| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Singular Integrals II | MAT540 | 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. Nejla ÖZMEN |
| Instructors | |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Differentiability Properties in Terms of Function Spaces,Riesz potentials,The Sobolev spaces,Bessel potentials,Lipschitz continuous functions,Extensions and Restrictions,Decomposition of open sets into cube, Extension theorems of Whitney type,Return to The Theory of Harmonic Functions,Non-tangential convergence and Fatou’s theorem,Application of the theory of H^p spaces ,Differentiation of Functions,Several notions of pointwise differentiability,A characterization of differentiability Another characterization of differentiability |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Differentiability Properties in Terms of Function Spaces | |
| 2. Week | Riesz potentials | |
| 3. Week | The Sobolev spaces | |
| 4. Week | Bessel potentials | |
| 5. Week | Lipschitz continuous functions | |
| 6. Week | Extensions and Restrictions | |
| 7. Week | Decomposition of open sets into cube, Extension theorems of Whitney type | |
| 8. Week | Mid-term Exam | |
| 9. Week | Return to The Theory of Harmonic Functions | |
| 10. Week | Non-tangential convergence and Fatou’s theorem | |
| 11. Week | Application of the theory of H^p spaces | |
| 12. Week | Differentiation of Functions | |
| 13. Week | Several notions of pointwise differentiability | |
| 14. Week | A characterization of differentiability Another characterization of differentiability |
| Elmas M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Pres Princeton, NEW JERSEY 1970 |
| Elmas M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Pres Princeton, NEW JERSEY 1970 |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 50 | 60 | 40 | - |
| PY2 | 50 | 60 | 40 | 40,60 |
| PY3 | 50 | 60 | 40 | 40,60 |
| PY4 | 50 | 60 | 40 | 40,60 |
| PY5 | 50 | 60 | 40 | 40,60 |
| PY6 | 50 | 0 | 0 | 40,60 |
| PY7 | 50 | 60 | 40 | 40,60 |
| PY8 | 50 | 60 | 40 | 40,60 |
| PY9 | 50 | 60 | 40 | 40,60 |
| PY10 | 50 | 0 | 0 | 40,60 |
| 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 |
| Preparation, After Class Study | 14 | 2 | 28 |
| Research | 14 | 2 | 28 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 1 | 14 |
| Homework 2 | 14 | 1 | 14 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 2 | 2 | 4 |
| Classroom Activities | 14 | 3 | 42 |
| Total Workload | 204 | ||
| ECTS Credit of the Course | 8.0 | ||
