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 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
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 | ||