ECTS - Theory of Differential Equations

Theory of Differential Equations (MATH562) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Theory of Differential Equations MATH562 3 0 0 3 5
Pre-requisite Course(s)
Consent of the Department
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, Question and Answer.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The course aims to introduce and present Initial Value Problem: Existence and Uniqueness of Solutions; Continuation of Solutions; Continuous and Differential Dependence of Solutions. Linear Systems: Linear Homogeneous And Nonhomogeneous Systems with Constant and Variable Coefficients; Structure of Solutions of Systems with Constant and Periodic Coefficients; Higher Order Linear Differential Equations; Sturmian Theory, Stability: Lyapunov Stability and Instability. Lyapunov Functions; Lyapunov's Second Method; Quasilinear Systems.
Course Learning Outcomes The students who succeeded in this course;
  • students are expected to know and understand various ideas, concepts and methods from ordinary differential equations and how these ideas may be used in, or are connected to, the fields of engineering and mathematics.
  • students will be able to learn how they can construct a Lyapunov function to determine the stability/instability of ordinary differential equations (ODE) and construct a new ODE to determine the oscillation/nonoscillation of an ODE.
Course Content IVP: existence and uniqueness, continuation and continuous dependence of solutions; linear systems: linear (non)homogeneous systems with constant and variable coefficients; structure of solutions of systems with periodic coefficients; higher order linear differential equations; Sturmian theory, stability: Lyapunov (in)stability, Lyapunov functions

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Initial Value Problem (IVP): Examples of (IVP) Read related sections in references
2 Fundamental Theory: Preliminaries, Existence and Uniqueness of Solutions; Read related sections in references
3 Continuation of Solutions; Continuity and Differentiability of Solutions with respect to parameters Read related sections in references
4 Linear Systems: Preliminaries, Linear Homogeneous and Nonhomogeneous Read related sections in references
5 Linear Systems with Constant and Variable Coefficients Read related sections in references
6 Structure of Solutions of Systems with Constant and Periodic Coefficients; Read related sections in references
7 Midterm
8 Higher Order Linear Differential Equations; Read related sections in references
9 Sturmian Theory: Sturm Comparison Theory, Sturm Oscillation Theory. Read related sections in references
10 Stability: Definitions of Stability and Boundedness. Read related sections in references
11 Lyapunov Stability and Instability Read related sections in references
12 Lyapunov Functions; Lyapunav stability and Instability results. Lyapunov's Second Method;. Read related sections in references
13 Quasilinear Systems; Linearization Read related sections in references
14 Stability of an Equilibrium and Stable Manifold Theorem for Nonautonomous Differential Equations Read related sections in references
15 Revision.
16 Midterm


Course Book 1. Richard K. Miller, Anthony N. Michel, Ordinary Differential Equations, 1982, Academic Press
Other Sources 2. W. Kelley, A. Peterson, The Theory of Differential Equations Classical and Qualitative,2004, Prentice–Hall.
3. C. A. Swanson, Comparison and Oscillation Theory, 1968, Academic Press.

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 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses
Major Area Courses
Supportive Courses X
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.
2 Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3 Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
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.
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.
6 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
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.
9 Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
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.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 77