| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Find the Frenet frame and curvatures of a regular parametric curve and interpret their meaning.
- Find and interpret the shape operator, the normal and
Gaussian curvatures of a surface.
- Understand at which direction, the geometric research
develop.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None. |
|---|
| Course Description | The course content includes the following topics: coordinate patches, surfaces in E3, differentiable functions on surfaces, tangent vectors, differential forms, surface transformations, integration on surfaces, topological properties of surfaces, manifolds, shape operators, normal curvature, gaussian curvature, special curves on surfaces, first and second principal forms. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Euclidean space and Cartesian coordinates |
|
2nd Week |
Parametric curves and arc length parameter |
|
3rd Week |
Serret-Frenet frame and curvatures |
|
4th Week |
Surfaces in Euclidean 3-space |
|
5th Week |
Differentiable functions on surfaces |
|
6th Week |
Tangent vectors |
|
7th Week |
Differential forms |
|
8th Week |
Midterm |
|
9th Week |
Surface transformations |
|
10th Week |
Shape operator |
|
11th Week |
Normal and Gaussian curves |
|
12th Week |
First and second fundamental forms |
|
13th Week |
Special curves on surfaces |
|
14th Week |
Special curves on surfaces |
|
15th Week |
General review |
|
| Recommended or Required Reading | Manfredo P. Do Carmo, Diferansiyel Geometri: Eğriler ve Yüzeyler, 2011, Tüba
Salim Yüce, Öklid Uzayında Diferansiyel Geometri, 2022, Pegem Akademi
|
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Other
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Total(%) |
|
40 |
| Contribution of In-term Studies to Overall Grade(%) |
|
40 |
| Contribution of Final Examination to Overall Grade(%) |
|
60 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
|
|
|
| Individual or group work |
13 |
3 |
39 |
| Preparation for Final exam |
1 |
23 |
23 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
15 |
15 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
