Information Package / Course Catalogue
Differential Geometry I
Course Code: MAT328
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The fundamental knowledges that are needed during students undergraduate and graduate education on differential geometry are taught.

Course Content

Euclidean space, topological and differential manifolds, vector fields, directional derivative, covariant derivative, curves , Frenet vector fields.

Name of Lecturer(s)
Lec. Dilek AÇIKGÖZ KAYA
Learning Outcomes
1.Defines basics of differential geometry
2.Compares affine and Euclidean spaces
3.Defines topological manifolds
4.Defines differential manifolds
5.Compares directional derivative with the one defined in the analysis course
6.Applies the concepts of gradient, divergent and rotational functions(taught in the analysis courses) to general spaces
7.Defines the curves
8.Calculates the Frenet frame of a curve
Recommended or Required Reading
1.Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi, Prof. Dr. Cumali Ekici
2.Elementary Differential Geometry, Barret O’Neill
3.Diferansiyel Geometri(Differential Geometry), Prof Dr. Arif Sabuncuoğlu
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Affine space and Euclidean Space
Week 2 - Theoretical & Practice
Topological manifold
Week 3 - Theoretical & Practice
Diffeomorphism
Week 4 - Theoretical & Practice
Differentiable manifolds
Week 5 - Theoretical & Practice
Tangent vectors and tangent space
Week 6 - Theoretical & Practice
Vector fields
Week 7 - Theoretical & Practice
Dimension of the tangent space
Week 8 - Theoretical & Practice
Directional derivative and covariant derivative (Midterm Exam)
Week 9 - Theoretical & Practice
Integral curves
Week 10 - Theoretical & Practice
Lie operator
Week 11 - Theoretical & Practice
Gradient, divergent, rotational function
Week 12 - Theoretical & Practice
Parametrizations of the surfaces
Week 13 - Theoretical & Practice
Curves and change of parametrization
Week 14 - Theoretical & Practice
Serret-Frenet vectors
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Reading142142
Individual Work140228
Midterm Examination1729
Final Examination113215
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
PÇ-16
PÇ-17
PÇ-18
OÇ-1
5
3
5
5
3
5
5
OÇ-2
5
3
5
5
3
5
5
OÇ-3
5
3
5
5
3
5
5
OÇ-4
5
3
5
5
3
5
5
OÇ-5
5
3
5
5
3
5
5
OÇ-6
5
3
5
5
3
5
5
OÇ-7
5
3
5
5
3
5
5
OÇ-8
5
3
5
5
3
5
5
Adnan Menderes University - Information Package / Course Catalogue
2026