ECTS - Numerical Analysis I
Numerical Analysis I (MATH521) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Analysis I | MATH521 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to give the expertise necessary to understand, construct and use computational methods for the numerical solution of linear algebra problems. The emphasis is on derivation and analysis of iterative methods for linear algebra problems as well as condition number, convergence, stability of algorithms and the criteria for choosing the best algorithm for the problem under consideration. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Matrix and vector norms, error analysis, solution of linear systems: Gaussian elimination and LU decomposition, condition number, stability analysis and computational complexity; least square problems: singular value decomposition, QR algorithm, stability analysis; matrix eigenvalue problems; iterative methods for solving linear systems: Jacobi, Ga |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Matrix and vector norms | Atkinson- Sec. 7.3, Kress- Sec. 3.4 |
| 2 | Error analysis: Absolute and relative error, floating point, round-off errors | Atkinson-Sec.1.2-1.5 |
| 3 | Solutions of linear systems: Gaussian elimination, pivoting and scaling | Atkinson-Sec. 8.1,8.2 Kress-Sec. 2.2 |
| 4 | LU decomposition | Kress-Sec. 2.3,2.4 |
| 5 | Condition numbers, stability, computational complexity | Kress- Sec. 5.1 |
| 6 | QR factorization: Householder transformation, Gram-Schmidt orthogonalization, Givens rotations | Atkinson-Sec. 9.3, 9.5 |
| 7 | Least square problems: Singular value decomposition | Atkinson-Sec. 9.7 Kress-Sec. 5.2 |
| 8 | Midterm Exam | |
| 9 | Matrix eigenvalue problems: Estimates for eigenvalues, Jacobi method | Atkinson-Sec. 9.1 Kress-Sec. 7.2,7.3 |
| 10 | QR algorithm, Hessenberg Matrices | Kress-Sec. 7.4,7.5 |
| 11 | Schur factorization, Power method, | Atkinson-Sec. 9.2, 9.6 |
| 12 | Inverse Power method | Atkinson-Sec. 9.2, 9.6 |
| 13 | Iterative methods for linear systems: Jacobi Method Gauss-Seidel Method | Kress-Sec. 4.1 |
| 14 | Relaxation Methods | Kress-Sec. 4.2 |
| 15 | Conjugate gradient type methods | Atkinson-Sec. 8.9 |
| 16 | Final Exam |
Sources
| Course Book | 1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998. |
|---|---|
| 2. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989 | |
| Other Sources | 3. G. H. Golub, C.F. Van Loan, “Matrix Computations”, North Oxford Academic, 1983. |
| 4. R. L. Burden, R.J. Faires, “Numerical Analysis”, 9th edition, Brooks/ Cole, 2011. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 30 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 3 | 15 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 125 | ||