TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF ENGINEERING |
| INDUSTRIAL ENGINEERING PR. | |
| Code | ENM105 |
| Name | Linear Algebra |
| Term | 2021-2022 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 ERSALAN |
| Course Instructor |
Doç. Dr. DİLEK ERSALAN
(Güz)
(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
Resources
Notes
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 | - | Adequate knowledge in mathematics, science and related engineering discipline; ability to use theoretical and practical knowledge in these areas in complex engineering problems. | 3 |
| PLO02 | - | An ability to identify, formulate, and solve complex industrial engineering problems; the ability to select and apply appropriate analysis and modeling methods for this purpose. | 2 |
| PLO03 | - | An ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; the ability to apply modern design methods for this purpose. | 2 |
| PLO04 | - | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications; ability to use information technologies effectively. | 2 |
| PLO05 | - | Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or discipline-specific research topics. | 3 |
| PLO06 | - | Ability to work effectively in disciplinary and multidisciplinary teams; self-study skills. | 1 |
| PLO07 | - | Ability to communicate effectively in Turkish presentation and in writing; knowledge of at least one foreign language; Ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and understandable instruction and receiving skills. | 3 |
| PLO08 | - | Awareness of the necessity of lifelong learning; the ability to access information, follow developments in science and technology, and constantly renew oneself. | 2 |
| PLO09 | - | To act in accordance with ethical principles, professional and ethical responsibility awareness; information about standards used in engineering applications. | 2 |
| PLO10 | - | Information on business practices such as project management, risk management and change management; awareness about entrepreneurship and innovation; information on sustainable development. | 2 |
| PLO11 | - | Information about the effects of engineering applications on health, environment and safety in universal and social dimensions and the problems reflected in the engineering field of the age; awareness of the legal consequences of engineering solutions. | 1 |
| PLO12 | - | Ability to make use of the power of effective communication in professional life, to interpret the developments correctly and to make decisions. | 1 |
| PLO13 | - | Ability to design, develop, implement and improve integrated systems including machinery, time, information and money. | 1 |
| PLO14 | - | Ability to design, develop, implement and improve complex product, process, business, system design by applying modern design methods under realistic conditions and constraints such as cost, environment, sustainability, productivity, ethics, health, safety and political issues. | 1 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Vector space, subspace | Required readings | |
| 2 | Linear dependence, independence and a basis of a vector space | Required readings | |
| 3 | Linear dependence, independence and a basis of a vector space | Required readings | |
| 4 | Sum of subspaces, direct sum | Required readings | |
| 5 | Linear transformations, their kernels and images | Required readings | |
| 6 | The rank of a linear transformation, isomorphism | Required readings | |
| 7 | Matrices | Required readings | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Representation of linear transformations by matrices | Required readings | |
| 10 | The rank of a matrix, echelon matrix | Required readings | |
| 11 | Row equivalent matrices and systems of linear equations | Required readings | |
| 12 | Determinant function, properties of determinant, evaluation of determinant | Required readings | |
| 13 | Determinant function, properties of determinant, evaluation of determinant | Required readings | |
| 14 | Cramer Rule, eigen values and eigen vectors | Required readings | |
| 15 | Characteristic spaces and characteristic polynomial | Required readings | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
Assessment (Exam) Methods and Criteria
| 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 | ||