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| MAT3011 | DIFFERENTIAL GEOMETRY | 4+0+0 | ECTS:7 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Ömer PEKŞEN | | Co-Lecturer | Prof. Dr. Yasemin SAĞIROĞLU | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Aim of the course is to introduce some of the main ideas of differential geometry of curves and surfaces in 3-dimensional space, to reinforce their advanced calculus and linear algebra knowledge giving a good opportunity to exhibit their interplay through application to geometry |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | familiar with the main ideas of differential geometry of curves and surfaces.
| 5 - 7 | 1, | | LO - 2 : | apply Frenet Formulas to find invariants of curves
| 5 - 7 | 1, | | LO - 3 : | use shape operator to evaluate curvatures of a surface
| 5 - 7 | 1, | | LO - 4 : | have a good opportunity to use their advance calculus and linear algebra knowledge to explore geometry
| 5 - 7 | 1, | | 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), LO : Learning Outcome | | |
| Euclidean Space; Tangent Vectors and Vector Fields in 3-dimensional Space, Directional Derivatives; Curves in 3-dimensional Space; 1-Forms; Differential Forms; Mappings Between Euclidean spaces; Dot Product; Curves; The Frenet Formulas; Arbitrary-Speed Curves; Covariant Derivatives; Frame Fields; Connection Forms; Surfaces3-dimensional Space; Patch Computations; Differentiable Functions and Tangent Vectors; The Shape Operator; Normal Curvature; Gaussian Curvature; Computational Techniques; Special Curves in a Surface; Surfaces of Revolution. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Euclidean Space | | | Week 2 | Tangent Vectors, Directional Derivatives | | | Week 3 | Curves in 3-dimensional space, 1-Forms | | | Week 4 | Differential Forms, Mappings | | | Week 5 | Dot Product, Curves | | | Week 6 | The Frenet Formulas, Arbitrary-Speed Curves | | | Week 7 | Covariant Derivatives, Frame Fields | | | Week 8 | Connection Forms | | | Week 9 | Mid-term exam
| | | Week 10 | Surfaces in 3-dimensional Space, Patch Computations | | | Week 11 | Differentiable Functions and Tangent Vectors, The Shape Operator | | | Week 12 | Normal Curvature, Gaussian Curvature | | | Week 13 | Computational Techniques | | | Week 14 | Special Curves in a Surface, Surfaces of Revolution | | | Week 15 | Completion | | | Week 16 | End-of-term exam | | | |
| 1 | O'Neill, B. 1966; Elementary Differential Geometry, Academic Press, New York and London | | | |
| 1 | Gray, A. 1999; Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press | | | 2 | Hacısalihoğlu, H.H. 1983; Diferansiyel Geometri, İnönü Üniversitesi, Fen-Ed. Fakültesi Yayınları, No:2, | | | 3 | Lipschutz, M.M. 1969; Theory and Problems of Differential Geometry, Schaum's Outline Series, McGraw-Hill Book Company. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22/11/2024 | 2 | 30 | | Quiz | 5
13 | 22/10-17/12/2024 | 1 | 20 | | End-of-term exam | 16 | 15/01/2025 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 6.5 | 14 | 91 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 2 | 2 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 2 | 4 | | Total work load | | | 180 |
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