Information Package / Course Catalogue
Differential Geometry of Curves and Surfaces I
Course Code: MTK526
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The purpose of this course is to learn some theories and applications of differential geometry and also the main theories of the differential geometry of curves and surfaces with using the basic concepts and the techniques of differential geometry.

Course Content

Basic Concepts, Differential Geometry of Curves, Theory of Curves, Geometric Meaning of Curves, Some Partner Curves and Their Properties.

Name of Lecturer(s)
Learning Outcomes
1.Ability to discuss about the basic concepts of Differential Geometry.
2.Ability to understand other Geometries and their concepts.
3.Ability to learn the concepts Topological Manifold, Differentiable Manifold.
4.Ability to learn the theories of curves.
5.Ability to do some applications with curves.
Recommended or Required Reading
1.Ekici, C., Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi
2.Montiel S., Ros A., Curves and Surfaces
3.O’Neil, B., Elementary Differential Geometry
4.Hacısalihoğlu, H. H., Diferensiyel Geometri, Cilt I-II-III
Weekly Detailed Course Contents
Week 1 - Theoretical
Basic Concepts
Week 2 - Theoretical
Some Other Geometries
Week 3 - Theoretical
Topological Manifold and Differetiable Manifold
Week 4 - Theoretical
Theory of Curves, Curves and their Parameters
Week 5 - Theoretical
Serret-Frenet Vectors
Week 6 - Theoretical
The Oscillator Hyperplanes of a Curve
Week 7 - Theoretical
Curvatures and Their Geometric Meanings
Week 8 - Theoretical
The Oscillator Spheres (MIDTERM EXAM)
Week 9 - Theoretical
Some Frame Structures- Bishop Curves
Week 10 - Theoretical
q-Frame Along a Space Curve
Week 11 - Theoretical
Some Partner Curves
Week 12 - Theoretical
Parallel Partner Curves
Week 13 - Theoretical
Involute and Evolute Curves
Week 14 - Theoretical
Bertrand Curves
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Quiz1%10
Midterm Examination1%15
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141356
Assignment1066
Individual Work140228
Quiz110111
Midterm Examination120222
Final Examination125227
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
2
3
4
2
2
2
2
2
OÇ-2
3
4
4
3
4
4
3
3
4
3
4
OÇ-3
3
3
4
4
3
3
3
OÇ-4
4
4
3
3
4
4
4
3
4
OÇ-5
4
4
4
4
3
4
4
4
3
2
2
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026