TÜRKÇE
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Information
| Code | CMZ205 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
| Course Instructor |
Arş.Gör.Dr. Mehmet GÜRSUL
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Objectives of this course is, to solve many problems in engineering, first, formulate these problems with mathematical statements and find solutions of problems by using initial and bounded condition.
Course Content
First order differential equations; separable equations, linear equations, Exact equations and integrating factor, Higher order differential equations; the method of variation of parameters, Constant coefficient equations, the method of undetermined coefficients/ Laplace transformation; basic definition and theorems.
Course Precondition
None
Resources
Differential Equations L.Shipley ROSS
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines the Differential Equation |
| LO02 | Classifies Differential Equations. |
| LO03 | Have knowledge about the solution of Differential Equations. |
| LO04 | Gain an idea about the application of Differential Equations to engineering. |
| LO05 | Solve problems with differential equations in the field of professional engineering. |
| LO06 | Learns about Initial and Boundary Value Problems. |
| LO07 | Recognizes the general type of first order differential equations. |
| LO08 | It solves separately for each of the first order differential equations. |
| LO09 | Learn about Higher Order Differential Equations. |
| LO10 | Solve Homogeneous Differential Equations with Constant Coefficients. |
| LO11 | Finds solutions of non-homogeneous Constant Coefficient Differential Equations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Becomes equipped with adequate knowledge in mathematics, science, environment and engineering sciences | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Becomes able to apply theoretical knowledge in mathematics, science, environment and engineering sciences | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Determines, describes, formulates and gains capabilities in solving engineering problems | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Analyzes a system, components of the system or process, gains the designing capabilities of the system under the real restrictive conditions. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Chooses ans uses the ability to apply modern tools and design technics, suitable analytical methods, modeling technics for the engineering applications | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Designs and performs experiments, data collection, has the ability of analyzing results | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Works individually and in inter-disciplinary teams effectively | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Becomes able to reach knowledge and for this purpose does literature research and to uses data base and other information sources | 3 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Becomes aware of the necessity of lifelong learning and continuously self renewal | 3 |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Capable of effective oral and written skills in at least one foreign language for technical or non-technical use | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Effective use of Information and communication technologies | 3 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Defines necessities in learning in scientific, social, cultural and artistic areas and improves himself/herself accordingly. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility | 5 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Project management, workplace practices, environmental and occupational safety; awareness about the legal implications of engineering applications | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation and to have idea of contemporary issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of Differential Equations and Classification | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 2 | Inıtial and Bounded Value Problem | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 3 | Obtained Differantial Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 4 | Exact Differential Equations and Integrating Factor | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 5 | Seperable Differential Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 6 | Homogenous Differential Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 7 | Linear and Bernouilli Differential Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Lecturer notes and related articles | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Main Theory of High order Linear Differential Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 10 | Homogenous Differential Equations with Costant Coefficient | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 11 | Homogenous Differential Equations with Costant Coefficient (Devam) | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 12 | Uncertain Coefficient Method | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 13 | Method of the variation of Parameters | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 14 | Cauchy Euler Equations | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 15 | General Rewiev | Lecturer notes and related articles | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Lecturer notes and related articles | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecturer notes and related articles | Ölçme Yöntemleri: Yazılı Sınav |
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) | 10 | 3 | 30 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 3 | 3 |
| Final Exam | 1 | 3 | 3 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||