Course Language:
İngilizce
Course Objectives:
To introduce the basic topics of Linear Algebra to engineering students.
Course Content:
| Systems of Equations, Matrices, Determinants, Vector Spaces, Linear Transformations, Orthogonality, Eigenvalues |
Course Methodology:
1: Lecture
Course Evaluation Methods:
A: Written examination
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Solves linear equations using Gauss or Gauss-Jordan elimination method. | 1 | A |
| 2) Knows matrix algebra, compute the inverse of a non-singular matrix using elementary matrices, LU-decompose a square matrix. | 1 | A |
| 3) Computes the determinant of a square matrix, Applies Cramer’s rule | 1 | A |
| 4) Knows the definition and basic examples of vector spaces, subspaces, linear independence, spanning set, basis and dimension. Know the definition and basic properties of linear transformations, Compute the matrix representation of a linear map with respect to fixed ordered-bases | 1 | A |
| 5) Knows inner-product spaces and applies Gram-Schmidt orthogonalization process. | 1 | A |
| 6) Computes eigenvalues and eigenvectors and knows diagonalization. | 1 | A |
Course Flow
| Course Content | ||
| Week | Topics | |
| 1 | Systems of Linear Equations, Row Echelon Form | |
| 2 | Matrix Arithmetic, Matrix Algebra | |
| 3 | Elementary Matrices, Partitioned Matrices | |
| 4 | Determinant of a Matrix, Properties of Determinant | |
| 5 | Cramer’s Rule | |
| 6 | Vectors, Subspaces | |
| 7 | Linear Independence, Basis and Dimension | |
| 8 | Change of Basis, Row Space and Column Space | |
| 9 | Linear Transformations, Matrix Representations of Linear Transformations | |
| 10 | Similarity | |
| 11 | The Scalar Product in R^n, Orthogonal Subspaces | |
| 12 | Orthonormal Sets | |
| 13 | The Gram Schmidt Orthogonalization Process | |
| 14 | Eigenvalues and Eigenvectors, Diagonalization | |
Recommended Sources
| RECOMMENDED SOURCES | |
| Textbook | “Linear Algebra With Applications” Steven J. Leon 8th Edition 2010 (Pearson Prentice Hall) |
| Additional Resources | |
Material Sharing
| MATERIAL SHARING | |
| Documents | |
| Assignments | |
| Exams | |
Assessment
| ASSESSMENT | ||
| IN-TERM STUDIES | NUMBER | |
| Mid-terms | 1 | |
| Quizzes | ||
| Assignments | ||
| Total | ||
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | ||
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | ||
| Total | ||
Course’s Contribution to Program
| COURSE'S CONTRIBUTION TO PROGRAM | |||||||
| No | Program Learning Outcomes | Contribution | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamental research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | ||||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | ||||||
| 3 | Ability to form and interpret the relations between research topics in mathematics | ||||||
| 4 | Ability to define, formulate and solve mathematical problems | ||||||
| 5 | Consciousness of professional ethics and responsibility | ||||||
| 6 | Ability to communicate actively | ||||||
| 7 | Ability of self-development in fields of interest | ||||||
| 8 | Ability to learn, choose and use necessary information technologies | ||||||
| 9 | Lifelong education | ||||||
ECTS
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 4 | 56 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 5 | 70 |
| Mid-terms (Including self study) | 1 | 14 | 14 |
| Quizzes | |||
| Assignments | |||
| Final examination (Including self study) | 1 | 10 | 10 |
| Total Work Load | 150 | ||
| Total Work Load / 25 (h) | 6 | ||
| ECTS Credit of the Course | 6 |