TÜRKÇE
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Information
| Code | MT235 |
| Name | Differential Equations |
| Term | 2023-2024 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. LEYLA BUGAY |
| Course Instructor |
Doç. Dr. LEYLA BUGAY
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to teach differential equations and its clasifications, first order differantial equations, exact differantial equations, linear differantial equations, Bernoulli differantial equations, Cauchy- Euler equations, systems of linear differantial equations and Laplace transformations to the students.
Course Content
In this course differential equations and their solutions, clasification of differential equations, initial value problems, boundary value problems and existence of solutions, exact differential equations and integrating factor, seperable equations and equations reducible to this form, Linear equations ve Bernoulli equations, explicit methods of solving higher order linear differantial equations, homogeneous linear equations with constant coefficients, the method of undetermined coefficients, variations of parameters, Cauchy- Euler equations, system of linear differantial equations, Laplace transformations, basic properties of Laplace transformations are described.
Course Precondition
Basic knowledge of derivatives and integrals is required.
Resources
Differentiel Equuations, L.Shipley Ross Differentiel Equuations, Frank Ayres Differential Equations, Lester R. Ford
Notes
Diferansiyel Denklemler ve Uygulamaları, mehmet Aydın, Gönül Gündüz,Beno Kuryel
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes some differential equations. |
| LO02 | Recognizes first order differantial equations. |
| LO03 | Recognizes exact differantial equations. |
| LO04 | Recognizes linear differantial equations. |
| LO05 | Recognizes and solves Cauchy - Euler equations. |
| LO06 | Recognizes the systems of linear differantial equations. |
| LO07 | Recognizes Laplace transformations. |
| LO08 | Recognizes to find the solution of certain differantial equations by using Laplace transformations. |
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 | Demonstrate the ability to express the basic theories of mathematics both correctly. | 4 |
| 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. | 2 |
| 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. | 1 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| 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. | 2 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 1 |
| 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. | 1 |
| 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. | 2 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 2 |
| 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. | 1 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Differential equations and their solutions | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Classification of differential equations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 3 | Initial value problemsand existence of their solutions | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 4 | Exact differential equations and integrating factor | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 5 | Seperable equations and equations reducible to this form | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 6 | Linear equations and Bernoulli equations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 7 | To find the solution of the linear differantial equations with higher order | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The homogeneous linear equations with constant coefficients | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 10 | The method of undetermined coefficients | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 11 | Variations of parameters | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 12 | Cauchy - Euler equations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 13 | System of linear differantial equations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 14 | Laplace transformations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 15 | Basic properties of Laplace transformations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
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 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 152 | ||
| Total Workload / 25 (h) | 6,08 | ||
| ECTS | 6 ECTS | ||