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| MAT7190 | Linear Operator and Spectrum Theory in Hilbert Space | 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 | Prof. Dr. Zameddin İSMAİLOV | | Co-Lecturer | Prof.Dr. Bahadır Ö. Güler | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to give necessary informations about spectrum theory of linear transformation on Hilbert space. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | easily solve difficult problems in the theory of differential and integral equations. | 2,3 | 1 | | PO - 2 : | use in the scientific researches. | 2,3 | 1 | | PO - 3 : | apply to physical models | 2,3 | 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 | | |
| Hilbert space , Important Results , Linear Operators and Linear Functionals , Self-adjoint Operators , Spectrum and Rezolventa , Some Application , The Spectral Separation of Self-adjoint Operator |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Hilbert Spaces and Properties | | | Week 2 | Orthonormal Bases, Fourier Series | | | Week 3 | Seperable and Non-Seperable Hilbert Spaces | | | Week 4 | Linear Bounded Operators and Their Properties | | | Week 5 | Adjoint Operators | | | Week 6 | Selfadjoint Operators | | | Week 7 | Compact Operators | | | Week 8 | Mid-term exam | | | Week 9 | The spectrum of an Operator | | | Week 10 | Resolvent Operator | | | Week 11 | Laurent Operators | | | Week 12 | Toeotlitz Operators | | | Week 13 | Compact Selfadjoint Operators | | | Week 14 | The Eigenvalues of Compact Operators | | | Week 15 | Spectral Theorem | | | Week 16 | End-of-term exam | | | |
| 1 | Gohberg, I., Goldberg, S., Kaashoek A.A. 2003; Basic Clases of Linear Operators, Birkhauser Verlag, Germany | | | |
| 1 | Dunford, N., Schwartz, J.T. 1958; Linear Operators, Part I General Theory, Interscience, New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 08/04/2019 | 2 | 30 | | Quiz | 13 | 06/05/2019 | 1,5 | 20 | | End-of-term exam | 15 | 20/05/2019 | 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 | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 3 | 10 | 30 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 7 | 7 | 49 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 10 | 10 | 100 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 225 |
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