TÜRKÇE
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Information
| Unit | FACULTY OF ENGINEERING |
| INDUSTRIAL ENGINEERING PR. | |
| Code | ENM215 |
| Name | Differential Equations |
| Term | 2025-2026 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-1 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 2.5 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
The current term course schedule has not been prepared yet. Previous term groups and teaching staff are shown.
|
Course Goal / Objective
This course aims to introduce basic ideas on differential equations and to solve this equations
Course Content
Differential equations and their classification, First order differential equations, Exact differential equations, Linear differential equations, Bernoulli differential equations, Cauchy Euler differential equations, Linear differential equations systems, Laplace transformations
Course Precondition
no
Resources
Shepley L. Ross. Differential equations
Notes
Schaum series Diferential Equations
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows differential equations and their classification |
| LO02 | Recognizes first order differential equations, |
| LO03 | Recognizes exact differential equations, |
| LO04 | Solves Linear Differential Equations |
| LO05 | Solves the Bernoulli differential equation, |
| LO06 | Solves the Cauchy Euler equation, |
| LO07 | Solves systems linear differential equations, |
| LO08 | Knows the Laplace transformations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Acquires sufficient knowledge in mathematics, science and Industrial Engineering discipline-specific subjects; acquires the ability to use theoretical and applied knowledge in these fields in complex engineering problems. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires the ability to identify, define, formulate and analytically solve complex Industrial Engineering problems; and has the ability to select and apply appropriate analysis and modelling methods for this purpose. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Acquires the ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; acquires the ability to apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquires the ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Industrial Engineering applications and acquires the ability to use information technologies effectively. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Acquire the skills to design and conduct experiments, collect data, analyze and interpret results to investigate complex Industrial Engineering problems or discipline-specific research topics. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Have the ability to work effectively in disciplinary and multi-disciplinary teams or individually. | 4 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Ability to communicate effectively in Turkish, both verbally and in writing; knowledge of at least one foreign language; ability to write and understand effective reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 1 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | They have awareness of the necessity of lifelong learning; they have the ability to access information, follow developments in science and technology, and constantly renew themselves. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Acting in accordance with ethical principles, becoming knowledgeable about the standards used in engineering practices with awareness of professional and ethical responsibility. | 3 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Learn about business practices such as project management, risk management and change management, and is aware of entrepreneurship and innovation. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Informed about the universal and societal impacts of engineering practices on health, environment and safety, and the contemporary problems reflected in the field of engineering, and is aware of the legal consequences of engineering solutions. | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Benefit from the power of effective communication in professional life and has the ability to interpret developments correctly. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve integrated systems that include machines, people, time, information or money. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | By applying modern design methods, they have the ability to design, develop, implement and improve complex products, processes, businesses and systems under realistic conditions and constraints such as cost, environment, sustainable development, energy, manufacturability, ethics, health, safety and political issues. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Differential equations and solutions | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 2 | Classification Differential equations | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 3 | The existence of initial and boundary value problems and solutions | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 4 | Exact Differential equations and Integral multiplier | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 5 | Separable equations and reducible equations for this form | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 6 | Linear equations and Bernoulli equations | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 7 | solving high order linear differential equations | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 9 | Constant Coefficient Homogen Differential Equations | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 10 | Indeterminate coefficient method | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 11 | Variable Parameter Method | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Cauchy Euler denklem | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 13 | Linear Differential Denklem System | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 14 | Laplace Transformation | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 15 | Basic Properties of Laplace Transformation | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Exercises | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
Assessment (Exam) Methods and Criteria
Current term shares have not yet been determined. Shares of the previous term are shown.
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 2 | 2 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 111 | ||
| Total Workload / 25 (h) | 4,44 | ||
| ECTS | 4 ECTS | ||