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 | Natural & Applied Sciences Master's Degree |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | 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 | ||