| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Singular Integrals I | MAT539 | 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 |
Nejla ÖZMEN |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Some Fundamental Notions of Real Variable Theory,The maximal functions,Behavior near general points of measurable sets,An interpolation theorem for L^p ,Singular Integrals,Review of certain aspects of harmonic analysis in R^n ,Singular integral operators which commute with dilations Riesz Transforms, Poisson Integrals and Spherical Harmonics ,Poisson integrals and approximations to the identity,Higher Riesz transforms and spherical harmonics,The Litlewood-Paley Theory and Multipliers,The Littewood-Paley g-function,Application of the partial sums operators |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Some Fundamental Notions of Real Variable Theory | |
| 2. Week | The maximal functions | |
| 3. Week | Behavior near general points of measurable sets | |
| 4. Week | An interpolation theorem for L^p Singular Integrals | |
| 5. Week | Review of certain aspects of harmonic analysis in R^n | |
| 6. Week | Singular integral operators | |
| 7. Week | Riesz Transforms, Poisson Integrals and Spherical Harmonics | |
| 8. Week | Mid-term Exam | |
| 9. Week | The Riesz transforms , Poisson integrals and approximations to the identity | |
| 10. Week | Higher Riesz transforms and spherical harmonics | |
| 11. Week | The Litlewood-Paley Theory and Multipliers | |
| 12. Week | The Littewood-Paley g-function | |
| 13. Week | The function | |
| 14. Week | Application of the partial sums operators The Marcinkiewicz multiplier theorem |
| 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 | 60 | 40 | 40,60 |
| PY7 | 50 | 60 | 40 | 40,60 |
| PY8 | 50 | 60 | 40 | 40,60 |
| PY9 | 50 | 60 | 40 | 40,60 |
| PY10 | 50 | 60 | 40 | 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 | ||
