TÜRKÇE
ENGLISH
Information
| Code | FZK203 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. AYSUN AKYÜZ |
| Course Instructor |
Doç. Dr. DOĞAN KAYA
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to learn the basic theories, solution methods and applications of differential equations.
Course Content
In this course, classification of differential equations, existence of solutions; First order differential equations; Applications of first order differential equations; Solutions of two and higher order linear differential equations; Applications of second order linear differential equations; Series solutions of differential equations, the Frobenius method, approximate methods for solving first-order equations, the Laplace transform and the solution of differential equations with constant coefficients using the Laplace transform are covered.
Course Precondition
none
Resources
Differential Equations Shepley Ross, John Willey&Sons
Notes
Diferansiyel Denklemler ve Uygulamalar, Mehmet Aydın
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Describes the differential equation, explains its formation and solution. |
| LO02 | Comprehends the solution methods of first order differential equations |
| LO03 | Understands, applications of first -order equations in mechanics |
| LO04 | Understands, solution methods of higher-order linear differential equations |
| LO05 | Understands applications of second- order linear differential equations |
| LO06 | Express the fundamental theorem of higher order linear differential equations. |
| LO07 | Determine the type of linear equation system |
| LO08 | Solve homogeneous linear systems with constant coefficients |
| LO09 | Understand the series solutions of linear equation systems |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and principles in the field of physics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Follows the developments in the field of Physics and uses scientific methods and techniques. | 1 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Combine the knowledge gained in the field of Physics with the knowledge in other scientific fields and explains the method of producing scientific knowledge. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identify problems in the field of physics and for the solutions apply the analytical and simulative methods. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use the advanced theoretical and practical knowledge he has acquired in the field of Physics and designs experiments related to his field. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Take responsibility as a team or alone to overcome the problems encountered in the field of physics . | 2 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Classify, use and critically evaluate the knowledg taken by his/her efforts. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Improves himself by knowing that the learning process is lifelong. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Knowing the importance of individual development, she/he implements what is necessary. | 1 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Evaluates the developments in the field of physics in terms of social ethics by watching and learning them. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Classification of differential equations, definitions, existence of solutions | no preparation | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Örnek Olay |
| 2 | Exact differential equations and Integral factors, separable equations | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 3 | Linear equations and Bernoulli equations, Special integrating factors | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay, Problem Çözme |
| 4 | Applications of first-order differential equations, applications in mechanics | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Problem Çözme |
| 5 | Second-order differential equations, Homogeneous linear equation with constant coefficient | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Grup Çalışması, Problem Çözme |
| 6 | The method of Undetermined coefficients | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 7 | Variation of parameters method | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Problem Çözme |
| 8 | Mid-Term Exam | review the topics | Öğretim Yöntemleri: Bireysel Çalışma |
| 9 | Applications of the second-order linear differential equations with constant coefficient | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Problem Çözme |
| 10 | Series solutions, Series solutions about an ordinary point | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 11 | Solutions about singular points, The Method of Frobenius | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 12 | Successive approximation method | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Problem Çözme |
| 13 | The Laplace transform, basic properties | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Örnek Olay, Bireysel Çalışma, Problem Çözme |
| 14 | Laplace transform solution of linear differential equations with constant coefficients | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 15 | The inverse Laplace transforms | Study the relevant chapter in the book | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Örnek Olay |
| 16 | Term Exams | review the topics | Öğretim Yöntemleri: Bireysel Çalışma |
| 17 | Term Exams | an overview | Öğretim Yöntemleri: Bireysel Çalışma |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| 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 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 122 | ||
| Total Workload / 25 (h) | 4,88 | ||
| ECTS | 5 ECTS | ||