ECTS - Calculus on Time Scales
Calculus on Time Scales (MATH363) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Calculus on Time Scales | MATH363 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH136 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion. |
| Course Lecturer(s) |
|
| Course Objectives | A time scale is an arbitrary nonempty closed subset of the real numbers. The calculus of time scales was initiated by B.Aulbach and S.Hilger in 1990 in order to create a theory that can unify discrete and continuous analysis. It allows a simultaneous treatment of differential and difference equations, extending those theories to so-called dynamic equations. This course gives an introduction to this subject. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | The h-derivative and the q-derivative, the concept of a time scale, differentiation on time scales, integration on time scales, Taylor?s Formula on time scales. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Rules of the h-differentiation | Kac and Cheung, pp. 80-84 |
| 2 | Rules of the q –differentiation | Kac and Cheung, pp. 1-3 |
| 3 | Definition of a time scale, examples | pp. 1-4 |
| 4 | Delta and nabla derivatives, Differentiation rules | pp. 5- 21, 331-332 |
| 5 | Chain rules on time scales | pp. 31-37 |
| 6 | Mean value theorems for delta and nabla derivatives | pp. 22-26 |
| 7 | Midterm | |
| 8 | The Riemann delta and nabla integrals on time scales | pp. 26-27, 332-333 |
| 9 | Properties of the integral, Integration by parts formulas | pp. 28-30 |
| 10 | The Fundamental Theorems of Caculus on time scales | p. 27 |
| 11 | Mean Value Theorems for integral on time scales | pp.48-49 |
| 12 | Improper integrals on time scales | pp. 30-31 |
| 13 | Generalized monomials on time scales | pp. 37-42 |
| 14 | Taylor’s formula on time scales | pp. 42-46 |
| 15 | h-Taylor’s formula and q-Taylor’s formula | Kac and Cheung, pp. 7-13 |
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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. | 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 | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 8 | 40 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 70 | ||