Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT40220121310 | FUNCTIONAL ANALYSIS | Compulsory | 4 | 8 | 5 |
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Level of Course Unit |
First Cycle |
Objectives of the Course |
To introduce the basics of functional analysis . |
Name of Lecturer(s) |
Yrd. Doç. Dr. Erdal ÜNLÜYOL |
Learning Outcomes |
1 | will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics. |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Metric Spaces, Normed Linear Spaces, Bounded Linear Maps,, Inner Product Spaces, Hilbert Spaces, Fourier Series in Hilbert Spaces, Applications of Fourier Series, Compact and Hermit Operators in Hilbert Spaces |
Weekly Detailed Course Contents |
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1 | Metric spaces, complete metric spaces
| | | 2 | Compactness of metric spaces
| | | 3 | Normed linear spaces
| | | 4 | Banach spaces
| | | 5 | inner product spaces
| | | 6 | Hilbert spaces
| | | 7 | Fourier series in Hilber spaces
| | | 8 | Midterm exam
| | | 9 | Applications of Fourier series
| | | 10 | Topological vector spaces
| | | 11 | Norm of continuous linear operators on normed spaces
| | | 12 | Theorem of Banach-Stayhaus
| | | 13 | Conjugate spaces, conjugate operators and the concept of strong convergence
| | | 14 | Kompat and Hermitian operators in Hilbert spaces
| | | 15 | L_p spaces and the space L_{\infty} | | | 16 | Final exam | | |
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Recommended or Required Reading |
1 Hüsnü KIZMAZ, Fonksiyonel ANALYSIS, Karadeniz Teknik Üniversitesi Yayınları 2098.
Other Textbook and /or References
2 Yosida K. Functional Analysis, Berlin, 1971
3 Danford N., Schwartz J.T. Lineer operators, New York, 1971
4 Kreyszig E. Introductory functional analysis with application, New York, 1978
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Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
SUM | 0 | |
SUM | 0 | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | SUM | 100 |
| Language of Instruction | Turkish | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Makeup Examination | 1 | 2 | 2 |
Attending Lectures | 10 | 4 | 40 |
Self Study | 10 | 3 | 30 |
Individual Study for Mid term Examination | 10 | 4 | 40 |
Individual Study for Final Examination | 10 | 4 | 40 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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