 | 3 | 33 | |
| Classroom Activities | 10 | 1 | 10 | |
| Total Workload | 102 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 4.0 | ||
