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| MAT7193 | Compact Operator Claseses | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring 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 | Prof. Dr. B. Ö.O.Guler | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Explanation of the linear compact operators theory and applications. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Will be help for the solution of linear integral equations | 2,3 | | | PO - 2 : | Will be help to scientific researches | 2,3 | | | PO - 3 : | Will be use in the other areas of the functional analysis | 2,3 | | | 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 | | |
| Compact operators in metric spaces; weak and strong convergents; Linear bounded operators; compact operators; classese of compact operators; applications |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Linear Bounded Operators in Hilbert Spaces | | | Week 2 | Adjoint and Selfadjoint Operators | | | Week 3 | Orhogonal Projections Operators | | | Week 4 | Compact Operators | | | Week 5 | Invariant Subspaces | | | Week 6 | Sopectrum and Resolvent Sets | | | Week 7 | Applications | | | Week 8 | Mid-term exam | | | Week 9 | Eigenvalues and Eigenvectors of Compact Operators | | | Week 10 | The Rank of Compact Operators | | | Week 11 | Nuclear Operators | | | Week 12 | Hilbert-Schimitd Operators | | | Week 13 | The Class of Compact Operators | | | Week 14 | Trace of Operators | | | Week 15 | Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Gohberg, I., Gohberg, 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 | 8 | 10/11/2019 | 2 | 30 | | Quiz | 12 | 09/12/2019 | 1,5 | 20 | | End-of-term exam | 17 | 05/01/2019 | 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 | | Kısa sınav | 1.5 | 1 | 1.5 | | Total work load | | | 1.5 |
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