| 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 |
| MAT5010 | Numerical Analysis | Fall | 3 | 0 | 3 | 8 |
| 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 : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Course Objectives: | Scientific computation and simulation require both a theoretical knowledge of the subject and computational experience with it. Understanding these aspects in terms of error analysis, stability and efficiency of the methods plays an important role. |
|
The students who have succeeded in this course; The students who succeeded in this course; o will be able to solve Linear and Non Linear Equations by using methods. o will be able to provide logical proofs of important theoratical results. o will be able to apply the theory of simulation by modeling real life examples. |
| Error analysis, root finding for nonlinear equations, interpolation theory, numerical solution of systems of linear and nonlinear equations, the matrix eigenvalue problem. |
| Week | Subject | Related Preparation | |
| 1) | Errors, Condition Numbers, Norms | ||
| 2) | Sources and Propagation of Errors | ||
| 3) | General Theory for One-point Iteration Methods | ||
| 4) | Error Analysis of Nonlinear Equations | ||
| 5) | Interpolation | ||
| 6) | Finite Differences and Table-Oriented Interpolation Formulas and Their Error Analysis | ||
| 7) | Further Results on Interpolation Error | ||
| 8) | Approximation of Functions: The Weierstrass Theorem and Taylor’s Theorem | ||
| 9) | Approximation of Functions: The Least Squares Approximation Problem | ||
| 10) | Numerical Solution of Systems of Linear Equations: Direct Methods and Their Error Analysis | ||
| 11) | Numerical Solution of Systems of Linear Equations: Iterative Methods and Their Error Analysis | ||
| 12) | The Matrix Eigenvalue Problem: Error and Stability Results | ||
| 13) | The Matrix Eigenvalue Problem: The Power Method and Eigenvalues of Special Matrices | ||
| 14) | Singular Value Decomposition | ||
| Course Notes: | An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 7 | % 30 |
| Presentation | 1 | % 30 |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | % 0 | |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 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 | 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 | 1 | 40 | 40 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 7 | 14 | 98 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 0 | 0 | 0 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 20 | 20 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |