| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Linear Algebra | BM213 | Turkish | Compulsory | 3. Semester | 3 + 0 | 3.0 | 3.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | |
| Course Coordinator | Dr. Öğr. Üyesi Mustafa İsa DOĞAN |
| Instructor(s) | Prof. Dr. Fatih TAŞPINAR (Güz) |
| Goals | 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 Content | Linear Algebra, Matrix theory, Vectors |
| # | Öğrenme Kazanımı |
| 1 | Solves the n dimensional linear systems by determinant(Cramer) method. |
| 2 | Calculates the values of n dimensional determinats by reducing to triangle matrix, and by reducing the dimension by Laplace method. Calculates the value of the special determinants which are the types of Wandermonde and three diagonal by using formulas |
| 3 | Finds the solution by using the inverse matrix method in the state of definite linear system. |
| 4 | Examines the general system by using rank method, when the condition is compatible the finds its solution. |
| 5 | Finds the eigenvalues and eigenvector of square matrix. |
| 6 | |
| 7 |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Introduction. Overview of the subjects, history and methods of the linear algebra. | Interview Presentation (Preparation) Practice Class Hours |
| 2. Week | Systems involving two and three variables. Gauss method. Determinants of 2- and 3-dimensional matrices. | Interview Practice Presentation (Preparation) Class Hours |
| 3. Week | Geometric interpretation of the two- and three-dimensional system. Definition of the n-dimensional determinant. | Class Hours Interview Presentation (Preparation) Practice |
| 4. Week | Characteristics of the n-dimensional determinant and its calculation methods | Presentation (Preparation) Practice Interview Class Hours |
| 5. Week | Special determinants. Triangular, Wandermond and Tridiagonal shape determinants. | Interview Presentation (Preparation) Practice Class Hours |
| 6. Week | Laplace and Anti-Laplace theorems. Cramer’s theorem for the square system. | Interview Practice Presentation (Preparation) Class Hours |
| 7. Week | Matrices, operations on matrices. Inverse matrix and its finding methods. | Interview Practice Class Hours Presentation (Preparation) |
| 8. Week | Transformations of the square system to matrix form and solution with inverse matrix method. | Practice Class Hours Presentation (Preparation) Interview |
| 9. Week | Kronecker-Kapelli for general systems. | Class Hours Presentation (Preparation) Interview Practice |
| 10. Week | n-dimensional real and complex vector spaces. Linear independence bases and coordinates. | Interview Practice Presentation (Preparation) Class Hours |
| 11. Week | Linear transformation and its matrix. Transformation of matrix by base change. | Presentation (Preparation) Class Hours Practice Interview |
| 12. Week | Eigenvalues and eigenvectors. Hamilton-Cayley and Silvester theorems. | Practice Interview Class Hours Presentation (Preparation) |
| 13. Week | Jordan normal form of matrix. Similarity. Similarity condition of diagonal matrix. | Interview Presentation (Preparation) Practice Class Hours |
| 14. Week | Metric, Normed and Euclidean space. Length, angle, quadratic forms, numerical image. | Interview Practice Presentation (Preparation) Class Hours |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge of mathematics, science and related engineering disciplines; Ability to use theoretical and applied knowledge in these fields in complex engineering problems | ✔ | |||||
| 2 | Ability to identify, define, formulate and solve complex engineering problems; for this purpose, the ability to select and apply appropriate analysis and modeling methods | ✔ | |||||
| 3 | Knowledge and awareness about the management, control, development and security/reliability of Information Technologies | ✔ | |||||
| 4 | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; for this purpose, the ability to apply modern design methods | ✔ | |||||
| 5 | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself | ✔ | |||||
| 6 | Ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics | ✔ | |||||
| 7 | Ability to work effectively in disciplinary and multi-disciplinary teams; individual study skills | ✔ | |||||
| 8 | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; Ability to use information technologies effectively | ✔ | |||||
| 9 | Knowledge of 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; awareness of the legal consequences of engineering solutions | ✔ | |||||
| 10 | Ability to communicate effectively in Turkish orally 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 and receive clear and understandable instructions | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 |
|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY3 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY4 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY5 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY6 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY7 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY8 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY9 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY10 | 3 | 3 | 3 | 3 | 3 | 3 |
| Ders Kitabı veya Notu |
|
|---|---|
| Diğer Kaynaklar |
|
| Güz Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Prof. Dr. Fatih TAŞPINAR | N.Ö | Vize | 50.00 |
| Prof. Dr. Fatih TAŞPINAR | N.Ö | Final | 50.00 |
| Toplam | 100.00 | ||
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 3 | 42 |
|
Ders Dışı |
Practice | 10 | 1 | 10 |
|
Sınavlar |
Midterm 1 | 1 | 12 | 12 |
| Final | 1 | 24 | 24 | |
| Classroom Activities | 14 | 1 | 14 | |
| Total Workload | 102 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 3.0 | ||
