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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (PhD) | |
| Code | MT602 |
| Name | Dynamic Equations on Time Scales |
| 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 | 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
This course covers the fundamentals of dynamic equations on time scales formed by combining discrete and continuous analysis, that is, differential and difference equations, and develops techniques for solving them.
Course Content
Differentiation on time scales, integration on time scales, first order linear differential equations on time scales, initial value problems, exponential functions on time scales, second order linear differential equations on time scale, boundary value problems, Green's function, Sturm-Liouville problem.
Course Precondition
none
Resources
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
Notes
V. Lakshimikantham, S Sivasundaram, and B. Kaymakçalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the definition and basic concepts of time scales, and explains why dynamic equations on time scales are necessary in modeling |
| LO02 | Learns and applies differentiation and integration on time scales. |
| LO03 | Knows the basic properties of dynamic equations on time scales. |
| LO04 | Defines the dynamic exponential function and states its properties. |
| LO05 | Learns the solution methods of dynamic equations. |
| LO06 | Learns about the dynamic Sturm-Liouville problem. |
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. | |
| 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 | 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. | 4 |
| 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 | Basic concepts of time scales, basic operations on time scales | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Zaman skalasında diferensiyelleme. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Integration on time scales. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | First order dynamic equations, Existence and uniqueness theorem. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Exponential function on time scale | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | First order linear dynamic equations with variable coefficients | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Second order linear homogeneous dynamic equations | 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 week 7 in the references. | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
| 9 | Trigonometric functions on time scales | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Second order dynamic equations with constant coefficients | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Second order nonhomogeneous linear dynamic equations, Variation of parameters. | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Boundary value problem for second order linear dynamic equations | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Green's function | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Dynamic Sturm-Liouville problem | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Higher order linear dynamic equations | 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 | ||