|
|
| MAT4014 | Introduction to Functional Analysis | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Zameddin İSMAİLOV | | Co-Lecturer | Prof. Dr. Bahadır Özgür GÜLER | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To present the basics of modern functional analysis, introducing the lineer normed spaces and transformations on these spaces.
|
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | calculate the Fourier coefficients of certain elementary functions. | 1,2,3,4,5,6,7,8 | 1 | | LO - 2 : | perform a range of calculations involving orthogonal expansions in Hilbert spaces and to prove the standard theorems associated with them. | 1,2,3,4,5,6,7,8 | 1 | | LO - 3 : | apply functional analytic techniques to the study of Fourier series. | 1,2,3,4,5,6,7,8 | 1 | | LO - 4 : | give the definitions and basic properties of various classes of operators on a Hilbert space and use them in specific examples. | 1,2,3,4,5,6,7,8 | 1 | | LO - 5 : | prove results related to the theorems in the course. | 1,2,3,4,5,6,7,8 | 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), LO : Learning Outcome | | |
| Metric spaces ,Normed lineer spaces, Inner product spaces, Orthogonal expansions, Lineer bounded transformations, Lineer bounded functionals,
Spectrum of an operator.
|
| |
| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Metric spaces,convegent sequences in metric spaces,complete metric spaces | | | Week 2 | The completion of a metric space,Limit an continuity in normed linear spaces | | | Week 3 | Banach fixed point theorem and its applications | | | Week 4 | Normed linear spaces | | | Week 5 | Banach spaces | | | Week 6 | Inner product spaces | | | Week 7 | Hilbert spaces | | | Week 8 | Bounded linear functionals and Riesz-Frechet's Theorem | | | Week 9 | Mid-term exam | | | Week 10 | Inner product spaces and orthogonal decompositions | | | Week 11 | Bounded linear transformations | | | Week 12 | Norm of linear bounded operator | | | Week 13 | Applications | | | Week 14 | Spectrum of an operator | | | Week 15 | Spectrum of an operator and applications | | | Week 16 | Final exam | | | |
| 1 | B. Musayev, M.Alp, Fonksiyonel Analiz, Kütahya, 2008 | | | |
| 1 | W.W.Chen, Introduction to Functional Analysis, Imperial College, University of London,, 2008. | | | 2 | Bryan P. Rynne and Martin A Younson,Linear Functional Analysis, Second Edition Springer-Verlag,2008. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 50 | | End-of-term exam | 16 | | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 4 | 12 | 48 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 7 | 5 | 35 | | 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 | 7 | 7 | 49 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 192 |
|