University :Mansoura University |
Faculty :Faculty of Science |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 114011 | | Course title: | تحليل دالى - مقرر إختيارى | | Year/Level: | رابعة رياضيات | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 1 | Practical: | |
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| 2- Course aims :- |
| - This course aims at familiarizing the student with the basic concepts, principles and methods of functional analysis and its applications. Functional analysis plays an important role in the applied sciences as well as in mathematics itself. Roughly speaking, functional analysis develops the tools from calculus and linear algebra further to the more general setting where one has vector spaces comprising functions or general abstract infinite-dimensional vector spaces. Problems from various application areas can then be conveniently posed in this common general set up, and solved using the techniques of functional analysis.
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
|---|
| 1 | Metric spaces : definition, examples and well- known inaqualities | | | 2 | topology in metric spaces | | | 3 | Normed spaces : definition and examples -convergence - Banach spaces and examples | | | 4 | subspaces - separable spaces - linear hulls. | | | 5 | Bounded linear transformations and functionals . | | | 6 | Finite-dimensional normed spaces . | | | 7 | The algebra of bounded linear operators (an introductory account of the spectral aspect) | | | 8 | Inner products : examples - Schwarz's inequality - parallelogram law - Hilbert spaces and examples. | | | 9 | Orthogonality in Hilbert spaces - Riesz's representation Theorem - Gram-Schmidt process . | | | 10 | The adjoint operator - properties - self-adjoint bounded linear operatorsoperators | | | 11 | Positive operators - properties - the spectrum, eigenvalues and eigen vectors. | | | 12 | Orthogonal projections . | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| Direct lecturing . | | Tutorials | | Quiz sheets |
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| 6- Teaching and learning methods of disables :- |
| No data found. |
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| 7- Student assessment :- |
| A. Timing |
| | No | Method | Week |
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| 1 | Oral test | 14 | | 2 | final exam | 15 |
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| B. Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | 0 | | 2 | Final_term examination | 90 | | 3 | Oral examination | 10 | | 4 | Practical examination | 0 | | 5 | Semester work | 0 | | 6 | Other types of asessment | 0 | | Total | 100% |
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| 8- List of books and references |
| | S | Item | Type |
|---|
| 1 | Course Notes | | | 2 | Essential Books (Text Books) | | | 3 | Recommended Books [1] Functional Analysis, W. Rudin, McGraw--Hill (1973). This book is thorough, | | | 4 | Periodicals, Web Sites, …etc http://www.mth.uea.ac.uk/~h720/teaching/functionalanalysis/materials/FAnotes.pdf | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| Metric spaces : definition, examples and well- known inaqualities | | | topology in metric spaces | | | Normed spaces : definition and examples -convergence - Banach spaces and examples | | | subspaces - separable spaces - linear hulls. | | | Bounded linear transformations and functionals . | | | Finite-dimensional normed spaces . | | | The algebra of bounded linear operators (an introductory account of the spectral aspect) | | | Inner products : examples - Schwarz's inequality - parallelogram law - Hilbert spaces and examples. | | | Orthogonality in Hilbert spaces - Riesz's representation Theorem - Gram-Schmidt process . | | | The adjoint operator - properties - self-adjoint bounded linear operatorsoperators | | | Positive operators - properties - the spectrum, eigenvalues and eigen vectors. | | | Orthogonal projections . | |
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| Course Coordinator(s): - |
| - Ahmed Sadeq Omar Hegazy
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
