# 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)
Math 276 Differential Equations or Math 262 Ordinary Differential Equations
Course Language English Core Course Ph.D. Face To Face Lecture. 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. The students who succeeded in this course; At the end of this course, students will learn; 1) formulating a model, using differential or difference equations; 2) analyzing the model, both by solving the differential (difference) 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). 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. 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

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 35 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

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