ECTS - Linear Algebra
Linear Algebra (MATH275) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Linear Algebra | MATH275 | 3. Semester | 4 | 0 | 0 | 4 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Drill and Practice. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to enrich the knowledge of engineering students in linear algebra, and to teach them the basics and application of the methods for the solution of linear systems occurring in engineering problems. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Linear equations and matrices, real vector spaces, inner product spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Systems of Linear Equations, Matrices, Matrix Multiplication, Algebraic Properties of Matrix Operations | pp. 1-39 |
| 2 | Special Types of Matrices and Partitioned Matrices, Echelon Form of a Matrix, Solving Linear Systems | pp. 42-49, 86-93, 95-103, 111-113 |
| 3 | Elementary Matrices; Finding Inverses, Equivalent Matrices | pp. 117-124, 126-129 |
| 4 | Determinants, Properties of Determinants, Cofactor Expansion | pp. 141-145, 146-154, 157-163 |
| 5 | Inverse of a Matrix (via Its Determinant), Other Applications of Determinants (Cramer’s Rule) | pp. 165-168, 169-172 |
| 6 | Vectors in the Plane and In 3-D Space, Vector Spaces, Subspaces | pp. 177-186, 188-196, 197-203 |
| 7 | Span, Linear Independence, Basis and Dimension | pp. 209-214, 216-226, 229-241 |
| 8 | Homogeneous Systems, Coordinates and Isomorphism, Rank of a Matrix | pp. 244-250, 253-266, 270-281 |
| 9 | Inner Product Spaces, Gram-Schmidt Process | pp. 290-296, 307-317, 320-329 |
| 10 | Orthogonal Complements, Linear Transformations and Matrices | pp. 332-343, 363-372 |
| 11 | Kernel and Range of a Linear Transformation | pp. 375-387 |
| 12 | Matrix of a Linear Transformation | pp. 389-397 |
| 13 | Eigenvalues and Eigenvectors | pp. 436-449 |
| 14 | Diagonalization and Similar Matrices, Diagonalization of Symmetric Matrices | pp. 453-461, 463-472 |
| 15 | General Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. Elementary Linear Algebra, B. Kolman and D.R. Hill, 9th Edition, Prentice Hall, New Jersey, 2008 |
|---|---|
| Other Sources | 2. Linear Algebra, S. H. Friedberg, A. J. Insel, L. E. Spence, Prentice Hall, New Jersey, 1979 |
| 3. Basic Linear Algebra, Cemal Koç, Matematik Vakfı Yay., Ankara, 1996 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. | X | ||||
| 2 | An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. | X | ||||
| 3 | An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) | |||||
| 4 | An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively. | |||||
| 5 | An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. | |||||
| 6 | An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. | X | ||||
| 7 | An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings. | |||||
| 8 | An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation. | |||||
| 9 | Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself. | |||||
| 10 | A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project. | |||||
| 11 | Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions. | X | ||||
| 12 | Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions. | |||||
| 13 | Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism. | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 86 | ||