| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2043 | Linear Algebra with Applications | Fall | 3 | 2 | 4 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. SÜREYYA AKYÜZ |
| Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ Prof. Dr. NAFİZ ARICA |
| Course Objectives: | To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties. |
|
The students who have succeeded in this course; The students who succeeded in this course; The students who have succeeded in this course; Students will be able to: 1) Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion. 2) Carry out matrix operations, including inverses and determinants. 3) Demonstrate understanding of the concepts of vector space and subspace. 4) Demonstrate understanding of linear independence, span, and basis. 5) Determine eigenvalues and eigenvectors and solve eigenvalue problems. 6) Apply principles of matrix algebra to linear transformations. 7)Apply linear algebra problems using MATLAB tools |
| Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices. |
| Week | Subject | Related Preparation | |
| 1) | Introduction to Systems of Linear Equations - Gaussian Elimination and Gauss-Jordan Elimination | ||
| 2) | Operations with Matrices - Properties of Matrix Operations | ||
| 3) | Bir Matrisin Tersi | ||
| 4) | The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations | ||
| 5) | Properties of Determinants | ||
| 6) | Vectors in n-dimensionVector spaces, vector spaces, | ||
| 7) | Subspaces of Vector Spaces - Spanning Sets and Linear Independence | ||
| 8) | Basis and Dimension | ||
| 9) | Rank of a Matrix and Systems of Linear Equations | ||
| 10) | Introduction to Linear Transformations | ||
| 11) | The Kernel and Range of a Linear Transformation | ||
| 12) | Matrices for Linear Transformations - Transition Matrices and Similarity | ||
| 13) | Eigenvalues and Eigenvectors - Diagonalization | ||
| 14) | Symmetric Matrices and Orthogonal Diagonalization | ||
| Course Notes: | Elementary Linear Algebra with Supplemental Applications, 10th Edition, Howard Anton and Chris Rorres, John Wiley, 2010. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 0 |
| Laboratory | % 0 | |
| Application | 14 | % 0 |
| Field Work | 0 | % 0 |
| Special Course Internship (Work Placement) | 0 | % 0 |
| Quizzes | 10 | % 20 |
| Homework Assignments | 5 | % 10 |
| Presentation | 0 | % 0 |
| Project | 0 | % 0 |
| Seminar | 0 | % 0 |
| Midterms | 1 | % 30 |
| Preliminary Jury | 0 | % 0 |
| Final | 1 | % 40 |
| Paper Submission | 0 | % 0 |
| Jury | 0 | % 0 |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 14 | 2 | 28 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 4 | 1 | 4 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 1 | 10 | 10 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 27 | 27 |
| Total Workload | 139 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |