Information Package / Course Catalogue
Introduction to Differential Manifolds
Course Code: MAT437
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
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

Topological and differentiable manifold,differentiable maps between manifolds,tangent space of manifold,Riemannian manifold,Levi-civita connection,Submanifolds,Gauss and Weingarten map,second fundamental form

Name of Lecturer(s)
Learning Outcomes
1.To define topological manifold
2.To define differentiable manifold
3.Ability to write differentiable fnctions between manifolds
4.To define tangent space
5.To define Riemannian metric and Riemannian manifold
6.To define conection on manifold
7.To define submanifold
8.To write the equations Gauss and Weingarten map
9.To learn first and second fundamental form on the manifold
Recommended or Required Reading
1.Diferansiyel geometri (Differantial Geometry ), Prof. Dr. Arif Sabuncuoğlu
2.Barret O’Neill , Elementary Differantial Geometry
Weekly Detailed Course Contents
Week 1 - Theoretical
Topological manifolds
Week 2 - Theoretical
Differentiable manifolds
Week 3 - Theoretical
Problem solving
Week 4 - Theoretical
Tangent space of manifold
Week 5 - Theoretical
Riemannian manifold
Week 6 - Theoretical
Submanifolds
Week 7 - Theoretical
Levi-civita connection
Week 8 - Theoretical
Problem solving (Midterm Exam)
Week 9 - Theoretical
Ask and answer
Week 10 - Theoretical
Gauss and Weingarten equations
Week 11 - Theoretical
First and second fundamental form
Week 12 - Theoretical
Riemannian curvatre tensor
Week 13 - Theoretical
Sectional curvature
Week 14 - Theoretical
Ricci and scalar curvature
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Assignment1%5
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141242
Lecture - Practice141242
Assignment1055
Individual Work140228
Midterm Examination112214
Final Examination117219
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
5
5
5
5
5
OÇ-2
5
5
5
5
5
5
OÇ-3
5
5
5
5
5
5
OÇ-4
5
5
5
5
5
5
OÇ-5
5
5
5
5
5
5
OÇ-6
5
5
5
5
5
5
OÇ-7
5
5
5
5
5
5
OÇ-8
5
5
5
5
5
5
OÇ-9
5
5
5
5
5
5
Adnan Menderes University - Information Package / Course Catalogue
2026