| TYPE OF COURSE UNIT | Elective Course |
| LEVEL OF COURSE UNIT | Bachelor's Degree |
| YEAR OF STUDY | - |
| SEMESTER | - |
| NUMBER OF ECTS CREDITS ALLOCATED | 4 |
| NAME OF LECTURER(S) | -
|
| LEARNING OUTCOMES OF THE COURSE UNIT |
At the end of this course, the students;
1) find the Frenet frame and curvatures of a regular parametric curve and interpret their meaning.
2) find and interpret the shape operator, the normal and
Gaussian curvatures of a surface
3) understand at which direction, the geometric research
develop
|
| MODE OF DELIVERY | Face to face |
| PRE-REQUISITES OF THE COURSE | No |
| RECOMMENDED OPTIONAL PROGRAMME COMPONENT | None. |
| COURSE DEFINITION | 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 fiunctions on Surfaces | | 6th Week | Tangent Vectors | | 7th Week | Differential Forms | | 8th Week | Midterm Exam | | 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 | General Review |
|
| RECOMENDED OR REQUIRED READING | 1) Manfredo P. Do Carmo, Diferansiyel Geometri: Eğriler ve Yüzeyler, 2011, Tüba
2) 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 WORKLOAD |
| Activities |
Number |
Hours |
Workload |
| Midterm exam | 1 | 2 | 2 | | Preparation for Quiz | | | | | Individual or group work | 13 | 3 | 39 | | Preparation for Final exam | 1 | 14 | 14 | | Course hours | 13 | 3 | 39 | | Preparation for Midterm exam | 1 | 10 | 10 | | Laboratory (including preparation) | | | | | Final exam | 1 | 2 | 2 | | Homework | | | | | Total Workload | | | 106 |
|---|
| Total Workload / 30 | | | 3,53 |
|---|
| ECTS Credits of the Course | | | 4 |
|---|
|
| LANGUAGE OF INSTRUCTION | Turkish |
| WORK PLACEMENT(S) | No |
| | |
