TÜRKÇE
ENGLISH
Information
| Code | FZK203 |
| Name | Differential Equations |
| 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 Goal
Teaching of basic theories of differential equations, solutions and applications
Course Content
Classification of diferential equations, Existence of solutions, First-order differential equations, Applications of first-order differential equations, Solutions of Second and Higher-order linear differential equations, Applications of Second-order linear diferential equations, Series solutions of differential equations, Frobenius method, Approximate methods of solving first-order equations, Laplace transform, Laplace transform solution of linear differential equations with constant coefficients
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 | Evaluate the developmets in the field of Physics by using scientific methods and techniques. | 1 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Combine the knowledge in the field of physics with the other scientific area | 2 |
| 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 | Explain the methods of producing scientific knowledge in the field of physics | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Reach the Information in the field of physics, for the purpose of classification, and uses. | 1 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Use the advanced theoretical and practical knowledge acquired in the field of physics. | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Design experiments in the field of physics. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Inform the specialist or non-specialist groups, orally or in writing on issues related to physics. | 2 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Use the information technologies in Physics area for their purpose. | 1 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Take responsibility as a team or alone to overcome the problems encountered in the field of physics . | 2 |
| PLO12 | Bilgi - Kuramsal, Olgusal | Plan and manage the activities for the professional developments of emplyees under his/her responsibilities. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Classify, use and critically evaluate the knowledg taken by his/her efforts. | 1 |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Know that learning process is life-long and acts accordingly. | 1 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Both with colleagues, as well as off the field of builds relationships ethically use information, communication technologies. Define necessities in learning in scientific, social, cultural and artistic areas and improve himself/herself accordingly. | 1 |
| PLO16 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have knowledge of a foreign language at least monitoring developments in the field of physics. | |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Know the importance of individual development. | 1 |
| PLO18 | Yetkinlikler - Öğrenme Yetkinliği | Monitor the developments in the field of physics, learn and evaluate in terms of social ethics. |
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 | ||