الجامعة :جامعة المنصورة |
الكلية :كلية العلوم |
القسم :الرياضيات |
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| 1- بيانات المقرر :- |
| | الرمز الكودى: | 114011 | | اسم المقرر: | تحليل دالى - مقرر إختيارى | | الفرقة: | رابعة رياضيات | | عنوان البرنامج: | | | التخصص: | | | عدد الساعات: | نظري: | 4 | فصل: | 1 | عملى: | |
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| 2- أهداف المقرر :- |
| - 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- نواتج التعلم المستهدفة للمقرر :- |
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| 4- محتويات المقرر :- |
| | م | الموضوع | الأسبوع |
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| 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- أساليب التعليم والتعلم :- |
| | م | الاسلوب |
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| Direct lecturing . | | Tutorials | | Quiz sheets |
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| 6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :- |
| لا توجد بيانات. |
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| 7- تقويم الطلاب :- |
| أ- التوقيت |
| | م | الطريقة | الأسبوع |
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| 1 | Oral test | 14 | | 2 | final exam | 15 |
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| ب- توزيع الدرجات |
| | م | الطريقة | الدرجة |
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| 1 | امتحان نصف الترم | 0 | | 2 | امتحان آخر الترم | 90 | | 3 | الامتحان الشفوى | 10 | | 4 | الامتحان العملى | 0 | | 5 | أعمال الترم | 0 | | 6 | طرق أخرى للتقييم | 0 | | المجموع | 100% |
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| 8- قائمة الكتب الدراسية والمراجع |
| | م | العنصر | النوع |
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| 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- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي |
| | م | المحتوى | أسبوع الدراسة |
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| 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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| اساتذة المادة: - |
| - أحمد صادق عمر حجازى
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| رئيس مجلس القسم العلمى: - |
| أحمد حبيب محمد نجيب البسيونى |
