| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Fractional Integrals I | MAT541 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Assoc. Prof. Dr. Tuba TUNÇ |
| Instructors |
HÜSEYİN BUDAK |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Riemann-Liouville Fractional Integrals and Derivatives,The Abel integral equation,On the solvability of the Abel equation in the space of integrable functions,Fractional integrals and derivatives of complex order,Fractional integrals of some elementary functions,The Fractional Integrals of Hölder and Summable Functions,Mapping properties in the space H^λ , Mapping properties in the space L^p,The Main Properties of Fractional Integrals and Derivatives,Fractional integrals of Hölderian functions ,Fractional integrals of summable functions,Representation of Function by Fractional Integrals of -L^pFunction |
| Learning Outcomes |
- Student’s ability of commenting and thinking truely will improve and the students will get basic information about mathematics. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Riemann-Liouville Fractional Integrals and Derivatives | |
| 2. Week | The Abel equation in the space of integrable functions | |
| 3. Week | The Abel equation in the space of integrable functions | |
| 4. Week | Solvability of Abel equation | |
| 5. Week | The Fractional Integrals and complex ordered derivative | |
| 6. Week | Fractional integrals of some elemanter functions | |
| 7. Week | Hölder Fractional integral and summability of the functions | |
| 8. Week | Midterm | |
| 9. Week | Properties of the transformations in H^lamda spaces | |
| 10. Week | Properties of the transformations in L^p spaces | |
| 11. Week | Fractional integrals and the main properties of derivatives | |
| 12. Week | Fractional integrals of Hölder functions | |
| 13. Week | Fractional integrals of summable functions | |
| 14. Week | Presentation with functions of L^p functions and fractional integrals of L^p functions |
| Samko, S.G., Kilbas, A.A., and Marichev, O.I., Fractional Integrals and Derivatives. 1993 |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 5 | 0 | 60 |
| PY2 | 5 | 0 | 60 |
| PY3 | 5 | 0 | 60 |
| PY4 | 5 | 0 | 60 |
| PY5 | 5 | 0 | 60 |
| PY6 | 5 | 0 | 60 |
| PY7 | 4 | 0 | 60 |
| PY8 | 5 | 0 | 60 |
| PY9 | 5 | 0 | 60 |
| PY10 | 5 | 0 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 3 | 42 |
| Research | 14 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 3 | 42 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 1 | 2 | 2 |
| Quiz 2 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 6 | 36 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 200 | ||
| ECTS Credit of the Course | 8.0 | ||
