| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Differential Geometry I | MAT303 | Turkish | Compulsory | 5. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Doç. Dr. GÜLHAN AYAR |
| Instructor(s) | |
| 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 |
| # | Öğrenme Kazanımı |
| 1 | Student’s ability of commenting and thinking truely will improve and the students will gain basic information associated with mathematic |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Euclidean Space | Class Hours |
| 2. Week | Differentiable Functions | Class Hours |
| 3. Week | Tangent Vectors | Class Hours |
| 4. Week | Vector Fields | Class Hours |
| 5. Week | Covariant Derivatives | Class Hours |
| 6. Week | Differential Forms | Class Hours |
| 7. Week | Curves | Class Hours |
| 8. Week | Mid-term Exam | Class Hours |
| 9. Week | Curves | Class Hours |
| 10. Week | Arc-Lenght Function | Class Hours |
| 11. Week | Frenet Formulas for Unit-Speed Curves | Class Hours |
| 12. Week | Frenet Formulas for unit-speed curve | Class Hours |
| 13. Week | Frenet Formulas for Non-Unit-Speed Curves | Class Hours |
| 14. Week | Frenet Formulas for any-speed curve | Class Hours |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Acquiring knowledge on theories and practice of education in general, subject teaching in particular, and the basic concepts and theories of the related disciplines, | ✔ | |||||
| 2 | Knowing how to obtain information geared towards lifelong learning, | ✔ | |||||
| 3 | Doing effective educational planning, organizing and evaluating based on theoretical and practical content matter and in relation to the needs of the learners, | ✔ | |||||
| 4 | Utilizing educational technologies in a variety of educational settings, | ✔ | |||||
| 5 | Analyzing studies in the field with a scientific perspective, assessing the findings and offering solutions, | ✔ | |||||
| 6 | Acquiring academic literacy and minimum B1 level competence at a foreign language in order to pursue the global developments in the area of study, | ✔ | |||||
| 7 | Pursuing the scientific discussions in the field and interpreting them through scientific examination, | ✔ | |||||
| 8 | Forming scientific study platforms in order to solve the problems in practice, | ✔ | |||||
| 9 | Preparing and conducting solution-based projects in response to social problems in an effort to contribute to the School-Society collaboration | ✔ | |||||
| 10 | Following the developments in the field through professional activities such as literature reviews, seminars, conferences and workshops, and sharing them with other expert and non-expert individuals, | ✔ | |||||
| 11 | Being an innovative and self-confident intellectual with a sense of society, environment, social justice and respect for ethical values. | ✔ | |||||
| 12 | To be able to analyse the notions and ideas in the field by using scientific methods, to identify problems, and to develop solutions based on proofs and researches | ✔ | |||||
| 13 | To be able to gain ability of doing academic research | ✔ | |||||
| 14 | To be able to work interactively | ✔ | |||||
| 15 | To be able gain necessary computer software for further studies | ||||||
| Program Requirements | DK1 |
|---|---|
| PY1 | 4 |
| PY2 | 5 |
| PY3 | 4 |
| PY4 | 4 |
| PY5 | 1 |
| PY6 | 1 |
| PY7 | 5 |
| PY8 | 5 |
| PY9 | 1 |
| PY10 | 5 |
| PY11 | 1 |
| PY12 | 4 |
| PY13 | 4 |
| PY14 | 2 |
| PY15 | 0 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Sınavlar |
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 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
