| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Linear Algebra | CE213 | 3. Semester | 3 + 0 | 3.0 | 3.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | |
| Course Coordinator | |
| Instructor(s) |
Esra KORKMAZ |
| 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. | |
| 2. Week | Systems involving two and three variables. Gauss method. Determinants of 2- and 3-dimensional matrices. | |
| 3. Week | Geometric interpretation of the two- and three-dimensional system. Definition of the n-dimensional determinant. | |
| 4. Week | Characteristics of the n-dimensional determinant and its calculation methods | |
| 5. Week | Special determinants. Triangular, Wandermond and Tridiagonal shape determinants. | |
| 6. Week | Laplace and Anti-Laplace theorems. Cramer’s theorem for the square system. | |
| 7. Week | Matrices, operations on matrices. Inverse matrix and its finding methods. | |
| 8. Week | Transformations of the square system to matrix form and solution with inverse matrix method. | |
| 9. Week | Kronecker-Kapelli for general systems. | |
| 10. Week | n-dimensional real and complex vector spaces. Linear independence bases and coordinates. | |
| 11. Week | Linear transformation and its matrix. Transformation of matrix by base change. | |
| 12. Week | Eigenvalues and eigenvectors. Hamilton-Cayley and Silvester theorems. | |
| 13. Week | Jordan normal form of matrix. Similarity. Similarity condition of diagonal matrix. | |
| 14. Week | Metric, Normed and Euclidean space. Length, angle, quadratic forms, numerical image. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | Measurement Method |
|---|
| 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 |
