| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MAT526 | ELEMANTARY DIFFERANTIAL GEOMETRY II | Elective | 1 | 1 | 6 |
|
| Level of Course Unit |
| Second Cycle |
| Objectives of the Course |
| The aim of this course is to give the basic definitions and theorems of ELEMENTARY DIFFERENTIAL GEOMETRY II. |
| Name of Lecturer(s) |
| Doç. Dr. Murat BABAARSLAN |
| Learning Outcomes |
| 1 | Dominate the theory of curves | | 2 | Find Serret-Frenet vectors | | 3 | Know Osculator hyperplanes | | 4 | Dominate the theory of surfaces | | 5 | Know concepts of Bertrand curves |
|
| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| The theory of curves, special curves, parameter change, regular curves, Serret-Frenet vectors, the normal rectification and osculator planes, curvatures and their geometric meaning, spherical curves, a pair of Bertrand curve. |
| Weekly Detailed Course Contents |
|
| 1 | The theory of curves | | | | 2 | Special curves, parameter change, regular curves | | | | 3 | Special curves, parameter change, regular curves | | | | 4 | Special curves, parameter change, regular curves | | | | 5 | Serret-Frenet vectors | | | | 6 | Serret-Frenet vectors | | | | 7 | The normal rectification and osculator planes | | | | 8 | MID-TERM EXAM | | | | 9 | The normal rectification and osculator planes | | | | 10 | Curvatures and their geometric meaning | | | | 11 | Curvatures and their geometric meaning | | | | 12 | Curvatures and their geometric meaning | | | | 13 | Spherical curves | | | | 14 | Spherical curves | | | | 15 | A pair of Bertrand curve | | | | 16 | FINAL EXAM | | |
|
| Recommended or Required Reading |
| Prof. Dr. H. H. Hacısalihoğlu, Diferensiyel Geometri, İnönü Üniversitesi Fen Ed. Fak. Yayınları Mat. No 2 1983.
B. O'Neill, Semi Riemannian Geometry-With Applications to Relativity, New York, Academic Press Inc. (1983).
M. Berger and B. Gostiaux, Differential geometry: Manifolds, Curves and Surfaces, Springer-Verlag New York 1987.
M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall (1976). |
| Planned Learning Activities and Teaching Methods |
|
| Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | | Work Placement(s) | | None |
|
| Workload Calculation |
|
| Midterm Examination | 1 | 80 | 80 |
| Final Examination | 1 | 70 | 70 |
| Makeup Examination | 1 | 40 | 40 |
|
| Contribution of Learning Outcomes to Programme Outcomes |
|
| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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| Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |