ECTS - Mathematical Modeling
Mathematical Modeling (MATH486) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Modeling | MATH486 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | Differential equations constitute main tools that scientists and engineers use to make mathematical models of important practical problems. This course discusses three major issues: 1) Formulating a model, using differential equations; 2) Analyzing the model, both by solving the differential equation and by extracting qualitative information about the solution from the equation; 3) Interpreting the analysis in light of the physical (practical) setting modeled in step 1). |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Differetial equations and solutions, models of vertical motion, single-species population models, multiple-species population models, mechanical oscillators, modeling electric circuits, diffusion models. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Some terminology, Examples, Separation of variables. | pp. 1-8 |
| 2 | The Euler method, Linear differential equations with constant coefficients. | p. 23, Exercise 8 |
| 3 | Vertical motion without air resistence. | pp. 29-37, 41-46 |
| 4 | Vertical motion with air resistence. | pp. 47-51 |
| 5 | Simple population model, Population with emigration. | pp. 65-71 |
| 6 | Population with competition (The logistic equation). | pp. 72-75 |
| 7 | Midterm | |
| 8 | Predator-prey (Fox-rabbit) population model, Epidemics (SIR). | pp. 203-215 |
| 9 | Two-species competition. | pp. 219-222 |
| 10 | Spring-mass without damping or forcing, Spring-mass with damping and forcing. | p. 77, Exercises 3 and 4, pp. 223-227 |
| 11 | Pendulum without damping, Approximate pendulum without damping. | pp. 227-230 |
| 12 | Series RC charge, Series RLC charge and current (First-order system). | pp. 428-435 |
| 13 | Parallel RLC voltage (Second-order scalar equation). | pp. 465-468 |
| 14 | Diffusion without convection or source, Diffusion with convection and source. | pp. 1-6 |
| 15 | Heat flow without heat source, Time-dependent diffusion. | p. 23, Exercise 8 |
| 16 | Final Exam |
Sources
| Course Book | 1. P. W. Davis, Differential Equations: Modeling with matlab, Prentice Hall, Upper Saddle River, New Jersey, 1999. |
|---|---|
| 3. S. L. Ross, Differential Equations, 3rd ed.,Wiley, New York, 1984. | |
| Other Sources | 2. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., Wiley, New York, 1999. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| 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 | Acquiring the skills of understanding, explaining, and using the fundamental concepts and methods of economics | |||||
| 2 | Acquiring the skills of macro level economic analysis | |||||
| 3 | Acquiring the skills of micro level economic analysis | |||||
| 4 | Understanding the formulation and implementation of economic policies at the local, national, regional, and/or global level | |||||
| 5 | Learning different approaches on economic and related issues | |||||
| 6 | Acquiring the quantitative and/or qualitative techniques in economic analysis | X | ||||
| 7 | Improving the ability to use the modern software, hardware and/or technological devices | |||||
| 8 | Developing intra-disciplinary and inter-disciplinary team work skills | X | ||||
| 9 | Acquiring an open-minded behavior through encouraging critical analysis, discussions, and/or life-long learning | |||||
| 10 | Adopting work ethic and social responsibility | |||||
| 11 | Developing the skills of communication. | |||||
| 12 | Improving the ability to effectively implement the knowledge and skills in at least one of the following areas: economic policy, public policy, international economic relations, industrial relations, monetary and financial affairs. | X | ||||
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 | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 4 | 20 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 20 | 20 |
| Total Workload | 150 | ||