| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Fractional Integrals II | MAT542 | 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 |
Tuba TUNÇ |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Integral Transforms of Fractional Integrals and Derivatives,The Fourier transform,The Laplace transform,The Mellin transform,Fractional Integrals and Derivatives of Generalized Functions,Lizorkin’s space of test functions,Schwartz’s approach , Compositions of Fractional Integrals and Derivatives With Weights,Compositions of two one-side integrals with power weights,Compositions of two-side integrals with power weights ,Compositions of several integrals with power weights, Fractional Integrals of The Potential Type, |
| 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 | Integral Transforms of Fractional Integrals and Derivatives | |
| 2. Week | Integral Transforms of Fractional Integrals and Derivatives | |
| 3. Week | The Fourier transform | |
| 4. Week | The Laplace transform | |
| 5. Week | The Mellin transformation | |
| 6. Week | Fractional Integrals and Derivatives of Generalized Functions | |
| 7. Week | Lizorkin’s space of test functions | |
| 8. Week | Midterm | |
| 9. Week | Schwartz’s approach | |
| 10. Week | Compositions of Weighted Fractional Integrals and Derivatives | |
| 11. Week | Compositions of two one-side integrals with power weights | |
| 12. Week | Compositions of two-side integrals with power weights | |
| 13. Week | Compositions of different integrals with power weights | |
| 14. Week | Fractional inegtrals of type potential |
| 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 | ||
