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| MAT7261 | 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. Yasemin SAĞIROĞLU | | Co-Lecturer | Assoc.Prof.Dr. Filiz OCAK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Investigation of local and common properties of surfaces used in differential geometry. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Recognizes regular surfaces and calculates geometric expressions defined on regular surfaces using differential. | 1,2,7,8 | 1, | | PO - 2 : | Distinguish between orientable and non-orientable surfaces. | 1,2,7,8 | 1, | | PO - 3 : | Calculates the area of a closed and bounded region on a regular surface. | 1,2,7,8 | 1, | | PO - 4 : | Recognizes the Gaussian map and makes applications related to the shape of the surface. | 1,2,7,8 | 1, | | PO - 5 : | Recognizes ruled and minimal surfaces. | 1,2,7,8 | 1, | | PO - 6 : | Determine the isometry transformation between regular surfaces. | 1,2,7,8 | 1, | | PO - 7 : | Knows the Gauss-Bonnet Theorem and its applications. | 1,2,7,8 | | | 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, Change of Parameter, Differentiable Functions on Surfaces, The Tangent Plane, The First Fundamental Form, Orientation of Surfaces, Compact Orientable Surfaces, Geometric Definition of Area, The Definition of the Gauss Map and Its Fundamental Properties, The Gauss Map in Local Coordinates, Ruled and Minimal Surfaces, Isometries, Gauss Theorem, The Gauss-Bonnet Theorem and Its Applications. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Regular Surfaces | | | Week 2 | Change of parameter | | | Week 3 | Differentiable Functions on Surfaces | | | Week 4 | The Tangent Plane | | | Week 5 | The First Fundamental Form | | | Week 6 | Orientation of Surfaces | | | Week 7 | Compact Orientable Surfaces, Geometric Definition of Area | | | Week 8 | The Definition of Gauss Map and its Fundamental Properties | | | Week 9 | Exam | | | Week 10 | The Gauss Map in Local Coordinates | | | Week 11 | Ruled and Minimal Surfaces | | | Week 12 | Isometries | | | Week 13 | Gauss Theorem, Short Exam | | | Week 14 | The Gauss-Bonnet Theorem and its Applications | | | Week 15 | Rectifying the lack of subject | | | Week 16 | Final sınavı | | | |
| 1 | Do Carmo, Manfredo. 2012; Diferansiyel Geometri: Eğriler ve Yüzeyler, Çeviri: Belgin Korkmaz, Türkiye Bilimler Akademisi, Ankara | | | |
| 1 | O'Neill, Barrett. 2006; Elementary Differential Geometry, Elsevier, Burlington, USA | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 16/04/2024 | 2 | 30 | | Quiz | 13 | 14/05/2024 | 1 | 20 | | End-of-term exam | 16 | 14/06/2024 | 2 | 50 | | |
| 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 | 9 | 14 | 126 | | Arasınav için hazırlık | 12 | 1 | 12 | | Arasınav | 2 | 1 | 2 | | Ödev | 2 | 14 | 28 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 225 |
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