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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (PhD) | |
| Code | MT603 |
| Name | Advanced Differential Equations |
| Term | 2026-2027 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 | Belirsiz |
| 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
This course comprehensively covers the theoretical foundations of ordinary differential equations. The main focal points of the course consist of the existence and uniqueness of initial value problems, qualitative analysis of linear and nonlinear systems, stability criteria, as well as the spectral properties of boundary value problems and Sturm-Liouville theory.
Course Content
This course provides a comprehensive coverage of the theoretical foundations of ordinary differential equations. The primary focus includes the existence and uniqueness of initial value problems, qualitative analysis of linear and nonlinear systems, stability criteria, the spectral properties of boundary value problems, and Sturm-Liouville theory.
Course Precondition
None
Resources
1. Coddington & Levinson – Theory of Differential Equations 2. W. Kelley, A. Peterson, The Theory of Differential Equations Classical and Qualitative,2004, Prentice–Hall.
Notes
Hartman – Ordinary Differential Equations
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | 1. Proves existence and uniqueness theorems for differential equations. |
| LO02 | Analyzes the behavior of linear and nonlinear systems. |
| LO03 | 3. Performs stability analysis using Lyapunov methods. |
| LO04 | 4. Comprehends Sturm–Liouville problems and oscillation theory. |
| LO05 | 5. Applies functional analysis methods to differential equations. |
| LO06 | 6. Reads and interprets research papers. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | 4 |
| 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 | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| 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 foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction, basic concepts | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Existence-Uniqueness Theorems | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Maximal interval of existence, continuity ith respect to parameters | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Linear Systems | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Exponential matrix, structure of solutions | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Introduction to staility theory | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Lyapunov methods | Review of the related chapters in 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 | Nonlinear systems | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Phase portraits and limit circles | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Sturm–Liouville theory | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Oscillation theory | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Boundary value problems | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Functional analysis techniques | Review of the related chapters in reference books | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Review | Review of related research papers | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | All the covered topics. | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | All the covered topics. | 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) | 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 | ||