TÜRKÇE
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Information
| Code | G244 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| Semester | 4. 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. MAHMUT ÇETİN |
| Course Instructor |
1 2 |
Course Goal / Objective
Primary objectives of the course are to: 1) formulate derivatively any engineering problem, 2) learn how to find general and particular solution of differential equations, 3) define initial and boundary values of the paroblem, and find the particular solution accordingly.
Course Content
Introduction to differential equations and general definitions; First-Order differential equations; One variable second order differential equations; Second-order linear differential equations with constant coefficients; Higher-order linear differential equations with constant coefficients; Linear differential equations with vaqriable coefficients; Systems of Differential Equations; Laplace transformations; Partial differential equations; Numerical solutions of differential equations (Euler, Heun and 4th order Runge-Kutta methods)
Course Precondition
There is no prerequisite for enrolling to this course.
Resources
1. Hoffman, J. D., 1993. Numerical Methods for Engineers and Scientists. McGraw-Hill International Editions, 825 p. 2. Karadeniz, A., 1996. Yüksek Matematik Problemleri. Çağlayan Kitabevi, İstanbul. 3. Karadeniz, A., 1997. Yüksek Matematik. Cilt 1-3, Çağlayan Kitabevi, İstanbul. 4. Pekol, S., Demirseren, 1975. Diferansiyel Denklemler, Uygulamaları ve Çözüm Tekniği. Çağlayan Kitabevi, İstanbul, 436 s. (Spiegel, M., 1967. Applied differential Equations isimli yayının Türkçe Çevirisi). 5. Rabenstein, A. L., 1975. Elementary Differential Equations with Linear Algebra. Academic Press, Inc., 374 p. 6. Spiegel, M., 1967. Applied differential Equations. Second Edition, Prentice-Hall, Inc., USA, 412 p.
Notes
Other supplementary materials uploaded to ÇUBIS web site.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns to formulate derivatively any engineering problem. |
| LO02 | Gain skills how to find general and particular solution of differential equations. |
| LO03 | Defines initial and boundary values of the paroblem in the hand |
| LO04 | Finds particular solutions based on initial and boundary values by applying numerical techniques, and interprets the solution for his own purposes. |
| LO05 | Learns how to formulate a differential equation. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have sufficient knowledge in the fields of basic sciences (mathematics / science) and food engineering and the ability to use theoretical and applied knowledge in these areas in complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Identifies, defines and solves complex engineering problems in applications in the fields of food engineering and technology. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Gains the ability to apply a complex system or process related to food products and production components using modern design methods under certain constraints and conditions. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Choosing and using modern technical tools necessary for analysis and solution of complex problems encountered in food engineering and technology applications; For this purpose, he/she uses information technologies. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Gaining laboratory skills for the analysis and solution of complex problems in the field of food engineering, designing an experiment, conducting an experiment, collecting data, analyzing and interpreting the results. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Takes responsibility individually and as a team member to solve problems encountered in food engineering applications. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Gains the ability to communicate verbally and in writing in Turkish / English related to the field of food engineering, to write reports, to prepare design and production reports, to present effectively and to use communication technologies. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Recognizing the necessity of lifelong learning and constantly improving himself/herself in the field of food engineering. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Gains the awareness of food legislation and management systems and professional ethics. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Using the knowledge of project design and management, he/she attempts to develop and realize new ideas about food engineering applications; have information about sustainability. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has awareness about the effects and legal consequences of engineering practices related to food safety and quality on consumer health and environmental safety within the framework of national and international legal regulations. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to differential equations and basic definitions regarding ordinary and partial differential equations including derivative, differentiation, general solution, solutions subject to the boundary-values etc. | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | First-Order Differential Equations: Separable Equations | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | First-Order Differential Equations: Homogeneous Differential Equations | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | First order differential equations: Application of separable and homogeneous type differential equations to some problems in real life | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | First-Order Differential Equations:Bernoulli Equation | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Gösterip Yaptırma, Problem Çözme |
| 6 | First-Order Differential Equations: Exact Differential Equations and Integrating Factor | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | First-Order Differential Equations: Clairaut and Lagrange Differential Equations | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Sections from different text books relevant to the subject | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Second-order linear differential equations with constant coefficients | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Benzetim, Problem Çözme |
| 10 | Second-order linear differential equations with constant coefficients - applications to real life problems | Study all the relevant subjects from different sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Higher-order linear differential equations with constant coefficients | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Differential Equations with Variable Coefficients: Euler equation | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 13 | Systems of First Order Linear Differential Equations | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | The Laplace Transformations; Numerical Methods for Solving Differential Equations (Euler, improved Euler formula or the Heun formula) | Sections from different chapters relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Numerical Methods for Solving Differential Equations (The fourth-order Runge-Kutta method); Some Partial Differential Equations and Solution Techniques | Sections from different text books relevant to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Gösterip Yaptırma, Beyin Fırtınası |
| 16 | Term Exams | Study all the relevant subjects for the final exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Study all the relevant subjects for the 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 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||