ECTS - Mathematical Modeling via Differential and Difference Equations
Mathematical Modeling via Differential and Difference Equations (MDES610) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Modeling via Differential and Difference Equations | MDES610 | 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. |
| Course Lecturer(s) |
|
| Course Objectives | Differential and difference equations constitute main tools that scientists and engineers use to make mathematical models of important practical problems. This course aims to involve engineering students in mathematical modelling by means of differential and difference equations and to develop skill with solution techniques in order to understand complex physical phenomena. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Differential equations and solutions, models of vertical motion, single-species population models, multiple-species population models, mechanical oscillators, modeling electric circuits, diffusion models, modeling by means of difference equations. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Some terminology. Examples. Separation of variables. | Read related sections in references |
| 2 | The Euler method. Linear differential equations with constant coefficients. | Read related sections in references |
| 3 | Vertical motion without air resistance. Vertical motion with air resistance. | Read related sections in references |
| 4 | Simple population model. Population with emigration. | Read related sections in references |
| 5 | Population with competition (the logistic equation). | Read related sections in references |
| 6 | Predator-prey (fox-rabbit) population model. Epidemics (SIR). Two-species competition. | Read related sections in references |
| 7 | Spring-mass without damping or forcing. Spring-mass with damping and forcing. | Read related sections in references |
| 8 | Pendulum without damping. Approximate pendulum without damping. | Read related sections in references |
| 9 | Series RC charge. Series RLC charge and current (first-order system). | Read related sections in references |
| 10 | Parallel RLC voltage (second-order scalar equation). | Read related sections in references |
| 11 | Diffusion without convection or source. Diffusion with convection and source. | Read related sections in references |
| 12 | Heat flow without heat source. Time-dependent diffusion. | Read related sections in references |
| 13 | Basics of difference equations | Read related sections in references |
| 14 | A crystal lattice. | Read related sections in references |
| 15 | Overall review | - |
| 16 | Final exam | - |
Sources
| Course Book | 1. P. W. Davis, Differential Equations: Modeling with matlab, Prentice Hall, Upper Saddle River, New Jersey, 1999. |
|---|---|
| 2. W. G. Kelley and A. C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, New York, 1991. | |
| Other Sources | 3. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., Wiley, New York, 1999. |
| 4. S. L. Ross, Differential Equations, 3rd ed.,Wiley, New York, 1984. | |
| 5. S. Elaydi, An Introduction to Difference Equations, Springer-Verlag, New York, 1996. |
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 | 2 | 35 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 8 | 100 |
| 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 | An ability to apply knowledge of mathematics, science, and engineering. | X | ||||
| 2 | An ability to design and conduct experiments, as well as to analyse and interpret data. | X | ||||
| 3 | An ability to design a system, component, or process to meet desired needs. | X | ||||
| 4 | An ability to function on multi-disciplinary domains. | |||||
| 5 | An ability to identify, formulate, and solve engineering problems. | X | ||||
| 6 | An understanding of professional and ethical responsibility. | |||||
| 7 | An ability to communicate effectively. | |||||
| 8 | Recognition of the need for, and an ability to engage in life-long learning. | X | ||||
| 9 | A knowledge of contemporary issues. | X | ||||
| 10 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. | X | ||||
| 11 | Skills in project management and recognition of international standards and methodologies | |||||
| 12 | An ability to produce engineering products or prototypes that solve real-life problems. | |||||
| 13 | Skills that contribute to professional knowledge. | X | ||||
| 14 | An ability to make methodological scientific research. | X | ||||
| 15 | An ability to produce, report and present an original or known scientific body of knowledge. | |||||
| 16 | An ability to defend an originally produced idea. | |||||
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 | 6 | 30 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 8 | 16 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 136 | ||