| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Distribution Theory and Fourier Transforms II | MAT561 | 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 | Solving partial differential equations; The Laplace equation; The heat equation; The wave equation; The structure of distributions; The support of a distributions; Structure theorems; Distributions with point support; Positive distributions; Continuity of distiribution; Fourier analysis; The Rieman-Lebesque lemma; Paley-Wiener theorems; Hermite functions |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Solving partial differential equations | |
| 2. Week | The Laplace equation | |
| 3. Week | The heat equation | |
| 4. Week | The wave equation | |
| 5. Week | The structure of distributions | |
| 6. Week | The support of a distribution | |
| 7. Week | Structure theorems, Distributions with point support | |
| 8. Week | Midterm | |
| 9. Week | Positive distributions | |
| 10. Week | Continuity of distiribution | |
| 11. Week | Fourier analysis | |
| 12. Week | The Rieman-Lebesque lemma | |
| 13. Week | Paley-Wiener theorems | |
| 14. Week | Hermite functions |
| 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 | 4 | 0 | 0 | 60 |
| PY3 | 4 | 0 | 0 | 40 |
| PY4 | 4 | 0 | 0 | 60 |
| PY5 | 5 | 0 | 0 | 40 |
| PY6 | 4 | 0 | 0 | 60 |
| PY7 | 5 | 0 | 0 | 40 |
| PY8 | 4 | 0 | 0 | 60 |
| PY9 | 4 | 0 | 0 | 60 |
| PY10 | 4 | 0 | 0 | 40 |
| 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 | ||
