ECTS - Numerical Analysis
Numerical Analysis (MATH381) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Analysis | MATH381 | Area Elective | 3 | 0 | 2 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| (MATH135 veya MATH231) |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of this course is to study the concepts, the fundamental results, the methods and the techniques of the Numerical Analysis for the numerical solution of mathematical problems. In this context it aims to teach the students how to implement numerical calculations effectively, how to understand the pros and cons of different methods and how to approach a problem numerically. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Computational and mathematical preliminaries, numerical solution of nonlinear equations and systems of nonlinear equations, numerical solution of systems of linear equations, direct and iterative methods, the Algebraic Eigenvalue Problem, interpolation and approximation, numerical differentiation and integration, numerical solution of ODE`s. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Mathematical preliminaries, Floating Point Arithmetic, Errors. | pp. 1-7,10, 12-13, 22-25, 28-33 |
| 2 | Numerical Solution of Nonlinear Equations: Bisection and Regula-Falsi Methods. Secant, Newton’s and Steffenson’s Methods. | pp. 43-61, 71-83 |
| 3 | Theory for One-Point Iteration Methods, Order of Convergence, Aitken’s Process. Nonlinear Systems of Equations, Jacobi, Gauss-Seidel and Newton’s Method for Nonlinear Systems. | pp. 44-50, 101-107, 112-115 |
| 4 | Numerical Solution of System of Lineer Equations: Direct Methods: Gaussian Elimination, Pivoting Strategies, LU Decomposition. | pp. 142-145, 148-156, 166-171 |
| 5 | Iterative Methods for Solving System of Lineer Equations: Jacobi, Gauss-Seidel and Successive Over Relaxation(SOR) Methods, Convergence Analysis. | pp. 180-186 |
| 6 | Interpolation: Interpolation Theory, Polynomial Interpolation, Lagrange Interpolation, Divided Differences, Finite Differences and Table-Based Newton Interpolation Methods. | pp. 207-212, 215-220, 227-233 |
| 7 | Midterm | |
| 8 | Approximation: Least-Squares Approximation, Data Linearization. Numerical Differentiation: Approximating the Derivative, Numerical Differentiation Formulas, Error Analysis. | pp. 258-263, 268-278 pp. 316-323, 333-336, |
| 9 | Numerical Integration: Trapezoidal and Simpson’s Rules, Newton-Cotes Integration Formulas, Error Analysis, Composite Rules for Numerical Integration, Romberg Integration, Error Analysis. | pp. 346-365, 374-378 |
| 10 | Eigenvalue Problem: The Power Method, Inverse Power Method, Householder’s Method and Eigenvalues of Symmetric Matrices. | pp. 549-556, 574-580 |
| 11 | Numerical Solution of Ordinary Differential Equations; Existence, Uniqueness and Stability Theories. | pp. 424-427 |
| 12 | Numerical Solution of Ordinary Differential Equations; Existence, Uniqueness and Stability Theories. | pp. 424-427 |
| 13 | Euler’s Method and Heun’s Method. Taylor Series Methods, Runge-Kutta Methods, Adams Method and Error Analysis, Systems of Differential Equations. | pp. 429-434, 437-439, 444-446, 450-454, 464-468, 475-479 |
| 14 | Euler’s Method and Heun’s Method. Taylor Series Methods, Runge-Kutta Methods, Adams Method and Error Analysis, Systems of Differential Equations. | pp. 429-434, 437-439, 444-446, 450-454, 464-468, 475-479 |
| 15 | General Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. Numerical Methods for Mathematics Science and Engineering, J.H.Mathews, Prentice Hall, 1992, second edition. |
|---|---|
| Other Sources | 2. Numerical Analysis, by L.W.Johnson & R.D.Riess, Addison Wesley, 1982 |
| 3. An Introduction to Numerical Analysis, by K.E.Atkinson, John Wiley and Sons, 1999 | |
| 4. Numerical Analysis, by R.L.Burden&J.D.Faires, Prindle, Weber and Schmidt, 1985. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 7 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 80 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 10 | 135 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| 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 | 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 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research | X | ||||
| 3 | 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 | ||||
| 4 | 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 | ||||
| 5 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework | X | ||||
| 6 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility | X | ||||
| 7 | 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 | ||||
| 8 | To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) | X | ||||
| 9 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge | X | ||||
| 10 | Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. | 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) | 16 | 5 | 80 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 5 | 80 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 7 | 5 | 35 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 12 | 24 |
| Prepration of Final Exams/Final Jury | 1 | 15 | 15 |
| Total Workload | 234 | ||