TÜRKÇE
ENGLISH
Information
| Code | ENM105 |
| Name | Linear Algebra |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 3-1 (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 | Doç. Dr. DİLEK KAHYALAR |
| Course Instructor |
Doç. Dr. DİLEK KAHYALAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The objectives of this course are to introduce the students with the basic ideas of linear algebra including vector spaces, subspaces, basis, dimension, linear transformations, matrices, systems of linear equations, eigenvalues and eigenvectors and to teach the understanding of abstract mathematical concepts and abstract thought arising from the concepts covered in this course.
Course Content
Vectors in the plane and space; vector spaces, subspaces, linear dependence, bases and finite dimensional vector spaces, linear transformations, matrices, representation of linear transformations by matrices, direct sum, systems of linear equations, determinants, characteristic vectors and diagonalization.
Course Precondition
NONE
Resources
Arif Sabuncuoğlu,Mühendislik ve İstatistik Bölümler İçin Lineer CebirNobel Akademik Yayıncılık 2012
Notes
Arif Sabuncuoğlu,Mühendislik ve İstatistik Bölümler İçin Lineer CebirNobel Akademik Yayıncılık 2012
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Is able to prove Mathematical facts encountered in secondary school. |
| LO02 | Recognizes the importance of basic notions in Algebra, Analysis and Topology |
| LO03 | Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
| LO04 | Is able to express basic theories of mathematics properly and correctly both written and verbally |
| LO05 | Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
| LO06 | Expresses clearly the relationship between objects while constructing a model |
| LO07 | Draws mathematical models such as formulas, graphs and tables and explains them |
| LO08 | Is able to mathematically reorganize, analyze and model problems encountered. |
| LO09 | Knows at least one computer programming language |
| LO10 | Uses effective scientific methods and appropriate technologies to solve problems |
| LO11 | Knows programming techniques and is able to write a computer program |
| LO12 | Is able to do mathematics both individually and in a group. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have sufficient knowledge of mathematics, science and related engineering disciplines; can use the theoretical and applied knowledge in these fields in complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquire the ability to identify, define, formulate and solve complex Industrial Engineering problems; for this purpose, will have the ability to choose and apply appropriate analysis and modeling methods. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; can apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Develops modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications, and has the ability to use information technologies effectively. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Have the ability to design experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Have the ability to work effectively in disciplinary and multi-disciplinary teams or individually. | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; have the ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Have the awareness of the necessity of lifelong learning; can follow the developments in science and technology and have the ability to constantly renew themselves. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Acts in accordance with ethical principles, has knowledge about the standards used in engineering applications with the awareness of professional and ethical responsibility. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Gain knowledge of business practices such as project management, risk management and change management; become aware of entrepreneurship and innovation. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains knowledge about 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 and has awareness of the legal consequences of engineering solutions. | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | They can benefit from the power of effective communication in their professional life and have the ability to interpret developments correctly. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve integrated systems involving machine, time, information and money. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve complex products, processes, businesses, systems by applying modern design methods, under realistic conditions and constraints such as cost, environment, sustainability, manufacturability, ethical, health, safety and political issues. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Vector space, subspace | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 2 | Linear dependence, independence and a basis of a vector space | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Fundamental properties of the base of a vector space and the dimension of the vector space | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 4 | Sum of subspaces, direct sum | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 5 | Linear transformations, their kernels and images | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 6 | The rank of a linear transformation, isomorphism | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Matrices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Representation of linear transformations by matrices | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 10 | The rank of a matrix, echelon matrix | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 11 | Row equivalent matrices and systems of linear equations | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 12 | Determinant function, properties of determinant, evaluation of determinant | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 13 | Cramer's Rule, Eigenvalues and Eigenvectors(characteristic values and vectors) | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Cramer Rule, eigen values and eigen vectors | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 15 | Characteristic spaces and characteristic polynomial | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | 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 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 153 | ||
| Total Workload / 25 (h) | 6,12 | ||
| ECTS | 6 ECTS | ||