ECTS - Numerical Analysis II
Numerical Analysis II (MATH522) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Analysis II | MATH522 | 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 graduate level course is designed to give math students the expertise necessary to understand, construct and use computational methods for the numerical solution of certain problems such as root finding, interpolation, approximation and integration. The emphasis is on numerical methods for solving nonlinear equations and systems, interpolation and approximation, numerical differentiation and integration as well as the error analysis 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 | Iterative methods for nonlinear equations and nonlinear systems, interpolation and approximation: polynomial trigonometric, spline interpolation; least squares and minimax approximations; numerical differentiation and integration: Newton-Cotes, Gauss, Romberg methods, extrapolation, error analysis. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Iterative methods for nonlinear equation and systems: Newton’s method, Secant Method | K. Atkinson- Sec. 2.1, 2.2 ,2.3 R. Kress- Sec. 6.2 |
| 2 | Iterative methods for nonlinear equation and systems: Regula Falsi, Zeros of polynomials | K.Atkinson- Sec. 2.9 R. Kress- Sec. 6.3 |
| 3 | Interpolation: Lagrange and Newton interpolating polynomials | K.Atkinson- Sec. 3.1, 3.2 R. Kress- Sec.8.1 |
| 4 | Interpolation: Hermite interpolating polynomial, Spline interpolation | K. Atkinson- Sec. 3.6,3.7 R. Kress- Sec. 8.3 |
| 5 | Interpolation: Fourier series, trigonometric interpolation | K. Atkinson-Sec. 3.8 R. Kress- Sec. 8.2 |
| 6 | Approximation: Least squres approximation | K. Atkinson- Sec. 4.1,4.3 |
| 7 | Approximation: Minimax approximation | K. Atkinson- Sec. 4.2 |
| 8 | Numerical differentiation | K.Atkinson- Sec. 5.7 |
| 9 | Midterm Exam | |
| 10 | Numerical differentiation: error analysis | K. Atkinson- Sec. 5.7 |
| 11 | Numerical integration: Newton-Cotes formulae | K. Atkinson- Sec. 5.2 R. Kress- Sec. 9.1 |
| 12 | Numerical integration: Gaussian quadrature | K. Atkinson-Sec. 5.3 R. Kress- Sec. 9.3 |
| 13 | Numerical integration: Romberg integration | R. Kress-Sec. 9.5 |
| 14 | Numerical integration: Error analysis | K. Atkinson- Sec. 5.4 R. Kress- Sec. 9.2 |
| 15 | Extrapolation methods: Richardson extrapolation, | Other references |
| 16 | Final Exam |
Sources
| Course Book | 1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998. |
|---|---|
| 3. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989 | |
| Other Sources | 4. J. Stoer, R. Bulirsch, “Introduction to Numerical Analysis”, 3rd edition |
| 5. 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) | |||
| 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 | 77 | ||