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 | Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. | X | ||||
| 2 | An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. | X | ||||
| 3 | An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) | X | ||||
| 4 | An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively. | X | ||||
| 5 | An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. | |||||
| 6 | An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. | |||||
| 7 | An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written. | |||||
| 8 | An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation. | |||||
| 9 | Be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself. | |||||
| 10 | A 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 | 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; consciousness on these issues; awareness of legal results of engineering solutions. | |||||
| 12 | Competency 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 | Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism | |||||
| 14 | A competency on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of qualitative processes. | |||||
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 | ||