ECTS - Impulsive Differential Equations
Impulsive Differential Equations (MATH564) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Impulsive Differential Equations | MATH564 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | 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. |
| Course Learning Outcomes |
The students who succeeded in this course;
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| Course Content | 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. |
|---|---|
| Other Sources | 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
| 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 | 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 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| 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 |
| Total Workload | 77 | ||