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
Mathematical Modeling via Differential and Difference Equations MDES610 3 0 0 3 5
Pre-requisite Course(s)
Math 276 Differential Equations or Math 262 Ordinary Differential Equations
Course Language English
Course Type N/A
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
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;
  • 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).
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
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 -


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.
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
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
Percentage of Final Work 35
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 Ability to expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement.
2 Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering.
3 To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines.
4 Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed.
5 Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions.
6 Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs.
7 Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process.
8 Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility.
9 To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level.
10 Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments.
11 To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications.
12 Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
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