University :Mansoura University |
Faculty :Faculty of Science |
Department :Mathematics Department |
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| 1- Course data :- |
| | Code: | 114011 | | Course title: | هندسة تفاضلية أو هندسية جبرية أو توبولوجى | | Year/Level: | رابعة رياضيات | | Program Title: | | | Specialization: | | | Teaching Hours: | Theoretical: | 4 | Tutorial: | 1 | Practical: | |
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| 2- Course aims :- |
| - This will be self contained course which uses little more than elementary vector calculus to develop the local differential geometry of curves and surfaces in the Euclidean space of dimension 3.And prepare students for high level abstract math.
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| 3- Course Learning Outcomes :- |
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| 4- Course contents :- |
| | No | Topics | Week |
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| 1 | 1) - The theory of curves : definition of a parametric and regular curve - Arc-length-Frenet frame | | | 2 | Special vectors ( tangent-normal-binormal vectors) | | | 3 | Frenet tryhedron in 3 Euclidean space | | | 4 | Evolute and invelute | | | 5 | Definition of regular surface in 3 Euclidean space and some examples | | | 6 | Normal vector and tangent plane - curve on a surface - First , Second fundamental forms and area | | | 7 | Normal and geodesic curvatures | | | 8 | Principals,Gaussian and mean curvatures | |
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| 5- Teaching and learning methods :- |
| | S | Method |
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| lectures | | Internet search |
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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 | Mid term exam | 5 | | 2 | sheet exam and Oral exam | 10 | | 3 | final exam | 13 |
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| B. Degree |
| | No | Method | Degree |
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| 1 | Mid_term examination | 10 | | 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 |
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| 1 | - Course Notes : Differential geometry | | | 2 | Essential Books (Text Books) Differential geometry ( Schaum series) | | | 3 | Recommended Books A.Gray "Modern differential geometry of curves and surfaces" | | | 4 | Periodicals, Web Sites, …etc http:/Mathworld.wolfram.com, http:/en.wikipedia.org | |
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| 9- Matrix of knowledge and skills of the course |
| | S | Content | Study week |
|---|
| 1) - The theory of curves : definition of a parametric and regular curve - Arc-length-Frenet frame | | | Special vectors ( tangent-normal-binormal vectors) | | | Frenet tryhedron in 3 Euclidean space | | | Evolute and invelute | | | Definition of regular surface in 3 Euclidean space and some examples | | | Normal vector and tangent plane - curve on a surface - First , Second fundamental forms and area | | | Normal and geodesic curvatures | | | Principals,Gaussian and mean curvatures | |
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| Course Coordinator(s): - |
| - Awatef Mohamed Abd Elghany Shahin
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| Head of department: - |
| Ahmed Habeb Mohamed Nageb Elbassiony |
