ECTS - Numerical Solution of Differential Equations
Numerical Solution of Differential Equations (MDES620) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Solution of Differential Equations | MDES620 | 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 course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of differential equations problems that arise in many different fields of science. |
| Course Learning Outcomes |
The students who succeeded in this course;
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| Course Content | Numerical solution of initial value problems; Euler, multistep and Runge-Kutta methods; numerical solution of boundary value problems; shooting and finite difference methods; stability, convergence and accuracy; numerical solution of partial differential equations; finite difference methods for parabolic, hyperbolic and elliptic equations; explic |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | 1. Week Review to differential equations 2. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 3. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 4. Week Numerical solutions of boundary value problems; finite difference methods 5. Week Numerical solutions of boundary value problems; finite difference methods 6. Week Stability, convergence and accuracy of the numerical techniques given 7. Week Stability, convergence and accuracy of the numerical techniques given 8. Week Midterm Exam 9. Week Partial differential equations and their solutions 10. Week Numerical solution of partial differential equations; finite difference methods 11. Week Numerical solution of partial differential equations; finite difference methods 12. Week Numerical solution of parabolic, hyperbolic and elliptic equations by finite difference methods 13. Week Explicit and implicit methods, Crank-Nicolson method 14. Week Explicit and implicit methods, Crank-Nicolson method. System of ordinary differential equations 15. Week Convergence, stability and consistency analysis of the methods 16. Week Final Exam |
Sources
| Course Book | 1. 1. Numerical Solution of Partial Differential Equations by K.W. Morton and D.F. Mayers, Cambridge University Press, 1994. 2.Numerical Analysis of Differential Equations by A. Iserles, Cambridge University Press, 1996. |
|---|---|
| Other Sources | 2. 1.Computer Methods for ODEs and Differential-Algebraic Equations by U.M. Ascher & L.R. Petzold, SIAM, 1998. 2.Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985. |
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 | |
|---|---|
| Percentage of Final Work | 100 |
| 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 | An ability to apply advanced knowledge in computational and/or manufacturing technologies to solve manufacturing engineering problems | |||||
| 2 | An ability to define and analyze issues related with manufacturing technologies | |||||
| 3 | An ability to develop a solution based approach and a model for an engineering problem and design and manage an experiment | |||||
| 4 | An ability to design a comprehensive manufacturing system based on creative utilization of fundamental engineering principles while fulfilling sustainability in environment and manufacturability and economic constraints | |||||
| 5 | An ability to chose and use modern technologies and engineering tools for manufacturing engineering applications | |||||
| 6 | Ability to perform scientific research and/or carry out innovative projects that are within the scope of manufacturing engineering | |||||
| 7 | An ability to utilize information technologies efficiently to acquire datum and analyze critically, articulate the outcome and make decision accordingly | |||||
| 8 | An ability to attain self-confidence and necessary organizational work skills to participate in multi-diciplinary and interdiciplinary teams as well as act individually | X | ||||
| 9 | An ability to attain efficient communication skills in Turkish and English both verbally and orally | |||||
| 10 | An ability to reach knowledge and to attain life-long learning and self-improvement skills, to follow recent advances in science and technology | |||||
| 11 | An awareness and responsibility about professional, legal, ethical and social issues in manufacturing engineering | |||||
| 12 | An awareness about solution focused project and risk management, enterpreneurship, innovative and sustainable development | |||||
| 13 | An understanding on the effects of engineering applications on health, social and legal aspects at universal and local level during decision making process | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 2 | 32 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 5 | 25 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 8 | 16 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 131 | ||