ECTS - Numerical Methods for Ordinary Differential Equations
Numerical Methods for Ordinary Differential Equations (MATH482) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Methods for Ordinary Differential Equations | MATH482 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| 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, Discussion, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to give the students the basic theory of numerical methods for solving Ordinary Differential Equations. In the course , first, the derivation, stability and convergence analysis of the methods for Initial Value Problems will be discussed , and than short introduction to the numerical methods for solving Boundary Value Problems will be given. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Existence, uniqueness and stability theory; IVP: Euler?s method, Taylor series method, Runge-Kutta methods, explicit and implicit methods; multistep methods based on integration and differentiation; predictor?corrector methods; stability, convergence and error estimates of the methods; boundary value problems: finite difference methods, shooting me |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | 1. Week Existence, Uniqueness and Stability Theory. 2. Week One-Step Methods: Euler’s Method , Taylor Series Method. 3. Week One-Step Methods: General Theory of Runge - Kutta Methods 4. Week One-Step Methods: Derivation and Error Analysis of Explicit Runge - Kutta Methods. 5. Week One-Step Methods: Derivation and Error Analysis of Implicit Runge - Kutta Methods. 6. Week One-Step Methods: Stability and Convergence Analysis 7. Week Multistep Methods:. Derivations of Explicit Multistep Methods , Error and Convergence Analysis. 8. Week Midterm Exam 9. Week Multistep Methods: Derivations of Implicit Multistep Methods , Error and Convergence Analysis. 10. Week Multistep Methods: Multistep Methods Based on Differentiation. 11. Week Multistep Methods: Relative and Absolute Stability of Multistep Methods. 12. Week Multistep Methods: Predictor – Corrector Methods. 13. Week Boundary Value Problems : Finite Difference Methods. 14. Week Boundary Value Problems : Shooting Methods. 15. Week Boundary Value Problems : Collocation Methods. 16. Week Final Exam |
Sources
| Course Book | 1. [1] Numerical Solution of Differential Equations , M.K.Jain , Wiley Eastern Limited,1979. |
|---|---|
| Other Sources | 2. [2] Numerical Analysis, by D. Kincaid & Ward Cheney Brooks/Cole Publishing Company , 1991. [3] Numerical Analysis, by L.W.Johnson & R.D.Riess, Addison Wesley, 1982. [4] An Introduction to Numerical Analysis, by K.E.Atkinson, John Wiley and Sons,1999 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 6 | 100 |
| Percentage of Semester Work | |
|---|---|
| Percentage of Final Work | 100 |
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | 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 the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | 16 | 3 | 48 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 3 | 10 | 30 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 16 | 32 |
| Prepration of Final Exams/Final Jury | 1 | 24 | 24 |
| Total Workload | 134 | ||