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| MATL7261 | Differential Geometry on Surfaces | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Selçuk Han AYDIN | | Co-Lecturer | none | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | Understand how much of the geometry of a surface is idependent of its shape. Investigate the geometric properties of surfaces independent of the space that they lie in. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Grasp Euclidean space and surfaces in Euclidean spaces | | | | PO - 2 : | Make alculations on surfaces in local koordinates | | | | PO - 3 : | Investigate surfaces and their geometric properties independent from the space that it is located | | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Regular Surfaces, Differential Function on Surfaces, The Tangent Plane, The First Fundamental Form, Orientation of Surfaces, Compact Orientable Surfaces, A Geometric Definition of Area, The Definition of Gauss the Map and its Fundamental Properties, The Gauss Map in Local Coordinates, Ruled and Minimal Surfaces, Isometries, Gauss Theorem, The Gauss-Bonet Theorem and its Aplications. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Regular Surfaces | | | Week 2 | Differential Function on Surfaces, | | | Week 3 | The Tangent Plane | | | Week 4 | The First Fundamental Form | | | Week 5 | Orientation of Surfaces | | | Week 6 | Compact Orientable Surfaces | | | Week 7 | A Geometric Definition of Area | | | Week 8 | The Definition of Gauss the Map and its Fundamental Properties | | | Week 9 | mid term exam | | | Week 10 | Yerel Koordinatlarda Gauss Dönüşümü | | | Week 11 | Ruled and Minimal Surfaces | | | Week 12 | Isometries | | | Week 13 | Gauss Theorem | | | Week 14 | The Gauss-Bonet Theorem and its Aplications. | | | Week 15 | The Gauss-Bonet Theorem and its Aplications. | | | Week 16 | final exam | | | |
| 1 | Carmo, M. P. do, 1976; Differentil Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, New Jersey | | | |
| 1 | O'Neill, B. 1966; Elementary Differential Geometry, Academic Press, New York and London | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 14042017 | 2 | 30 | | Quiz | 6 | 24032017 | 2 | 30 | | End-of-term exam | 16 | 02062017 | 2 | 40 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 12 | 14 | 168 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 226 |
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