TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ201 |
| Name | Differential Equations |
| Term | 2026-2027 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YUSUF ALPER KAPLAN |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
Objectives of this course are in order to solve many problems in algorithms, 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, Shepley L. Ross.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Can make definition and classification of differential equations |
| LO02 | Knows the first order differantial equations and their solutions |
| LO03 | Can use the methods; Exact, Separeble, Homogeneus, Linear and Bernoulli. |
| LO04 | Can solve higher order linear equations and some types |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | |
| PLO04 | - | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops the ability to solve complex problems. |
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 | ||