ECTS - Linear Algebra
Linear Algebra (MATH275) Course Detail
Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
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Linear Algebra | MATH275 | 3. Semester | 4 | 0 | 0 | 4 | 6 |
Pre-requisite Course(s) |
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N/A |
Course Language | English |
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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) |
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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;
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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 |
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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 |
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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 |
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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 |
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Percentage of Final Work | 40 |
Total | 100 |
Course Category
Core Courses | |
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Major Area Courses | |
Supportive Courses | X |
Media and Managment Skills Courses | |
Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
# | Program Qualifications / Competencies | Level of Contribution | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | Gains sufficient knowledge in subjects specific to mathematics, natural sciences, and engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields to solve complex engineering problems. | X | ||||
2 | Defines, formulates, and solves complex engineering problems; selects and applies appropriate analysis and modeling methods for this purpose. | X | ||||
3 | Designs a complex system, process, device, or product under realistic constraints and conditions to meet specific requirements; applies modern design methods. | X | ||||
4 | Selects and uses modern techniques and tools necessary for analyzing and solving complex problems encountered in engineering applications; gains the ability to use information technologies effectively. | X | ||||
5 | Designs experiments, conducts experiments, collects data, and analyzes and interprets the results for studying complex engineering problems or research topics specific to engineering disciplines. | X | ||||
6 | Works effectively in both disciplinary and multidisciplinary teams; gains the ability to work individually. | |||||
7 | Develops effective oral and written communication skills; acquires proficiency in at least one foreign language; writes effective reports and understands written reports, prepares design and production reports, delivers effective presentations, and gives and receives clear and understandable instructions. | |||||
8 | Develops awareness of the necessity of lifelong learning; gains access to information, follows developments in science and technology, and continuously renews oneself. | |||||
9 | Acts in accordance with ethical principles, takes professional and ethical responsibility, and possesses knowledge of standards used in engineering applications. | |||||
10 | Gains knowledge of business practices such as project management, risk management, and change management; develops awareness of entrepreneurship and innovation; possesses knowledge of sustainable development. | |||||
11 | Gains knowledge of the impacts of engineering applications on health, environment, and safety in universal and societal dimensions, and the issues reflected in contemporary engineering fields; develops awareness of the legal consequences of engineering solutions. | |||||
12 | Gains the ability to work in both thermal and mechanical systems fields, including the design and implementation of such systems. |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |