BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
| Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT5010 | Numerical Analysis | Fall Spring |
3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Recommended Optional Program Components: | None |
| 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. |
Learning Outcomes
|
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. |
Course Content
| Error analysis, root finding for nonlinear equations, interpolation theory, numerical solution of systems of linear and nonlinear equations, the matrix eigenvalue problem. |
Weekly Detailed Course Contents
| 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 |
Sources
| Course Notes / Textbooks: | An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc. |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Homework Assignments | 7 | % 30 |
| Presentation | 1 | % 30 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Presentations / Seminar | 1 | 40 | 40 |
| Homework Assignments | 7 | 14 | 98 |
| Final | 1 | 20 | 20 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |