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| MAT5320 | Advanced Functional Analysis | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Bahadır Özgür GÜLER | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | intoduce the basic concepts, principles and methods of functional analysis and its applications. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Knows metric spaces and their properties. | | | | PO - 2 : | Knows normed spaces and their properties | | | | PO - 3 : | Knows inner product spaces and their properties. | | | | 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 | | |
| Metric spaces, Vector spaces, Normed spaces and Banach space, Inner product spaces and Hilbert space |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Fundamentals of functional analysis-I (function and space concepts) | | | Week 2 | Fundamentals of functional analysis-II (set theory and Lebesgue integral) | | | Week 3 | Fundamentals of functional analysis-III (differential and integral equations) | | | Week 4 | Metric spaces | | | Week 5 | Convergence, Cauchy sequence, completeness | | | Week 6 | Vector spaces | | | Week 7 | Normed spaces and Banach spaces | | | Week 8 | Inequalities (Cauchy-Schwarz, Hölder, Minkowski) | | | Week 9 | MIDTERM EXAM | | | Week 10 | Linear operators | | | Week 11 | Bounded and continuous linear operators | | | Week 12 | Linear functionals | | | Week 13 | Inner product spaces and Hilbert spaces | | | Week 14 | Orthogonal complements and orthonormal sets | | | Week 15 | Fourier series | | | Week 16 | FINAL | | | |
| 1 | E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley, Hoboken, 1978. | | | |
| 1 | Birkhoff, Garrett and Kreyszig, Erwin. The Establishment of Functional Analysis.
Historia Mathematica, 11:258-321, 1984.
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| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 15/11/2024 | 2 | 30 | | Presentation | 12 | 15/12/2024 | 1 | 20 | | End-of-term exam | 16 | 15/01/2025 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 4 | 8 | 32 | | Arasınav | 2 | 1 | 2 | | Ödev | 4 | 9 | 36 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 5 | 8 | 40 | | Dönem sonu sınavı | 1 | 2 | 2 | | Total work load | | | 225 |
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