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| MATL7861 | Unbounded Sefadjoint Operators. | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is the introduction of unbounded self-adjoint operators and, teaching knowledge on this operator class. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Knows the classes of unbounded operators | | 1 | | PO - 2 : | Learns closed, closeble operators and defect numbers | | 1 | | PO - 3 : | Grasp the theoretical basis of unbounded operators with differential operators | | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| The closed and closable operator, differential operators, invariant subspaces, the spectrum of a closed operator, the unbounded symmetric operator, the unbounded self-adjoint operator, the unbounded accretive and sectorial operators, the unbounded normal operator, spectral measures, spectral ıntegrals, ıntegrals of unbounded measurable functions, the spectral theorem for bounded self-adjoint operators, the spectral theorem for unbounded self-adjoint theorem and their applications. |
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| 1 | Schmüdgen K. Unbounded Self-adjoint Operators, Springer , 2012. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 14/10/2017 | 2 | 50 | | In-term studies (second mid-term exam) | 16 | 02/01/2018 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | | | | |
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