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Information
| Unit | FACULTY OF ENGINEERING |
| INDUSTRIAL ENGINEERING PR. | |
| Code | ENM105 |
| Name | Linear Algebra |
| Term | 2025-2026 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 3-1 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3.5 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. DİLEK KAHYALAR |
| Course Instructor |
The current term course schedule has not been prepared yet. Previous term groups and teaching staff are shown.
|
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 | Acquires sufficient knowledge in mathematics, science and Industrial Engineering discipline-specific subjects; acquires the ability to use theoretical and applied knowledge in these fields in complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires the ability to identify, define, formulate and analytically solve complex Industrial Engineering problems; and has the ability to select and apply appropriate analysis and modelling methods for this purpose. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Acquires the ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; acquires the ability to apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquires the ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Industrial Engineering applications and acquires the ability to use information technologies effectively. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Acquire the skills to design and conduct experiments, collect data, analyze and interpret results to investigate complex Industrial 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, both verbally and in writing; knowledge of at least one foreign language; ability to write and understand effective reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | They have awareness of the necessity of lifelong learning; they have the ability to access information, follow developments in science and technology, and constantly renew themselves. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Acting in accordance with ethical principles, becoming knowledgeable about the standards used in engineering practices with awareness of professional and ethical responsibility. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Learn about business practices such as project management, risk management and change management, and is aware of entrepreneurship and innovation. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Informed about the universal and societal impacts of engineering practices on health, environment and safety, and the contemporary problems reflected in the field of engineering, and is aware of the legal consequences of engineering solutions. | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Benefit from the power of effective communication in professional life and has the ability to interpret developments correctly. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Have the ability to design, develop, implement and improve integrated systems that include machines, people, time, information or money. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | By applying modern design methods, they have the ability to design, develop, implement and improve complex products, processes, businesses and systems under realistic conditions and constraints such as cost, environment, sustainable development, energy, manufacturability, ethics, 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 |
Assessment (Exam) Methods and Criteria
Current term shares have not yet been determined. Shares of the previous term are shown.
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||