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 | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| Math 276 Differential Equations |
| Course Language | English |
|---|---|
| Course Type | N/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) |
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| 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 | Ability to expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement. | |||||
| 2 | Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering. | |||||
| 3 | To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines. | |||||
| 4 | Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed. | |||||
| 5 | Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions. | |||||
| 6 | Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs. | |||||
| 7 | Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process. | |||||
| 8 | Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility. | |||||
| 9 | To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level. | |||||
| 10 | Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments. | |||||
| 11 | To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications. | |||||
| 12 | Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities. | |||||
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 | ||