University :Mansoura University |
Faculty :Faculty of Science |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 15403 | | Course title: | تحليل عددى (2) - تحليل دالى | | Year/Level: | رابعة الإحصاء وعلوم الحاسب | | Program Title: | - Statistics & Computer science
| | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 2 | Practical: | |
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| 2- Course aims :- |
| - At the end of this course, students should be able to obtain approximations of the solutions of boundary value problems nonlinear systems of equations and obtain the solution of linear systems
- 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 | Power method for eigenvalues and eigenvectors | | | 2 | Solution of Linear System of Equations - Iterative Methods | | | 3 | Least Square approximations and curve fitting | | | 4 | sApproximation theory, Chebyshev poly. | | | 5 | Fast Fourier transform | | | 6 | Numerical solution of nonlinear systems of Equation ( Newton’s method) | | | 7 | Numerical solution for boundary value problems h | | | 8 | Metric spaces : definition, examples and well- known inequalities | | | 9 | topology in metric spaces | | | 10 | Normed spaces : definition and examples -convergence - Banach spaces and examples | | | 11 | subspaces - separable spaces - linear hulls. | | | 12 | Bounded linear transformations and functionals . | | | 13 | Finite-dimensional normed spaces . | | | 14 | The algebra of bounded linear operators (an introductory account of the spectral aspect) | | | 15 | Inner products : examples - Schwarz’s inequality - parallelogram law - Hilbert spaces and examples. | |
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| 5- Teaching and learning methods :- |
| | S | Method |
|---|
| Two hours lecture weekly with exercising sheets and solution sheets. | | Weekly one hour tutorial in groups | | Tutorials, Direct lecturing . | | 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 exam. | 15 | | 2 | final exam | 16 |
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| B. Degree |
| | No | Method | Degree |
|---|
| 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 | 1Burden R.L. and J. D. Faires, Numerical Analysis, Sixth edition, Brooks/Cole, Pacific Grove, CA, 1997. | | | 3 | 2. Mathews, J. H., and K. D. Fink. Numerical Methods Using MATLAB®. 3rd ed. Prentice Hall, 1999. | | | 4 | Functional Analysis, W. Rudin, McGraw--Hill (1973). This book is thorough, | | | 5 | Functional Analysis, F. Riesz and B. Sz.-Nagy, Dover (1990). This is a classic text, | | | 6 | Functional Analysis in Modern Applied Mathematics, R.F. Curtain and A.J. | | | 7 | A.L.Brown &A.Page"Elements of Functional Analysis", London, 1970. | | | 8 | Periodicals | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| Power method for eigenvalues and eigenvectors | | | Solution of Linear System of Equations - Iterative Methods | | | Least Square approximations and curve fitting | | | sApproximation theory, Chebyshev poly. | | | Fast Fourier transform | | | Numerical solution of nonlinear systems of Equation ( Newton’s method) | | | Numerical solution for boundary value problems h | | | Metric spaces : definition, examples and well- known inequalities | | | 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. | |
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| Course Coordinator(s): - |
| - Samia Elsaid Abdo Abo Awad
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
