Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | FMA646 | RIEMANNIAN SURFACES II | Compulsory | 1 | 1 | 6 |
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Level of Course Unit |
Second Cycle |
Objectives of the Course |
Objectives of Course is learning Riemannian Spaces. |
Name of Lecturer(s) |
Yrd. Doç. dr Seher ASLANCI |
Learning Outcomes |
1 | Knows the definition of Manifolds | 2 | Learns the Characteristics of Riemannian Manifolds | 3 | Knows the Torsion -Free Riemannian Spaces |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Differential Manifolds, Connection, Affine Connection, Covariant Derivative, Curvature and Torsion, Torsion -Free Spaces, Riemannian Manifolds, Riemannian Spaces with Constant Curvature. |
Weekly Detailed Course Contents |
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1 | Differential Manifolds | | | 2 | Lineer Connection on Manifold | | | 3 | Absolute Differential | | | 4 | Manifold with Affine Connection | | | 5 | Covariant Derivative | | | 6 | Curvature and Torsion | | | 7 | Torsion -Free Spaces | | | 8 | Midterm Exam | | | 9 | Equal-Affine Connection | | | 10 | Metric Spaces | | | 11 | Weyl Spaces | | | 12 | Riemannian Manifolds | | | 13 | Riemannian Connections | | | 14 | Curvature tensors on Riemannian Spaces | | | 15 | Riemannian Spaces with Constant Curvature | | | 16 | Final Exam | | |
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Recommended or Required Reading |
1.Salimov, A. Ve Magden, A.,( 2008) Diferensiyel Geometri. Aktif Yayınevi. Erzurum
2.Kühnel, W.( 2005) Differential Geometry. American Mathematical Society, 380, USA |
Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
SUM | 0 | |
SUM | 0 | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | SUM | 100 |
| Language of Instruction | Turkish | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Attending Lectures | 14 | 3 | 42 |
Problem Solving | 14 | 1 | 14 |
Self Study | 14 | 6 | 84 |
Individual Study for Homework Problems | 7 | 3 | 21 |
Individual Study for Mid term Examination | 1 | 10 | 10 |
Individual Study for Final Examination | 1 | 20 | 20 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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