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;
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| 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 | Gains accumulated knowledge on mathematics, science and mechatronics engineering; develops an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. | X | ||||
| 2 | Develops ability to differentiate, identify, formulate, and solve complex engineering problems; develops ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. | X | ||||
| 3 | Develops ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; develops ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions includes economics, environment, sustainability, producibility, ethics, human health, social and political problems.) | X | ||||
| 4 | Gains ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; develops ability to use information and communications technologies effectively. | X | ||||
| 5 | Develops ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. | |||||
| 6 | Develops ability to work effectively on single disciplinary and multi-disciplinary teams; gains ability for individual work; develops ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. | |||||
| 7 | Develops ability to express creative and original concepts and ideas orally or written effectively, in Turkish and English language. | |||||
| 8 | Develops ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; gains consciousness on the necessity of improvement and sustainability as a result of life-long learning; gains ability for monitoring the developments on science and technology; develops awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation. | |||||
| 9 | Gains ability to be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself. | |||||
| 10 | Gains knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project. | |||||
| 11 | Gains knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; develops consciousness on these issues and develops awareness of legal results of engineering solutions. | |||||
| 12 | Gains the competence on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions. | |||||
| 13 | Gains conciousness on the environmental and social responsibility and develops conciousness to be an individual in society. Gains ability to develop and implement projects and asses them with a critical view for their social implications and gains ability to change the related norms if necessary. | |||||
| 14 | Gains the competence on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of quality standarts. | |||||
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 | ||