ECTS - Dynamic Systems on Time Scales
Dynamic Systems on Time Scales (MATH565) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Dynamic Systems on Time Scales | MATH565 | 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, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | Bu ders özellikle matematik, fizik ve mühendislik bölümü öğrencilerinden diskrit (fark) ve sürekli (diferensiyel) denklemlerin birleştirilmesinden ortaya çıkan melez denklemleri kullanan öğrencilere hitap etmektedir. Bu amaçla bu ders zaman skalasında diferensiyel denklemleri sunarak onların çözim yöntemlerini verecektir. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Differentiation on time scales, integration on time scales, the first-order linear differential equations on time scales, initial value problem, the exponential function on time scales, the second-order linear differential equations on time scales, boundary value problem, Green?s function, the Sturm-Liouville eigenvalue problem. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Differentiation on time scales. | pp. 5-21 |
| 2 | Integration on time scales. | pp. 22-31 |
| 3 | The existence and uniqueness theorem for solution of the initial value problem for first-order differential equations on time scales. | pp. 321-326 |
| 4 | Definition of the exponential function on time scales via a differential equation and properties of the exponential function. | pp. 58-68 |
| 5 | Examples of exponential functions on time scales. | pp. 69-74 |
| 6 | Solution of the first-order linear differential equations with variable coefficients on time scales. | pp. 75-78 |
| 7 | Midterm | |
| 8 | The second-order linear homogeneous differential equations on time scales, The Wronskian. | pp. 81-87 |
| 9 | Definitions of the cosine and sine on time scales, and their properties. | pp. 87-93 |
| 10 | Solving of the second order linear differential equations with constant coefficients on time scales. | pp. 93-96 |
| 11 | The second order linear nonhomogeneous differential equations on time scales, Variations of parameters. | pp. 113-116 |
| 12 | Boundary value problems for second-order linear differential equations on time scales, The Green function. | pp. 164-177 |
| 13 | The Sturm-Liouville eigenvalue problem on time scales. | pp. 177-183 |
| 14 | Expansion formulas in eigenfunctions on time scales. | pp. 183-187 |
| 15 | Higher-order linear differential equations on time scales. | pp. 238-253 |
| 16 | Final Exam |
Sources
| Course Book | 1. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001. |
|---|---|
| Other Sources | 2. V. Kac and P. Cheung, Quantum Calculus, Springer, New York, 2002. |
| 3. V. Lakshimikantham, S Sivasundaram, and B. Kaymakçalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996. | |
| 4. M. Bohner and A. Peterson, editors, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 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 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
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 | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 2 | 10 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 7 | 14 |
| Prepration of Final Exams/Final Jury | 1 | 11 | 11 |
| Total Workload | 35 | ||