| 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 |
| MAT5003 | Linear Algebra and Its Applications | Fall | 3 | 0 | 3 | 12 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
| Course Objectives: | The purpose of this course is to give the basic concepts of linear algebra with applications to students who intend to study applied mathematics. |
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The students who have succeeded in this course; The students who succeeded in this course; o will be able to describe solution methods for systems of linear equations. o will be able to apply the fundamental properties of determinants to solve the systems of equations, inverting matrices and also to decide whether a subset is linearly independent or not, spans the space or does not. o will be able to apply concepts of vector spaces to all relating areas including matrices. o will be able to formulate the change of basis , to obtain an orthonormal basis and to diagonalize a square matrix, to develop matrix representation of linear mappings. o will be able to distinguish the subsets that span the space or not , are linear independent or not, and the matrices are orthogonal diagonalizable or not, mappings are linear or not. o will be able to use determinants to solve the systems of equations, inverting matrices and also to evaluate the eigen vectors , effectively. o will be able to write equations of Curves and Surfaces passing through given points and apply linear algebra to Leontief economic model applications, Geometric Programming, Cryptography. |
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| Week | Subject | Related Preparation | |
| 1) | Systems of linear equations, network analysis, Balancing Chemical Equations, Design of Traffic Patterns | ||
| 2) | Matrices, LU decomposition, | ||
| 3) | Vector spaces,subspaces, bases and the dimension | ||
| 4) | Determinants, multilinear functions , Cramer systems | ||
| 5) | Inner product spaces, orthonormal sets, QR decomposition, least squares method | ||
| 6) | Linear mappings, space of linear mappings | ||
| 7) | Matrices and linear mappings | ||
| 8) | Matrix polynomials, characteristic values, characteristic vectors, diagonalization of matrices | ||
| 9) | Applications; genetics, population problems | ||
| 10) | Qudratic forms, geometric applications | ||
| 11) | Special mappings of iner product spaces | ||
| 12) | Equation of curves and surfaces passing through given points, geometric programming | ||
| 13) | Cryptography | ||
| 14) | Leontief economical models | ||
| Course Notes: | . |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 5 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 2 | % 10 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 35 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 0 | 0 | 0 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 2 | 40 | 80 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 30 | 30 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 40 | 40 |
| Total Workload | 192 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |