TÜRKÇE
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Information
| Code | CKZ205 |
| Name | Differential Equations |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ABDULKADİR YAŞAR |
Course Goal
The aim of this course is to realize fundaemental mathematical concepts found in engineering problems and showing them the basic analytical solution methods.
Course Content
Series.Power Series. Taylor and MacLaurin Series. Complex Numbers. Vektor Functions. Gradient., Divergence, Laplacian Operators. Directional Derivative. Line Integrals. Area Integrals. Differential Equations: Definition and Types. First-Order Equations. Linear Equations. First-Order Partial Differential Equations. Second-Order Equations with Constant Coefficients. Laplace Transformations.
Course Precondition
Yok
Resources
Calculus and Analytic Geometry (Sherman K. STEIN, Anthony BARCELLOS, McGraw-Hill, Inc.)Mühendisler için Matematik Ders Notları (Ali Hamza TANRIKULU)
Notes
Mathematics for Engineers, Prof.Dr. Hamza TANRIKULU, Lectures Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand establish differential equations. |
| LO02 | Perceive an ability to solve first order differential equations. |
| LO03 | Understand an ability to solve first-order nonlinear differential equations of certain types. |
| LO04 | Understand the ability to interpret solutions of first-order differential equations. |
| LO05 | Understand an ability to solve higher order differential equations with constant coefficients. |
| LO06 | Understand he ability to find series solutions near ordinary and regular singular points of second-order linear differential equations |
| LO07 | Understand an ability to solve to using Laplace transformation for higher-order linear differential equations. |
| LO08 | Understand an ability to solving to using Fourier series methods of linear differential equations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Student become equipped with the basic knowledge of math, science and engineering | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Students gain a command of basic concepts, theories and principles in chemical engineering | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Students are able to design and carry out experiments in the basic fields of chemical engineering, and interpret the results and the data obtained from the experiments | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Students become equipped with a variety of skills and knowledge regarding engineering techniques | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Students are able to design a system, component or process in order to meet the needs of various engineering problems within technical, economic, environmental, manufacturability, and sustainability limits. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Students independently review and learn the applications in an enterprise, make a critical assessment of the problems faced with, formulate problems and propose solutions by selecting the proper technique | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Students take initiative in identification, design, development and use of a product or production process | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Students become aware of the necessity of lifelong learning and continuously self-renew | 2 |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students use Turkish effectively for technical or non-technical topics orally or in wirtten form, and at least one foreign language | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students become effective in using computer, computer-aided drafting, design, analysis, and presentation | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students have good communicatino skills with a tendency to work in teams, and are able to work effectively as a member of an interdisciplinary team | 2 |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Students become aware of the technical and ethical responsibilities, as well as being inquisitive and innovative |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sequences. Series. Convergence-Divergence | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Power Series. Taylor and Maclaurin Series | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | Complex Numbers | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Partial Differentiation. Chain Rule | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | Vector Calculus. Gradient and Directional Derivative | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Multiple Integrals: Double Integrals | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Area Integrals using Polar Coordinates | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Midterm Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Divergence, Curl and Laplacian. Line Integrals | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | Differential Equations (DE), First-order DE | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | Linear First-order Partial DE | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Nonhomogeneous DE | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Laplace Transformation | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Second-order Linear Partial DE | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | DE Applications | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 16 | Term Exams | Final Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Final Exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 5 | 70 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 5 | 5 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 5 | 5 |
| Final Exam | 1 | 5 | 5 |
| Total Workload (Hour) | 155 | ||
| Total Workload / 25 (h) | 6,20 | ||
| ECTS | 6 ECTS | ||