| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Harmonic Analysis and Applications | MAT607 | 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. Mehmet Zeki SARIKAYA Res. Assist. Burcu FEDAKAR |
| Instructors | |
| Assistants | |
| Goals | Teaching doctoral students about Harmonic analysis and its aplications. |
| Course Content | Scalar Multiplication in Functions; Orthogonal Systems; Fourier series, the various forms and its applications; Complex form of Fourier series; Pratic Harmonic Analysis; Accelaration of convergence of Fourier series; Mean square deviation; Bessel inequality; Fourier integral, Fourier transformation, Double- order Fourier series |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Scalar multiplication in functions | |
| 2. Week | Orthogonal Systems | |
| 3. Week | Fourier series, the various forms and its applications | |
| 4. Week | Complex form of Fourier series | |
| 5. Week | Pratic Harmonic Analysis | |
| 6. Week | Accelaration of convergence of Fourier series | |
| 7. Week | Mean square deviation | |
| 8. Week | Midterm | |
| 9. Week | Bessel inequality | |
| 10. Week | Bessel inequality | |
| 11. Week | Fourier integral | |
| 12. Week | Fourier transformation | |
| 13. Week | Double-order Fourier series | |
| 14. Week | Double-order Fourier series |
| 1.Advansed Enginering Mathemetics. C. Ray Wylie. Mc Graw-Hill İnt. 1995. |
| 2.An İntroduction to Differential Equations and their Applications. Stanley J. Farlow. Mc Graw-Hill İnt. 1994. |
| 3.Fourier Analysis and Boundary Value Problems, Enrigue A. Gonzalez-Velaco, Academic Pres. 1995. |
| 4.Advansed Enginering Mathemetics. Erwin Kreyszing. John Wiley-Sons. 1988. |
| 5.Elementary Differential Equations and Boundary Value Problems. William E. Boyce, Richard C. Di.Prima. John Wiley-Sons. 1992. |
| 6.Analiz II. Binali Musayev, Murat Alp, Nizami Mustafayev. Tek Ağaç.2003 |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 5 | 0 | 5 | 40 |
| PY2 | 5 | 0 | 5 | 40 |
| PY3 | 4 | 0 | 4 | 60 |
| PY4 | 5 | 0 | 5 | 60 |
| PY5 | 5 | 0 | 5 | 40 |
| PY6 | 5 | 0 | 5 | 60 |
| PY7 | 5 | 0 | 5 | 40 |
| PY8 | 4 | 0 | 4 | 60 |
| PY9 | 5 | 0 | 5 | 60 |
| PY10 | 4 | 0 | 4 | 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 | 1 | 3 | 3 |
| 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 | 12 | 72 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 197 | ||
| ECTS Credit of the Course | 8.0 | ||
