University :Mansoura University |
Faculty :Faculty of Educations |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 08 | | Course title: | Analysis | | Year/Level: | رابعة رياضيات | | Program Title: | - بكالوريوس العلوم والتربية تعليم أساسي رياضيات
| | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 4 | Practical: | |
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| 2- Course aims :- |
| - This course is designed to introduce and develop skill in the mathematics needed to guarantee a solid foundation for the applications of calculus to follow in later courses. The course also aims to provide some basic tools and concepts for mathematics at the first year, with particular emphasis on introducing rigorous mathematical treatments of some fundamental topics in mathematics
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
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| 1 | Leibniz rule | | | 2 | Further functions and its derivatives : Inverse functions; the log function ln; the exponential function exp and ax; the inverse trigonometric functions sin-1, cos-1, tan-1; the hyperbolic functions sinh, cosh, tanh and their inverses sinh-1, cosh-1, tanh-1; complex exponentials | | | 3 | Applications of Calculus | | | 4 | Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan | | | 5 | Limits of functions (epsilon-delta definition of limit; negation). | | | 6 | Differentiation ~ Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); the idea of implicit functions, implicit differentiation; use of derivatives in curve sketching; higher derivatives; maxima and minima of functions; conic sections, Leibniz rule. | | | 7 | Intermediate Value and Rolle Theorems | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| Lectures supported by problem sheets and weekly small-group tutorials |
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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_Term Examination | 16 |
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| B. Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | | | 2 | Final_term examination | 90 | | 3 | Oral examination | | | 4 | Practical examination | | | 5 | Semester work | 10 | | 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 | . C. Burkill, A First Course in Mathematical Analysis, Cambridge University Press is strongly recommended | | | 2 | Howard Anton, Calculus, John Wily & Sons, INC 1999 | | | 3 | Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (3rd edition), Oxford University Press, Oxford, 2002 | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| Leibniz rule | | | Further functions and its derivatives : Inverse functions; the log function ln; the exponential function exp and ax; the inverse trigonometric functions sin-1, cos-1, tan-1; the hyperbolic functions sinh, cosh, tanh and their inverses sinh-1, cosh-1, tanh-1; complex exponentials | | | Applications of Calculus | | | Functions ~ Inequalities; domain and co-domain of a function; types of function; graph of a function; continuity; curve sketching; the function sin, cos, tan | | | Limits of functions (epsilon-delta definition of limit; negation). | | | Differentiation ~ Basic ideas; tangent to a curve; the product and quotient rule; the chain rule for differentiating f(g(x)); the idea of implicit functions, implicit differentiation; use of derivatives in curve sketching; higher derivatives; maxima and minima of functions; conic sections, Leibniz rule. | | | Intermediate Value and Rolle Theorems | |
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| Course Coordinator(s): - |
| - Mohamed Samir Mahmoud Qasem
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| Head of department: - |
| Mohamed Kamal Abd Elsalam Auf Elkasar |
