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 Technical Electives (Group A)
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Team/Group.
Course Coordinator
Course Lecturer(s)
Course Assistants
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;
  • understand and apply the differentiation and integration on time scales,
  • understand the basic properties of differential equations (dynamic systems) on time scales and know methods of their solution,
  • know the basic results related to the Sturm-Liouville eigenvalue problem on time scales.
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
Major Area Courses X
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 Gains accumulated knowledge on mathematics, science and mechatronics engineering; develops an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 Develops ability to differentiate, identify, formulate, and solve complex engineering problems; develops ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 Develops ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; develops ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions includes economics, environment, sustainability, producibility, ethics, human health, social and political problems.) X
4 Gains ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; develops ability to use information and communications technologies effectively.
5 Develops ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies.
6 Develops ability to work effectively on single disciplinary and multi-disciplinary teams; gains ability for individual work; develops ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines.
7 Develops ability to express creative and original concepts and ideas orally or written effectively, in Turkish and English language.
8 Develops ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; gains consciousness on the necessity of improvement and sustainability as a result of life-long learning; gains ability for monitoring the developments on science and technology; develops awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Gains ability to be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 Gains knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Gains knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; develops consciousness on these issues and develops awareness of legal results of engineering solutions.
12 Gains the competence on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Gains conciousness on the environmental and social responsibility and develops conciousness to be an individual in society. Gains ability to develop and implement projects and asses them with a critical view for their social implications and gains ability to change the related norms if necessary.
14 Gains the competence on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of quality standarts.

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