Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | FMA605 | FUNCTIONAL ANALYSIS I | Compulsory | 1 | 1 | 6 |
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Level of Course Unit |
Second Cycle |
Objectives of the Course |
• to gain the basic information necessary in the field of functional analysis |
Name of Lecturer(s) |
Yrd. Doç. Dr. Erdal ÜNLÜYOL |
Learning Outcomes |
1 | Alanı ile ilgili ileri düzeyde alan bilgisine, becerisine sahip olmak ve bunu gerçek öğretim ortamlarında kullanmak |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
• Basic Concepts of normed spaces
• Hahn-Banach theorem
• Uniform Boundedness Theorem
• Open Conversion Theorem
• Closed Graph Theorem
• Banach Fixed Point Theorem and application of this theorem to linear, Differential and Integral Equations
• Spectral Theory of Linear Operators in Normed Spaces
• Resolvent and Spectrum Properties
• Banach Algebras and Properties
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Weekly Detailed Course Contents |
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1 | Basic Concepts of normed spaces
| | | 2 | Hahn-Banach theorem
| | | 3 | Uniform Boundedness Theorem
| | | 4 | Open Conversion Theorem
| | | 5 | Closed Graph Theorem
| | | 6 | Banach Fixed Point Theorem and application of this theorem to linear, Differential and Integral Equations
| | | 7 | Banach Fixed Point Theorem and bu Application of this theorem to linear, Differential and Integral Equations
| | | 8 | Midterm exam
| | | 9 | Spectral Theory of Linear Operators in Normed Spaces
| | | 10 | Spectral Theory of Linear Operators in Normed Spaces
| | | 11 | Paracompactness of Metric Spaces
| | | 12 | Resolvent and Spectrum Properties
| | | 13 | Resolvent and Spectrum Properties
| | | 14 | Banach Algebras and Properties
| | | 15 | Banach Algebras and Properties
| | | 16 | Final exam | | |
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Recommended or Required Reading |
1 Yuli Eidelman, Vitali D.Milman, Antonis Tsolomitis; Functional Analysis: An introduction, American Mathematical Society
Other References
1 Reed, M. and Simon, Nad B. 1972;Methods of Modern Mathematical Physics. 1. Functional Analysis, Academic Press, New York
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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 | 15 | 3 | 45 |
Problem Solving | 8 | 5 | 40 |
Discussion | 8 | 5 | 40 |
Self Study | 10 | 4 | 40 |
Individual Study for Mid term Examination | 8 | 5 | 40 |
Individual Study for Final Examination | 8 | 5 | 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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Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
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