APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5010 | Numerical Analysis | Spring | 3 | 0 | 3 | 8 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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. |
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 / Textbooks: | An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc. |
References: | . |
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 |
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 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |