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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT571 |
| Name | Theory of Differential Equations I |
| Term | 2025-2026 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. Sibel DOĞRU AKGÖL |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of this course is to provide basic information about the theory of ordinary differential equations.
Course Content
Introduction to the basic theory of differential equation systems, Proof of Existence and Uniqueness theorems, Introduction of the concepts of continuation of solutions and continuous dependence, Examination of periodic linear systems, Stability in the sense of Lyapunov, uniform stability, asymptotic stability, Necessary and sufficient conditions for stability in linear systems, Interpretation of the asymptotic behavior of solutions.
Course Precondition
None
Resources
Richard K. Miller, Anthony N. Michel, Ordinary Differential Equations, 1982, Academic Press
Notes
1. W. Kelley, A. Peterson, The Theory of Differential Equations Classical and Qualitative,2004, Prentice–Hall. 2. C. A. Swanson, Comparison and Oscillation Theory, 1968, Academic Press.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the methods of examining the existence and uniqueness of the solutions of Initial Value Problems. |
| LO02 | Learns about the continuation of solutions of Initial Value Problems and their continuous dependence on parameters . |
| LO03 | Learns the solution methods of linear systems. |
| LO04 | Learns about the structure of solutions of systems with periodic coefficients. |
| LO05 | Understands the Sturm theory and uses related methods to test the oscillation of the solution. |
| LO06 | Learns the concept of stability. Learns to determine whether an equation is stable by constructing a Lyapunov function. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 2 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Initial Value Problem, Preliminaries | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 2 | Existence and Uniqueness of Solutions | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Anlatım |
| 3 | Continuation of Solutions, Continuous Dependence on Initial Parameters | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Linear Systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Homogeneous and Non-homogeneous Linear Systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Constant/ Variable Coefficient Linear Systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Systems with Periodic Coefficients | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | All topics covered up to the 7th week in the references. | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 9 | Higher Order Linear Differential Equations | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Sturmian Theory, Sturm-Picone Theorems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Stability: Definition and Types of Stability | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Lapunov type Stability | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Lyapunov functions | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Lyapunov's Second Method | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Review | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | All the covered topics. | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 17 | Term Exams | All the covered topics. | Ölçme Yöntemleri: Ödev, 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) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 5 | 10 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 10 | 10 |
| Final Exam | 1 | 25 | 25 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||