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Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MAT-23-206 | FunctIonal AnalysIs II | Elective | 1 | 2 | 6 |
| | Level of Course Unit | | Third Cycle | | Objectives of the Course | | Describe the orthogonalization, orthonormality, linear functionals and hyperplanes of the orthogonal system in Hilbert spaces, the results of the Hahn-Banach theorem, the Banach-Steinhaus theorem, the Banach fixed point theorem and its application, the weak topology in the Banach space and its application. For example, Lebesgue, Sobolev et al. space and differential, integral and other linear transformations. | | Name of Lecturer(s) | | Prof. Dr. Kamal Soltanov | | Learning Outcomes | | 1 | Students will be able to understand the orthogonal system, orthogonalization, orthonormal systems in Hilbert spaces; linear functionals and Hyperplanes and apply the results. | | 2 | Students will be able to understand the results of the Hahn-Banach theorem, applications of the results of the Hahn-Banach theorem in Lebesgue spaces and Sobolev spaces | | 3 | Students will be able to understand the linear functional space, Geometric Hahn-Banach theorem and its results, Banach-Steinhaus theorem and their applications. | | 4 | Students will be able to understand the Banach fixed point theorem and its application, the weak topology in the Banach space and its properties, Reflexive spaces; and moreover these can apply the results that they have studied for understand of the articles that need to be read |
| | Mode of Delivery | | Daytime Class | | Prerequisites and co-requisities | | It is need to know the basic facts of Mathematical Analysis, Linear Algebra, Real analysis, Ordinary and Partial Differential Equations, Algebra and Topology in the graduate level. | | Recommended Optional Programme Components | | | Course Contents | | -To explain the students of the orthogonal system, orthogonalization, orthonormality in Hilbert spaces, linear functionals and Hyperplanes, Hahn-Banach theorem and why are important to know their properties.
-To explain the students of the application of the results of the Hahn-Banach theorem in Lebesgue spaces, the functionals spaces, the adaptation of the results of the Hahn-Banach theoremin in Sobolev spaces: in abstract form and examples.
-To explain the students of the results of the Geometric Hahn-Banach theorem and its results, the Banach-Steinhaus theorem; Describe the linear bounded and unbounded operators (and linear functionales), defined on the above mentioned spaces, their properties.
-To explain the students the Banach fixed point theorem and its application, the spaces of the bounded and unbounded linear operators in Banach space, the weak topology on Banach space and properties, Reflexive spaces and their properties in general case and in examples | | Weekly Detailed Course Contents | |
| 1 | | | | | 2 | | | | | 3 | | | | | 4 | | | | | 5 | | | | | 6 | | | | | 7 | Midterm Exam | | | | 8 | | | | | 9 | | | | | 10 | | | | | 11 | | | | | 12 | | | | | 13 | | | | | 14 | | | | | 15 | | | |
| | Recommended or Required Reading | | Lusternik, L. A; Sobolev, V. J: Elements of Functional Analysis. Wiley 1974.
Yoshida, K: Functional Analysis. Springer Verlag 1980.
Rudin, W : Functional Analysis. Mc Graw Hill 1985.
Kirillov A., Gvishiani A. D.: Theorems and Problems in Functional Analysis. Springer-Verlag, New York, 1982
Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2011, Springer, N.Y.
| | Planned Learning Activities and Teaching Methods | | | 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) | |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 2 | 2 | | Practice | 14 | 3 | 42 | | Criticising Paper | 14 | 3 | 42 | | Individual Study for Mid term Examination | 1 | 50 | 50 | | Individual Study for Final Examination | 1 | 50 | 50 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | LO2 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | LO3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | LO4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
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