| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Methods of Hilbert Spaces | MAT538 | 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. Emrah Evren KARA |
| Instructors |
Emrah Evren KARA |
| Assistants | |
| Goals | Teaching Masters students about Hilbert spaces and operators in these spaces. |
| Course Content | Spectral representation of unit matrix and its Applications to ODE,Elements of Hilbert Spaces,Self-Adjointness, Unitary and Normal Operators,Unbounded Operators in Hilbert Space,Hyperbolic differential equations,Parabolic differential equations,Elliptic differential equations |
| Learning Outcomes |
- Student’s ability of commenting and thinking truely will improve and the students will get basic information about mathematics. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Spectral representation of unit matrix and its Applications to ODE | |
| 2. Week | Spectral representation of unit matrix and its Applications to ODE | |
| 3. Week | Hilbert Spaces, Self-Adjoint, Unitary and Normal Operators | |
| 4. Week | Hilbert Spaces, Self-Adjoint, Unitary and Normal Operators | |
| 5. Week | Hilbert Spaces, Self-Adjoint, Unitary and Normal Operators | |
| 6. Week | Hilbert Spaces, Self-Adjoint, Unitary and Normal Operators | |
| 7. Week | Unbounded Operators in Hilbert Space | |
| 8. Week | Midterm | |
| 9. Week | Unbounded Operators on Hibert Spaces | |
| 10. Week | Unbounded Operators in Hilbert Space | |
| 11. Week | Hyperbolic differential equations | |
| 12. Week | Hyperbolic differential equations | |
| 13. Week | Parabolic differential equations | |
| 14. Week | Elliptic differential equations |
| Ashyralyev A. and Sobolevskii P.E. Well-Posedness of Parabolic Difference Equations. Birkhauser Verlag: Basel. Boston. Berlin, 1994. |
| .Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations (Dover Books on Mathematics) by Samuel S. Holland. |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 5 | 5 | 40,60 |
| PY2 | 5 | 5 | 40,60 |
| PY3 | 1 | 1 | 40,60 |
| PY4 | 3 | 3 | 40,60 |
| PY5 | 4 | 4 | 40,60 |
| PY6 | 3 | 3 | 40,60 |
| PY7 | 2 | 2 | 40,60 |
| PY8 | 4 | 4 | 40,60 |
| PY9 | 4 | 4 | 40,60 |
| PY10 | 4 | 4 | 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 | 1 | 14 |
| Research | 14 | 1 | 14 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 7 | 3 | 21 |
| Homework 2 | 7 | 3.5 | 24.5 |
| Final | 1 | 2.5 | 2.5 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 14 | 2 | 28 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 204 | ||
| ECTS Credit of the Course | 8.0 | ||
