| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential Geometry I | MAT321 | 5. 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 give students basic concepts of differantial geometry. |
| Course Content | Euclidean Space, Differentiable Functions, Tangent Vectors, Vector Fields, Covariant Derivatives, Differential Forms, Curves, Arc-Lenght Function, Frenet Formulas for Unit-Speed Curves, Frenet Formulas for Non-Unit-Speed Curves |
| 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 | Euclidean Space | |
| 2. Week | Differentiable Functions | |
| 3. Week | Tangent Vectors | |
| 4. Week | Vector Fields | |
| 5. Week | Covariant Derivatives | |
| 6. Week | Differential Forms | |
| 7. Week | Curves | |
| 8. Week | Mid-term Exam | |
| 9. Week | Curves | |
| 10. Week | Arc-Lenght Function | |
| 11. Week | Frenet Formulas for Unit-Speed Curves | |
| 12. Week | Frenet Formulas for unit-speed curve | |
| 13. Week | Frenet Formulas for Non-Unit-Speed Curves | |
| 14. Week | Frenet Formulas for any-speed curve |
| 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 | 4 | 4 | 60 |
| PY13 | 4 | 4 | 60 |
| PY14 | 2 | 2 | 60 |
| PY15 | 0 | 0 | 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 | 2 | 28 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 14 | 1 | 14 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 158 | ||
| ECTS Credit of the Course | 6.0 | ||
