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 | Technical 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 | Adequate knowledge in mathematics, science and subjects specific to the software engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems. | X | ||||
| 2 | The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. | |||||
| 3 | The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. | |||||
| 4 | The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in software engineering applications; the ability to utilize information technologies effectively. | |||||
| 5 | The ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the software engineering discipline. | |||||
| 6 | The ability to work effectively in inter/inner disciplinary teams; ability to work individually. | |||||
| 7 | Effective oral and written communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |||||
| 8 | The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |||||
| 9 | Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development | |||||
| 10 | The ability to behave according to ethical principles, awareness of professional and ethical responsibility. | |||||
| 11 | Knowledge of the standards utilized in software engineering applications. | |||||
| 12 | Knowledge on business practices such as project management, risk management and change management. | |||||
| 13 | Awareness about entrepreneurship, and innovation. | |||||
| 14 | Knowledge on sustainable development. | |||||
| 15 | Knowledge of the effects of software engineering applications on the universal and social dimensions of health, environment, and safety. | |||||
| 16 | Awareness of the legal consequences of engineering solutions. | |||||
| 17 | An ability to apply algorithmic principles, mathematical foundations, and computer science theory in the modeling and design of computer-based systems with the trade-offs involved in design choices. | |||||
| 18 | The ability to apply engineering approach to the development of software systems by analyzing, designing, implementing, verifying, validating and maintaining software systems. | |||||
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 | ||