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 |
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Mathematical Modeling via Differential and Difference Equations | MDES610 | 3 | 0 | 0 | 3 | 5 |
Pre-requisite Course(s) |
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Math 276 Differential Equations or Math 262 Ordinary Differential Equations |
Course Language | English |
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Course Type | N/A |
Course Level | Ph.D. |
Mode of Delivery | Face To Face |
Learning and Teaching Strategies | Lecture. |
Course Lecturer(s) |
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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 |
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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. |
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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 |
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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 |
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Percentage of Final Work | 35 |
Total | 100 |
Course Category
Core Courses | |
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Major Area Courses | X |
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 | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | Gains the ability to understand and apply knowledge in the fields of mathematics, science and basic sciences at the level of expertise. | |||||
2 | Gains the ability to access wide and deep knowledge in the field of Engineering by doing scientific research with current techniques and methods, evaluate, interpret and implement the gained knowledge. | |||||
3 | Being aware of the latest developments his/her field of study, defines problems, formulates and develops new and/or original ideas and methods in solutions. | |||||
4 | Designs and applies theoretical, experimental, and model-based research, analyzes and interprets the results obtained at the level of expertise. | |||||
5 | Gains the ability to use the applications, techniques, modern tools and equipment in his/her field of study at the level of expertise. | |||||
6 | Designs, executes and finalizes an original work process independently. | |||||
7 | Can work in interdisciplinary and interdisciplinary teams, lead teams, use the information of different disciplines together and develop solution approaches. | |||||
8 | Pays regard to scientific, social and ethical values in all professional activities and acquires responsibility consciousness at the level of expertise. | |||||
9 | Contributes to the literature by communicating the processes and results of his/her academic studies in written form or orally in national and international academic environments, communicates effectively with communities and scientific staff working in the field of specialization. | |||||
10 | Gains the skill of lifelong learning at the level of expertise. | |||||
11 | Communicates verbally and in written form using a foreign language at least at the European Language Portfolio B2 General Level. | |||||
12 | Recognizes the social, environmental, health, safety, legal aspects of engineering applications, as well as project management and business life practices, being aware of the limitations they place on engineering applications. |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |