| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential equations | BSM209 | 3. Semester | 2 + 2 | 3.0 | 4.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to face |
| Course Coordinator |
Assoc. Prof. Dr. Fatih HEZENCİ |
| Instructors |
Fatih HEZENCİ |
| Assistants | |
| Goals | General concepts and classification First order differential equations Variable separable equations, exact differential equations Integral multiplier, linear equations in first order, variable change; homogeneous equations Bernoulli equation, Riccati equation Existence and uniqueness theorems, applications of first order differential equations Higher order equations in the first order Linear differential equations in n-order: constant coefficient equations (uncertain coefficient methods) Variable coefficient differential equations (operator is divided into multipliers, method of changing parameters Order reduction method, Cauchy-Euler equation Laplace transformations, definitions and theorems Application of Laplace transformations to ordinary differential equations Power series method: solutions around ordinary and singular points Systems of linear differential equations: basic theory and solutions, solution using Laplace transform |
| Course Content | Introducing students to differential equations and systems which are encountered in many engineering applications and investigating their solutions. |
| Learning Outcomes |
- To gain the ability of modeling and interpreting some events. - To solve differential equations in the first order. - To solve high-order equations in the first order. - n. to understand the theory of linear differential equations. - To teach solution methods of linear differential equations with constant coefficients. - To know solution methods for variable coefficient equations. - To understand the solution methods of non-linear differential equations of high order. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | General concepts and classification | Verbal Expression Visual Presentation |
| 2. Week | First order differential equations | Verbal Expression Visual Presentation |
| 3. Week | Variable separable equations, exact differential equations | Verbal Expression Visual Presentation |
| 4. Week | Integral multiplier, linear equations in first order, variable change; homogeneous equations | Visual Presentation Verbal Expression |
| 5. Week | Bernoulli equation, Riccati equation | Visual Presentation Verbal Expression |
| 6. Week | Existence and uniqueness theorems, applications of first order differential equations | Visual Presentation Verbal Expression |
| 7. Week | Higher order equations in the first order | Verbal Expression Visual Presentation |
| 8. Week | Midterm | Course Hours |
| 9. Week | Linear differential equations in n-order: constant coefficient equations (uncertain coefficient methods) | Visual Presentation Verbal Expression |
| 10. Week | Variable coefficient differential equations (operator is divided into multipliers, method of changing parameters | Verbal Expression Visual Presentation |
| 11. Week | Order reduction method, Cauchy-Euler equation | Visual Presentation Verbal Expression |
| 12. Week | Laplace transformations, definitions and theorems | Verbal Expression Visual Presentation |
| 13. Week | Application of Laplace transformations to ordinary differential equations | Visual Presentation Verbal Expression |
| 14. Week | Power series method: solutions around ordinary and singular points, Systems of linear differential equations: basic theory and solutions, solution using Laplace transform | Verbal Expression Visual Presentation |
| 1) H. Kurt, M. Özkaymak, Z. Recebli, Mühendislikte Diferansiyel Denklemler, Seçkin Yayıncılık, Ankara, 2013 2) M. Aydın, B. Kuryel, G. Gündüz, G. Oturanç, Diferansiyel Denklemler ve Uygulamaları, Fakülteler Barış Kitabevi, 2011. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | Measurement Method |
|---|---|---|---|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 40,60 |
| PY4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 40,60 |
| PY5 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY6 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 40,60 |
| PY7 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY9 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 40,60 |
| PY11 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 40,60 |
| 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) |
|---|---|---|---|
| Midterm 1 | 1 | 10 | 10 |
| Final | 1 | 30 | 30 |
| Practice | 1 | 6 | 6 |
| Classroom Activities | 14 | 4 | 56 |
| Total Workload | 102 | ||
| ECTS Credit of the Course | 4.0 | ||
