Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | ZARİFE ZARARSIZ (zarifezararsiz@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | To teach applications of functional analysis |
PO- |
Examination |
| LO-2 | To give basic theorems of applied functional analysis |
PO- |
Examination |
| LO-3 | To teach the students fourier series and ortagonal polynomials in detail. |
PO- |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Definition of a Hilbert Space, Review of Continuous Linear and Bilinear Operators, The Best Approximation Theorem, Orthogonal Projectors, Closed Subspaces, Quotient Spaces, and Finite Products of Hilbert Spaces, Orthogonal Bases for a Separable Hilbert Space, Separation Theorems, The Duality Theorem in Convex Optimization, Von Neumann's Minimax Theorem, The Dual of a Hilbert Space, Approximation by Orthogonal Polynomials, Legendre, Laguerre, and Hermite Polynomials, Fourier Series, | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Minimal and Maximal Domains of a Closed Family of Operators, 104 | |
| 2 | Unbounded Operators and Their Adjoints | |
| 3 | Completion of a Pre-Hilbert Space Contained in a Hilbert Space, Hausdor¨ Completion | |
| 4 | The Hilbert Sum of Hilbert Spaces, Reproducing Kernels of a Hilbert Space of Functions | |
| 5 | L^2_p uzayı | |
| 6 | Convolution Operators | |
| 7 | Approximation by Orthogonal Polynomials | |
| 8 | mid-term exam | |
| 9 | Legendre, Laguerre, and Hermite Polynomials, 170 8.3. Fourier Series | |
| 10 | Approximation by Step Functions, Approximation by Piecewise Polynomial Functions | |
| 11 | Compact Operators | |
| 12 | The Theory of Riesz-Fredholm | |
| 13 | Characterization of Compact Operators from One Hilbert Space to Another | |
| 14 | The Fredholm Alternative | |
| 15 | The Hilbert Space of Hilbert-Schmidt Operators | |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Applied Functional Analysis, JEAN-PIERRE AUBIN, JOHN WILEY & SONS, INC., 2000 | |
| Required Course instruments and materials | ||
| Lecture notes and APPLIED FUNCTIONAL ANALYSIS JEAN-PIERRE AUBIN University of Paris±Dauphine | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 15 | 45 |
| Outside Class | |||
| a) Reading | 3 | 15 | 45 |
| b) Search in internet/Library | 2 | 15 | 30 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 2 | 15 | 30 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 178 | ||