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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (PhD) | |
| Code | MT601 |
| Name | Impulsive Differential Equations |
| Term | 2025-2026 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora 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
To introduce impulsive differential equations and provide information about their solutions.
Course Content
General description of impulsive differential equations: Systems with fixed moments of impulses; systems with variable moments of impulses; discontinuous dynamical systems. Linear systems: General properties of solutions; periodic solutions; Floquet theory; adjoint systems. Stability: Stability criterion based on linearization of systems; direct Lyapunov method.
Course Precondition
none
Resources
Aruğaslan Çinçin, Duygu, İmpalsif Diferansiyel Denklemlere Giriş(2015). Palme Yayıncılık.
Notes
1-Lakshmikantham, V., Bainov, D. and Simeonov, P. (1989) Theory of Impulsive Differential Equations. World Scientific, Singapore. 2. Samoilenko, A.M. and Perestyuk, N.A. (1995) Impulsive Differential Equations. World Scientific,
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the general properties of impulsive differential equations and explains the models established with these equations. |
| LO02 | Explain the difference between impulsive systems of fixed moments and variable moments. |
| LO03 | Learn about solutions of linear impulsive systems. |
| LO04 | Tests the stability of Solutions |
| LO05 | Learn about the solutions of the Periodic Systems. |
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 | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her 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. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | |
| 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 | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | 3 |
| 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. | 4 |
| 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. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | General Description of Impulsive Differential Equations (IDEs). Mathematical Models | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Systems with fixed moment of impulses. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Systems with variable moments of impulses. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 4 | Discontinuous dynamical systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 5 | Linear Systems: General properties of solutions. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Stability of Solutions | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Adjoint Systems | 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 | Hamiltonian systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Direct Lyapunov method | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Stability of impulsive systems with variable moments of impulses | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Nonhomogeneous linear periodic systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Nonlinear periodic systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Almost periodic systems | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Integral sets | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | All covered topics. | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 17 | Term Exams | All covered topics | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
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 | ||