| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Distribution Theory and Fourier Transforms I | MAT560 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Prof. Dr. HÜSEYİN BUDAK |
| Instructors |
HÜSEYİN BUDAK |
| Assistants | |
| Goals | The aim of this course can be thought of as the completion of differential calculus, just as the other great revolution, measure theory(or Lebesgue integration theory), can be thought of as the completion of integral calculas. The techniques of distribution theory can be used, confidently and effectively-just like the techniques of calculus are used-without a complete knowledge of the formal mathematical foundations of the subject. |
| Course Content | What are distributions; Generalized function and test function; Examples of distributions; The calculus of distributions; Functions as distributions; Operators on distributions; Adjoint identities; Consisttency of derivatives; Distiributional solutions of differential equations; Fourier transforms; From Fourier series to Fourier integrals,; The Schwarz class S , Properties of the Fourier Transform on S, The Fourier inversion formula on S |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | What are distributions? | |
| 2. Week | Generalized function and test function | |
| 3. Week | Examples of distributions | |
| 4. Week | The calculus of distributions | |
| 5. Week | Functions as distributions | |
| 6. Week | Operators on distributions | |
| 7. Week | Adjoint identities, Consisttency of derivatives | |
| 8. Week | Midterm | |
| 9. Week | Distiributional solutions of differential equations | |
| 10. Week | Fourier transforms from Fourier series to Fourier integrals | |
| 11. Week | Fourier transforms from Fourier series to Fourier integrals | |
| 12. Week | The class of S Schwarz | |
| 13. Week | Properties of the Fourier transform on S | |
| 14. Week | S inversion Fourier transformation |
| Robert S. Strichartz, A Guide to Disrtibution Theory and Fourier Transforms, 2000 , Florida |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 4 | 0 | 0 | 40 |
| PY2 | 5 | 0 | 0 | 60 |
| PY3 | 4 | 0 | 0 | 40 |
| PY4 | 4 | 0 | 0 | 60 |
| PY5 | 4 | 0 | 0 | 60 |
| PY6 | 4 | 0 | 0 | 40 |
| PY7 | 5 | 0 | 0 | 60 |
| PY8 | 4 | 0 | 0 | 40 |
| PY9 | 4 | 0 | 0 | 40 |
| PY10 | 4 | 0 | 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 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 2 | 28 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 3 | 42 |
| Practice End-Of-Term | 14 | 3 | 42 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 200 | ||
| ECTS Credit of the Course | 8.0 | ||
