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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT410 |
| Name | Dynamic Systems |
| Term | 2025-2026 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | FE Field Education Courses E Elective |
| 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 course provides theoretical frameworks for analyzing the structural characteristics of differential equation systems.
Course Content
Autonomous systems, Classification and stability analysis of equilibrium points, Construction and interpretation of phase space geometry, Derivation of stability criteria using Lyapunov methods, Discussion of existence conditions for limit cycles via the Poincaré-Bendixson theorem.
Course Precondition
none
Resources
L. Perko, Differential Equations and Dynamical Systems: 3rd Edition, Springer, New York, 2000.
Notes
Ross, S.L., Differential Equations, john Wiley and Sons, Inc., New York, 1974.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Determines the equilibrium points of systems of differential equations. |
| LO02 | Interprets the stability of equilibrium points. |
| LO03 | Constructs the phase diagram. |
| LO04 | Determines simple critical points of nonlinear equation systems. |
| LO05 | Lineerleştirme yöntemini uygular. |
| LO06 | Periyodik çözümlerin varlığını ve tekliğini incelemek için Poincaré-Bendixson teoremini uygular. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 4 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Doğrusal Sistemler: Çift olmayan Lineer Sistemler, Köşegenleştirme | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Exponentials of Operators, Linear Systems in R^2 | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Complex Eigenvalues, Multiple Eigenvalues | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Jordan form | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Kararlılık Teorisi, Homojen Olmayan Lineer Sistemler | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 6 | Nonlinear Systems: Preliminaries | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | The Flow Defined by a Differential Equation, Linearization | 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 7th week | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The Stable Manifold Theorem | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Lyapunov Functions | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Types of critical points: Node, saddle point, Foci and Centers | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Nonhyperbolic Critical Points in R^2, Center Manifold Theory | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Nonlinear Systems: Global theory | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Limit sets and attractors, Periodic Orbits, Limit Cycles, | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Hamiltonian Systems, The Poincare-Bendixson Theory in R^2 | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | All topics covered | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | All topics covered | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||