Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT520 | COMPLETE FUNCTIONS THEORY AND APPLICATIONS II | Elective | 1 | 2 | 6 |
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Level of Course Unit |
Second Cycle |
Objectives of the Course |
With the help of inner product spaces and Hilbert spaces discrete approach to student |
Name of Lecturer(s) |
Prof. Dr. Mammad Mustafayev |
Learning Outcomes |
1 | Defining Dual spaces and the Adjoint operators. | 2 | Learning compactness in normed spaces and compact operators | 3 | Learning inner product space rigidity and vertical projection operator | 4 | Explaining method of sequential approaches | 5 | Defining the conversion principle of shrinking | 6 | The ability to prove being and uniqueness theorem to integral equations | 7 | To ability Fredholm and Volterra integral equations expression |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Classification of full functions, Phragmen Lindölf principle, exponential complete functions, Borel transformation, Wiener-Paley theorem, opening of complete functions to infinite products, application of complete functions and control problems |
Weekly Detailed Course Contents |
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1 | Dual spaces and Adjoint operators | | | 2 | Theorem of Hanh-Banach | | | 3 | Compactness in Normed spaces and the compact operators | | | 4 | Compactness in Normed spaces and the compact operators | | | 5 | Inner product space rigidity and vertical projection operator | | | 6 | Inner product space rigidity and vertical projection operator | | | 7 | The method of sequential approaches | | | 8 | The method of sequential approaches | | | 9 | Midterm exam | | | 10 | Narrowing conversion principle | | | 11 | Narrowing conversion principle | | | 12 | Being and uniqueness theorem for ıntegral equations | | | 13 | Being and uniqueness theorem for ıntegral equations | | | 14 | Fredholm and Volterra integral equations | | | 15 | Fredholm and Volterra integral equations | | | 16 | Final Exam | | |
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Recommended or Required Reading |
Musayev B., Alp M., Fonksiyonel Analiz, Bole Yayınları, Ankara, (2002)
Erwin Kreyszig, Introductory functional analysis with applications, John Wiley and Sons. Inc., (1978)
I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, (1988) |
Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 40 | End Of Term (or Year) Learning Activities | 60 | SUM | 100 |
| Language of Instruction | | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Self Study | 6 | 3 | 18 |
Individual Study for Homework Problems | 8 | 7 | 56 |
Individual Study for Mid term Examination | 8 | 7 | 56 |
Individual Study for Final Examination | 8 | 7 | 56 |
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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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Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |