TÜRKÇE
ENGLISH
Information
| Code | CEN209 |
| Name | Differential Equations |
| Term | 2024-2025 Academic Year |
| 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 Instructor |
Arş.Gör.Dr. Mehmet GÜRSUL
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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 | Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills. | 2 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development. | 5 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions. |
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 | ||