TÜRKÇE
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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT417 |
| Name | Introduction to the Theory of Differential Equations |
| Term | 2025-2026 Academic Year |
| Semester | 7. 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 aim is to provide theoretical depth to students who are familiar with the basic solution methods of ordinary differential equations. The focus will be on qualitative analyses such as the existence and uniqueness conditions of solutions and the long-time behavior of systems.
Course Content
Initial value problem (IVP) for ordinary differential equations (ODEs), Existence-Uniqueness theorems, Continuation of solution and dependence on initial condition, Writing higher order ODEs as a system, Vector Notation, Wronskian Identity, Variation of Parameters, Boundary Value Problems and Eigenvalue Problems
Course Precondition
none
Resources
Introduction to Theoretical Aspects of Ordinary Differential Equations, A. K. Erkip
Notes
Lectures on Differential Equations, Yılmaz Akyıldız and Ali Yazıcı.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learn and prove the existence-uniqueness theorems for IVPs. |
| LO02 | Learn the conditions for the continuation of solutions and dependence on Initial Parameters. |
| LO03 | Write higher order ODEs as a first order system and learn vector notation. |
| LO04 | Understands the concept of linear dependence/independence. Learns the Wronskian identity. |
| LO05 | Write the solution operator of nonomogeneous equations by the method of variation of parameters. |
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. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| 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. | |
| 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 | 2 |
| 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. | 3 |
| 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. | |
| 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 | First Order Ordinary Differential Equations, Preliminaries | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Tangent Line Approximation, Cauchy-Euler Method | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Graph Method, Direction Fields | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Existence-Uniqueness Theorem | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Proof of the Existence-Uniqueness Theorem | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Differential Inequalities, Integral Inequalities | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Gronwall's Lemma, integral 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 the 7th week. | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Uniqueness Theorem, Picard Method | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Existence Theorem and its Proof | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Continuability of solutions, Dependence on initial value | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Systems and Higher Order Ordinary Differential Equations | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Uniqueness Theorem for Systems, Picard Method, Existence Theorem | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | General Theory of Linear Differential Equations, Second Order Linear Equations, Wronskian Identity | Studying the pages related to the subject in the reference books. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Boundary Value Problems, Eigenvalue Problems | 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 |
| 17 | Term Exams | All 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 | 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 | ||