# Impulsive Differential Equations (MATH564) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Impulsive Differential Equations MATH564 3 0 0 3 5
Pre-requisite Course(s)
Consent of the Department
Course Language English N/A Natural & Applied Sciences Master's Degree Face To Face Lecture, Question and Answer. The course aims to introduce and present General Description of IDE: Description of mathematical model. Systems with impulses at fixed times. Systems with impulses at variable times. Discontinuous dynamical systems. Impulsive oscillator. Linear Systems of IDE: General properties of solutions. Stability of solutions. Adjoint systems, Perron theorem. Linear Hamiltonian systems of IDE. Stability of Solutions of IDE: Stability criterion based on first order approximation. Stability in systems of IDE with variable times of impulsive effect. Direct Lyapunov method. Periodic and Almost Periodic Systems of IDE: Nonhomogeneous linear periodic systems. Nonlinear periodic systems. Almost periodic functions and sequences. Almost periodic IDE. Integral Sets of Systems of IDE: Bounded solutions of nonhomogeneous linear systems. Integral sets of quasilinear systems with hyperbolic linear part and with non-fixed moments of impulse actions. The students who succeeded in this course; to know and understand various ideas, concepts and methods from impulsive differential equations and how these ideas may be used in, or are connected to, the fields of engineering and mathematics. General description of IDE, systems with impulses at fixed times, systems with impulses at variable times, discontinuous dynamical systems, general properties of solutions, stability of solutions, adjoint systems, Perron theorem, linear Hamiltonian systems of IDE, direct Lyapunov method, periodic and almost periodic systems of IDE, almost periodic

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 General Description of Impulsive Differential Equations (IDE): Description of mathematical model. Read related sections in references
2 Systems with impulses at fixed times. Read related sections in references
3 Systems with impulses at variable times. Read related sections in references
4 Discontinuous dynamical systems. Impulsive oscillator. Read related sections in references
5 Linear Systems of IDE: General properties of solutions. Read related sections in references
6 Stability of solutions. Adjoint systems, Perron theorem. Read related sections in references
7 Midterm
8 Linear Hamiltonian systems of IDE. Read related sections in references
9 Stability of Solutions of IDE: Stability criterion based on first order approximation. Read related sections in references
10 Stability in systems of IDE with variable times of impulsive effect. Read related sections in references
11 Direct Lyapunov method. Read related sections in references
12 Periodic and Almost Periodic Systems of IDE: Nonhomogeneous linear periodic systems. Read related sections in references
13 Nonlinear periodic systems. Almost periodic functions and sequences. Almost periodic IDE. Read related sections in references
14 Integral Sets of Systems of IDE: Bounded solutions of nonhomogeneous linear systems. Read related sections in references
15 Integral sets of quasilinear systems with hyperbolic linear part and with non-fixed moments of impulse actions. Read related sections in references
16 Final Exam

### Sources

Course Book 1. A. M. Samoilenko and N. A. Perestjuk, Impulsive Differential Equations, 1995, Series A, World Scientific Publishing Co. Pte. Ltd. 2. V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, 1989, World Scientific Publishing Co. Pte. Ltd. 3. D. D. Bainov, P. S. Simeonov, Systems with Impulse Effect: Stability, Theory and Applications, 1989, Ellis Horwood 4. D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, 1993, Longman Scientific and Technical. 5. D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations, Asymptotic Properties of the Solutions, 1995, World Scientific Publishing Co. Pte. Ltd., 6. D. D. Bainov, P. S. Simeonov, Oscillation Theory of Impulsive Differential Equations, 1998, International Publications.

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

### 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 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.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
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