| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential Geometry II | MAT322 | 6. Semester | 2 + 2 | 3.0 | 6.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Assoc. Prof. Dr. Fatih HEZENCİ |
| Instructors |
Fatih HEZENCİ |
| Assistants | |
| Goals | To explain the detailed information about the surfaces by giving the definition of the surface and the basic theorems in the surface theory. |
| Course Content | Concept of Surface, Parameter Curves on Surface, Tangent Space of Surface, Derivative by Direction on Surface, Vector Area on Surface, Lie Product of Vector Areas on Euclidean Space , Riemann Curvature Tensor, Isometry, Concept of Manifold, Uniform Manifolds, Curves in Manifold, Differential Forms, Connection Forms, Structure Equations |
| Learning Outcomes |
- Student’s ability of commenting and thinking truely will improve and the students will gain basic information associated with mathematic |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Concept of Surface | Course Hours |
| 2. Week | Parameter Curves on Surface | Course Hours |
| 3. Week | Tangent Space of Surface | Course Hours |
| 4. Week | Derivative by Direction on Surface | Course Hours |
| 5. Week | Vector Area on Surface | Course Hours |
| 6. Week | Lie Product of Vector Areas on Euclidean Space | Course Hours |
| 7. Week | Riemann Curvature Tensor | Course Hours |
| 8. Week | Midterm | Course Hours |
| 9. Week | Isometry | Course Hours |
| 10. Week | Concept of Manifold, Uniform Manifolds | Course Hours |
| 11. Week | Curves in Manifold | Course Hours |
| 12. Week | Differential Forms | Course Hours |
| 13. Week | Connection Forms | Course Hours |
| 14. Week | Yapı Denklemleri | Course Hours |
| 3.Arif Sabuncuoğlu, Diferensiyel Geometri, Nobel yayınları, 2001 |
| 1.Barret O’Neill, Elementary Differential Geometry, Academıc Pres Inc.1966 |
| 2.H.Hilmi Hacısalihoğlu, Diferensiyel Geometri,İnönü Üniversitesi, 1983 |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 4 | 4 | 60 |
| PY2 | 5 | 5 | 60 |
| PY3 | 4 | 4 | 60 |
| PY4 | 4 | 4 | 60 |
| PY5 | 1 | 1 | 60 |
| PY6 | 1 | 1 | 60 |
| PY7 | 5 | 5 | 60 |
| PY8 | 5 | 5 | 60 |
| PY9 | 1 | 1 | 60 |
| PY10 | 5 | 5 | 60 |
| PY11 | 1 | 1 | 60 |
| PY12 | 5 | 5 | 60 |
| PY13 | 2 | 2 | 60 |
| PY14 | 2 | 2 | 60 |
| PY15 | 1 | 1 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 4 | 56 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 1 | 14 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 14 | 2 | 28 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 158 | ||
| ECTS Credit of the Course | 6.0 | ||
