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 | Natural & Applied Sciences Master's Degree |
| 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 | |
|---|---|
| Major Area Courses | |
| Supportive Courses | X |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | 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 | ||