TÜRKÇE
ENGLISH
Information
| Code | ENM215 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-1 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
Doç. Dr. ZEYNEP ÖZKURT
(A Group)
(Ins. in Charge)
|
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 | Have sufficient knowledge of mathematics, science and related engineering disciplines; can use the theoretical and applied knowledge in these fields in complex engineering problems. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquire the ability to identify, define, formulate and solve complex Industrial Engineering problems; for this purpose, will have the ability to choose and apply appropriate analysis and modeling methods. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; can apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Develops modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications, and has the ability to use information technologies effectively. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Have the ability to design experiments, collect data, analyze and interpret results for the investigation of complex 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 orally and in writing; knowledge of at least one foreign language; have the 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. | 1 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Have the awareness of the necessity of lifelong learning; can follow the developments in science and technology and have the ability to constantly renew themselves. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Acts in accordance with ethical principles, has knowledge about the standards used in engineering applications with the awareness of professional and ethical responsibility. | 3 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Gain knowledge of business practices such as project management, risk management and change management; become aware of entrepreneurship and innovation. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains knowledge about 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 and has awareness of the legal consequences of engineering solutions. | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | They can benefit from the power of effective communication in their professional life and have the ability to interpret developments correctly. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve integrated systems involving machine, time, information and money. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve complex products, processes, businesses, systems by applying modern design methods, under realistic conditions and constraints such as cost, environment, sustainability, manufacturability, ethical, 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 |
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 | ||