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 | Technical Electives (Group A) |
| 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 | X |
| 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 | Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. | X | ||||
| 2 | An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. | X | ||||
| 3 | An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) | X | ||||
| 4 | An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively. | |||||
| 5 | An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. | |||||
| 6 | An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. | |||||
| 7 | An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written. | |||||
| 8 | An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation. | |||||
| 9 | Be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself. | |||||
| 10 | A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project. | |||||
| 11 | Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions. | |||||
| 12 | Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions. | |||||
| 13 | Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism. | |||||
| 14 | A competency on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of qualitative processes. | |||||
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 | ||