| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Linear Algebra | BM213 | 3. Semester | 3 + 0 | 3.0 | 3.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | |
| Course Coordinator |
Assist. Prof. Dr. Mustafa İsa DOĞAN |
| Instructor(s) |
Mustafa İsa DOĞAN |
| Assistants | |
| 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 |
| Learning Outcomes |
- Solves the n dimensional linear systems by determinant(Cramer) method. - 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 - Finds the solution by using the inverse matrix method in the state of definite linear system. - Examines the general system by using rank method, when the condition is compatible the finds its solution. - Finds the eigenvalues and eigenvector of square matrix. - - |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Introduction. Overview of the subjects, history and methods of the linear algebra. | Visual Presentation Verbal Expression Course Hours Practice |
| 2. Week | Systems involving two and three variables. Gauss method. Determinants of 2- and 3-dimensional matrices. | Visual Presentation Practice Verbal Expression Course Hours |
| 3. Week | Geometric interpretation of the two- and three-dimensional system. Definition of the n-dimensional determinant. | Visual Presentation Course Hours Verbal Expression Practice |
| 4. Week | Characteristics of the n-dimensional determinant and its calculation methods | Course Hours Verbal Expression Practice Visual Presentation |
| 5. Week | Special determinants. Triangular, Wandermond and Tridiagonal shape determinants. | Verbal Expression Course Hours Practice Visual Presentation |
| 6. Week | Laplace and Anti-Laplace theorems. Cramer’s theorem for the square system. | Practice Course Hours Verbal Expression Visual Presentation |
| 7. Week | Matrices, operations on matrices. Inverse matrix and its finding methods. | Practice Visual Presentation Course Hours Verbal Expression |
| 8. Week | Transformations of the square system to matrix form and solution with inverse matrix method. | Verbal Expression Course Hours Visual Presentation Practice |
| 9. Week | Kronecker-Kapelli for general systems. | Visual Presentation Practice Course Hours Verbal Expression |
| 10. Week | n-dimensional real and complex vector spaces. Linear independence bases and coordinates. | Visual Presentation Practice Verbal Expression Course Hours |
| 11. Week | Linear transformation and its matrix. Transformation of matrix by base change. | Verbal Expression Practice Visual Presentation Course Hours |
| 12. Week | Eigenvalues and eigenvectors. Hamilton-Cayley and Silvester theorems. | Verbal Expression Visual Presentation Practice Course Hours |
| 13. Week | Jordan normal form of matrix. Similarity. Similarity condition of diagonal matrix. | Course Hours Verbal Expression Practice Visual Presentation |
| 14. Week | Metric, Normed and Euclidean space. Length, angle, quadratic forms, numerical image. | Course Hours Visual Presentation Verbal Expression Practice |
| Linear Algebra with Applications Steven j.Leon |
| Linear Algebra with Applications Steven j.Leon |
| Text | doğrusal cebir |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | Measurement Method |
|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY2 | 5 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY3 | 2 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY4 | 1 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY5 | 1 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY6 | 2 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY7 | 3 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY8 | 2 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY9 | 1 | 0 | 0 | 0 | 0 | 0 | - | - |
| PY10 | 3 | 0 | 0 | 0 | 0 | 0 | - | - |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 3 | 42 |
| Practice | 10 | 1 | 10 |
| Midterm 1 | 1 | 12 | 12 |
| Final | 1 | 24 | 24 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 102 | ||
| ECTS Credit of the Course | 3.0 | ||
