TÜRKÇE
ENGLISH
Information
| Code | CEN209 |
| Name | Differential Equations |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
Course Goal
Objectives of this course are in order to solve many problems in enginering, first, to formulate these problems with mathematical statements and find solutions to these problems by using initial and bounded conditions. To give insight and skill about the concrete aspects of linear algebra,To provide basic concepts of matrices and the systems of homogeny and linear equations,To solve the systems using matrices, To teach vector spaces and abstract mathematical concepts,To teach abstract thought. know the equations of circle and sphere and do their applications
Course Content
First order differential equations; separable equations, linear equations, Exact equations and integrating factor, Higher order differential equations the method of variation of parameters, Constant coefficient equations, the method of undetermined coefficients Laplace transformation; basic definition and theorems. System of linear equations, elementary operations, finding solutions of linear and homıogen systems of equations using elementary operations, matrices and special types of matrices, finding inverses of matrices in elementary operations, determinants, finding determinants of blocked and special types of matrices, using determinant for solving Cramer systems. Vectors in the plane and space, vector spaces, subspaces, linear dependence of vectors, bases of vector spaces,
Course Precondition
NONE
Resources
Differantial Equation, Shepley L. Ross.
Notes
Differantial Equation, Shaum Series.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Can make definition and classification of differential equations |
| LO02 | Can obtained a differential equations eleminating arbitrary constants that given a function |
| LO03 | Knows the first order differantial equations and their solutions |
| LO04 | Can use the methods; Exact, Separeble, Homogeneus, Linear and Bernoulli. |
| LO05 | Can know the higher order linear equations and solve some of them. |
| LO06 | Can solve some of liear equations systems. |
| LO07 | Can solve differential equations by using Laplaca Transformations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has capability in the fields of mathematics, science and computer that form the foundations of engineering | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Identifies, formulates, and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques, | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Analyzes a system, its component, or process and designs under realistic constraints to meet the desired requirements,gains the ability to apply the methods of modern design accordingly. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to use modern techniques and tools necessary for engineering practice and information technologies effectively. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and to conduct experiments, to collect data, to analyze and to interpret results | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Has ability to work effectively as an individual and in multi-disciplinary teams, take sresponsibility and builds self-confidence | 2 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Can access information,gains the ability to do resource research and uses information resources | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Awareness of the requirement of lifelong learning, to follow developments in science and technology and continuous self-renewal ability | 5 |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to communicate effectively orally and in writing, and to read and understand technical publications in at least one foreign language | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility, | 5 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Awareness about project management, workplace practices, employee health, environmental and occupational safety, and the legal implications of engineering applications, | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation, and knowledge of contemporary issues | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition and Classification of Differential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Examples from Applied Sciences | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | First Order First Degree Differential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | First Order Higher Degree Differential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Higher Order Linear Differential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Homogeneous Linear Differential Equations with Constant Coefficients | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Nonhomogeneous Differential Equations with Constant Coefficients | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Prepare exam quations | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Linear Differential Equations with Variable Coefficients | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Nonlinear Differential Equations with Variable Coefficients | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Series Solution of Second Order Linear Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | The Laplace Transform | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | The Systems of First Order Linear Differential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Systems of Homogeneous Linear Equtions with Constant Coefficients | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Systems of Homogeneous Linear Equtions with Constant Coefficients 1 | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 16 | Term Exams | Prepare exam quations | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Prepare exam quations | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||