| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Differential Equations | BMZ203 | Turkish | Compulsory | 3. Semester | 3 + 0 | 3.0 | 3.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Face to face |
| Course Coordinator | Doç. Dr. Fatih HEZENCİ |
| Instructor(s) | |
| Goals | The objective of this course is to impart in students in-depth knowledge and proficiency regarding differential equations and systems. |
| Course Content | Introducing students to differential equations and systems which are encountered in many engineering applications and investigating their solutions. |
| # | Öğrenme Kazanımı |
| 1 | The student models and interprets certain phenomena. |
| 2 | The student solves first-order differential equations |
| 3 | The student solves first-order differential equations of a higher degree. |
| 4 | The student defines the theory of n-th order linear differential equations and applies it. |
| 5 | The student applies the solution methods for linear differential equations with constant coefficients. |
| 6 | The student comprehends the solution methods for differential equations with variable coefficients. |
| 7 | The student articulates and applies the solution methods for higher-order nonlinear differential equations. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | General concepts and classification | Interview Presentation (Preparation) |
| 2. Week | First order differential equations | Presentation (Preparation) Interview |
| 3. Week | Variable separable equations, exact differential equations | Interview Presentation (Preparation) |
| 4. Week | Integral multiplier, linear equations in first order, variable change; homogeneous equations | Interview Presentation (Preparation) |
| 5. Week | Bernoulli equation, Riccati equation | Interview Presentation (Preparation) |
| 6. Week | Existence and uniqueness theorems, applications of first order differential equations | Interview Presentation (Preparation) |
| 7. Week | Higher order equations in the first order | Interview Presentation (Preparation) |
| 8. Week | Higher order equations in the first order | Interview Presentation (Preparation) |
| 9. Week | Linear differential equations in n-order: constant coefficient equations (uncertain coefficient methods) | Interview Presentation (Preparation) |
| 10. Week | Variable coefficient differential equations (operator is divided into multipliers, method of changing parameters | Interview Presentation (Preparation) |
| 11. Week | Order reduction method, Cauchy-Euler equation | Presentation (Preparation) Interview |
| 12. Week | Laplace transformations, definitions and theorems | Interview Presentation (Preparation) |
| 13. Week | Application of Laplace transformations to ordinary differential equations | Interview Presentation (Preparation) |
| 14. Week | Power series method: solutions around ordinary and singular points, Systems of linear differential equations: basic theory and solutions, solution using Laplace transform | Interview Presentation (Preparation) |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Utilizes (or Applies) knowledge of natural sciences and mathematics in developing various processes in their field. | ✔ | |||||
| 2 | Demonstrates adherence (or behaves) to ethical and deontological principles in decision-making and implementation processes. | ✔ | |||||
| 3 | Utilizes (or Applies) scientific and technological developments in the applications within their field. | ✔ | |||||
| 4 | Integrates (or Combines) fundamental engineering knowledge with technical tools to solve engineering problems in their field using an analytical approach. | ✔ | |||||
| 5 | Designs all technical systems, system components, and production processes relevant to their field. | ✔ | |||||
| 6 | Implements (or Applies) plant and animal production processes in accordance with scientific and technical principles. | ✔ | |||||
| 7 | Utilizes (or Employs) data-driven core technologies in agricultural production processes. | ✔ | |||||
| 8 | Applies (or Implements) sustainability principles and approaches to agricultural processes. | ✔ | |||||
| 9 | Utilizes (or Applies) managerial and institutional knowledge related to agriculture, while considering (or observing) global and local developments. | ✔ | |||||
| 10 | Manages soil and water resources and agricultural waste sustainably by integrating scientifically based irrigation, drainage, and soil conservation systems with precision agriculture and digital water management technologies. | ✔ | |||||
| 11 | Designs agricultural machinery and equipment for agricultural production and post-harvest processes, evaluates their performance, and enhances their efficiency through automation. | ✔ | |||||
| 12 | Develops functional and environmentally sensitive (or sustainable) solutions in the design of agricultural structures (such as greenhouses, barns, and pens) by utilizing modern engineering and construction technologies. | ✔ | |||||
| 13 | Analyzes energy efficiency for agriculture and develops effective systems by integrating biofuel production and other sustainable energy sources | ✔ | |||||
| 14 | Analyzes precision agriculture data (such as satellite imagery, unmanned aerial vehicles (UAVs), and handheld radiometers) to develop and implement systems that optimize resource management. | ✔ | |||||
| 15 | Executes entrepreneurial projects developed based on legal and ethical boundaries by following current developments, manages them through interdisciplinary collaboration, and transfers the acquired knowledge to stakeholders. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 |
|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY13 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY14 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY15 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 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 | 3 | 42 |
|
Ders Dışı |
Research | 14 | 2 | 28 |
| Other Activities | 3 | 1.5 | 4.5 | |
|
Sınavlar |
Midterm 1 | 1 | 1 | 1 |
| Final | 1 | 1 | 1 | |
| Total Workload | 76.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 3.0 | ||
