| 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 | English |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to Face |
| Course Coordinator |
Assoc. Prof. Dr. Nejla ÖZMEN Assist. Prof. Dr. Esra KORKMAZ |
| Instructors |
Esra KORKMAZ |
| Assistants | |
| Goals | The aim of this lecture is to introduce the fundamental concepts of linear algebra and their applications in computer engineering. |
| Course Content | Linear Equation Systems, Matrices, Determinants,Vector spaces, Linear Transformations, Matrix Representations of Linear Transformations, Inner Product Spaces, Eigenvalues and Eigenvectors |
| Learning Outcomes |
- Solves linear systems of equations using various methods, and understands the geometric interpretation of solutions. - Applies matrix operations to solve systems of linear equations, analyze data, and represent transformations. - Transforms systems of linear equations into their reduced row echelon form using Gaussian elimination and applies these techniques to solve practical problems. - Solves linear systems using the Cramer's rule, understands the relationship between determinants and the solution of linear systems, and applies these concepts to analyze and manipulate data. - Knows how to use tools from linear algebra to solve the problems of computer science. - Express data and problems using vectors and vector spaces; understand the basic concepts of spanning and linear independence. - Calculates eigenvalues and eigenvectors of matrices and applies them to understand and analyze systems with linear behavior. - Understands the role of linear transformations in representing and manipulating data, applying these concepts to solve problems in diverse fields. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Linear Equation Systems, Matrices | |
| 2. Week | Matrix Multiplication, Algebraic Properties of Matrix Operations, Special Types of Matrices | |
| 3. Week | Echelon Form of a Matrix, Solution of Linear Equation Systems | |
| 4. Week | Elementary Matrices, Finding the Inverse of a Matrix | |
| 5. Week | Determinants, Cramer's Rule | |
| 6. Week | Vector Spaces, Subspaces | |
| 7. Week | Spanning, Linear Independence | |
| 8. Week | Midterm | |
| 9. Week | Basis and Dimension | |
| 10. Week | Inner Product Spaces and Gram-Schmidt Method | |
| 11. Week | Linear Transformations, Kernel and Image of Linear Transformations | |
| 12. Week | Matrix Representation of Linear Transformations | |
| 13. Week | Eigenvalues and Eigenvectors | |
| 14. Week | Diagonalization |
| Cemal Koç, Basic Linear Algebra, METU Mathematics Foundation, 1996 |
| B. Kolman, D. Hill, Elementary Linear Algebra with Applications, 9th edition, Pearson, 2008. |
| H. Anton, C. Rorres, Elementary Linear Algebra: Applications Version, Wiley; 11th edition, 2013. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | DK8 | Measurement Method |
|---|---|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 4 | 5 | 5 | 4 | 5 | 4 | 5 | 5 | - |
| PY2 | 4 | 4 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | - |
| PY8 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 3 | 3 | - |
| 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) |
|---|---|---|---|
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 2 | 7 | 14 |
| Homework 2 | 2 | 7 | 14 |
| Final | 1 | 2 | 2 |
| Practice | 13 | 1 | 13 |
| Practice End-Of-Term | 2 | 2 | 4 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 77 | ||
| ECTS Credit of the Course | 3.0 | ||
