TÜRKÇE
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Information
| Code | TYP201 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-2 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Arş.Gör.Dr. MELEK YAĞCI |
| Course Instructor |
Doç. Dr. DOĞAN KAYA
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
This course aims to introduce basic ideas on differential equations and to solve this equations to the students.
Course Content
Differential equations and their classification, First order differential equations, Exact differential equations, Linear differential equations, Bernoulli differential equations, Cauchy Euler differential equations, Linear differential equations systems, Laplace transformations
Course Precondition
None
Resources
Shepley L.Ross, Differential Equations
Notes
Boyce E. W. and DiPrima C. R., Elementary Differential Equations and Boundary Value Problems
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Student, who succeed this course ; Makes definition and classification of differential equations |
| LO02 | Obtains a differential equations eliminating arbitrary constants that given in a function |
| LO03 | Knows general types of differential equations of first order and finds general solutions of them |
| LO04 | Knows main theory of higher order Linear differential equations |
| LO05 | Finds general solutions homogeneous and nonhomogeneous Linear differential equations with constant coefficients |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Makes aplication of engineering design of irrigation systems and conducts tests about the materıals used ın these systems and preapares reports | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Developes and implements strategies for wastewater, drainage water, runoff water such as treated waste water re-use of non-conventional water without adversely affecting the environment, makes laboratory analysis about saline alkali soils and water suitability to irrigation and reports. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Prepares project about soil and water structures, animal houses, storage structures and crop production structures. Analyzes in terms of static and strength. Determines the properties of materials used in construction and makes the relevant tests. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Designs crop production systems, controls environmental domestic conditions and operates, makes the selection of materials to be used, tests and prepares a report. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Designs and projects small dams, ponds. Prepares and implements flood action plans within the scope of integrated watershed management. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Developes and implement s strategies of sustainable water management for the purposes of protecting water resources and agricultural production. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Developes and implements irrigation programmes using the soil-plant-water relations and soil engineering properties | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Prepares land consolidation projects and applies. Provides farm developing systems. Prepares and implements rural development projects. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Exposes the problems about soil and water conservation (erosion) and water harvesting, prepares and implements the project. | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Etudes drainage of agricultural lands, plans drainage systems,prepares projects and makes aplications, selects materials to be used, tests and prepares a report | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Plans activities related to operation, maintenance and repairs irrigation network,developes project formulations in monitoring and evaluations, operates the irrigation networks. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Works independently and takes responsibility | 5 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Has the ability to design and apply analytical, modelling and experimental researches,and acquires the skill of analyzing and interpreting the complex issiues occured during this process . | 5 |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Creates effective solutions for sustainable agricultural production | 5 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Accesses to the resources in the field, uses of these resources and continuous self-improvement | |
| PLO16 | Yetkinlikler - Alana Özgü Yetkinlik | Developes projects to protect natural resources like water,and offers the benefit to society, using the information of basic engineering, basic agricultural engineering and agricultural structures and irrigation engineering . | 5 |
| PLO17 | Yetkinlikler - Alana Özgü Yetkinlik | Has the ability to analyze problems ,make decisions and solve about professional subjects | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of Differential Equations and Classification | Lecture notes | Öğretim Yöntemleri: Anlatım, Gösteri |
| 2 | Iitial and Bounded Value Problems | Lecture notes | Öğretim Yöntemleri: Anlatım, Gösteri |
| 3 | Obtained Differential Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösteri |
| 4 | Exact Differential Equations and Integrating Factor | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Bireysel Çalışma |
| 5 | Seperable Differential Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösteri, Örnek Olay |
| 6 | Homogenous Differential Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Gösteri, Gösterip Yaptırma, Grup Çalışması |
| 7 | Linear and Bernouilli Differential Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama, Gösteri, Gösterip Yaptırma, Örnek Olay, Bireysel Çalışma, Problem Çözme |
| 8 | Midterm Exam | Lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Main theory of High order Linear Differential Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösteri, Grup Çalışması |
| 10 | Homogenous Differential Equations with Costant Coefficient | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösteri |
| 11 | Nonhomogenous Differential Equations with Costant Coefficient | Lecture notes | Öğretim Yöntemleri: Anlatım, Gösteri, Grup Çalışması, Örnek Olay, Problem Çözme |
| 12 | The method of undetermined coefficients | Lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama, Gösteri |
| 13 | Method of the variation of Parameters | Lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Gösteri, Gösterip Yaptırma, Grup Çalışması |
| 14 | Cauchy Euler Equations | Lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösteri, Grup Çalışması, Beyin Fırtınası |
| 15 | Laplace Dönüşümleri | Lecture notes | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Gösterip Yaptırma, Örnek Olay, Bireysel Çalışma, Problem Çözme |
| 16 | Final Exam | Review the topics | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Final Exam | Review the topics | 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 | 1 | 1 | 1 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 2 | 2 |
| Final Exam | 1 | 2 | 2 |
| Total Workload (Hour) | 117 | ||
| Total Workload / 25 (h) | 4,68 | ||
| ECTS | 5 ECTS | ||