University :Mansoura University |
Faculty :Faculty of Educations |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 03 | | Course title: | Analysis | | Year/Level: | ثالثة رياضيات | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 4 | Practical: | |
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| 2- Course aims :- |
| - A core course unit for second year Mathematics. The main purpose of this course is to provide an informal introduction to the concept of limit in its simplest setting: sequences and series
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
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| 1 | Bounded sets ,upper and lower limits of functions, Sequences of real numbers, Limits of sequences | | | 2 | Convergence and divergence of sequenc. Bounded and monotone sequences , Cauchy sequences | | | 3 | Real series, Convergent series, the geometric series and the the harmonic series | | | 4 | Series with positive and negative terms. Alternating series test. | | | 5 | Series with non-negative terms, the Comparison , nth root and the Ratio tests | | | 6 | Absolute and conditional convergence, Power series and radius of convergence | | | 7 | Absolute and conditional convergence, Power series and radius of convergence | | | 8 | Convergence Tests: Integral, Rabbe , Logarithimic, De Morgan and Gauss | | | 9 | Series of functions and uniform convergence, Virstrass, Dirchlet tests | | | 10 | Infinite Product of Series | | | 11 | Fourier series, Sin Cos series | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| Three hours of lectures and 3 hours of tutorials | | Tutorial sheets will be handed out in lectures | | Solutions to tutorial problems will be available | | Power point slides are used in this course
Power point slides are used in this course
Power point slides are used in this course
Power point slides are used in this course
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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 semester exam | 10 | | 2 | Final Exam | 14 |
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| B. Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | 90 | | 2 | Final_term examination | 10 | | 3 | Oral examination | | | 4 | Practical examination | | | 5 | Semester work | | | 6 | Other types of asessment | | | Total | 100% |
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| 8- List of books and references |
| | S | Item | Type |
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| 1 | 6.1- Course Notes(Avaliable in the Dept.) | | | 2 | 6.2- Essential Books (Text Books)Haggerty, Rod ‘Fundamentals of Mathematical Analysis’ Second Edition, Addison-Wesley 1993. | | | 3 | 6.3- Recommended Books,White, A. J., ’Real Analysis, an Introduction’, Addison-Wesley | | | 4 | 6.4- Periodicals, Web Sites, …etc | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
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| Bounded sets ,upper and lower limits of functions, Sequences of real numbers, Limits of sequences | | | Convergence and divergence of sequenc. Bounded and monotone sequences , Cauchy sequences | | | Real series, Convergent series, the geometric series and the the harmonic series | | | Series with positive and negative terms. Alternating series test. | | | Series with non-negative terms, the Comparison , nth root and the Ratio tests | | | Absolute and conditional convergence, Power series and radius of convergence | | | Absolute and conditional convergence, Power series and radius of convergence | | | Convergence Tests: Integral, Rabbe , Logarithimic, De Morgan and Gauss | | | Series of functions and uniform convergence, Virstrass, Dirchlet tests | | | Infinite Product of Series | | | Fourier series, Sin Cos series | |
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| Course Coordinator(s): - |
| - Hanan Elsaid Awad Darwesh
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| Head of department: - |
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