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;
|
| 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 | Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir | X | ||||
| 2 | Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur. | X | ||||
| 3 | Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir | X | ||||
| 4 | Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir | X | ||||
| 5 | Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir. | X | ||||
| 6 | Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir | X | ||||
| 7 | Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir. | X | ||||
| 8 | Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur. | X | ||||
| 9 | Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir. | X | ||||
| 10 | Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir. | 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 | ||