Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT-23-103	DIFFERENTIABLE MANIFOLDS-I	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

The aim of this course is to teach the students the manifolds, the construction of the tangent bundle of the manifold, the concept of the Riemannian manifold, the Riemannian submanifolds and the investigation of the geometric structures reduced on these manifolds.

Name of Lecturer(s)

Dr. Öğr. Üyesi Lokman BİLEN

Learning Outcomes

1	At the end of this course, students will be able to produce solutions to the problems they may encounter.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

It is need to know the basic facts of Mathematical Analysis, Linear Algebra

Recommended Optional Programme Components

Course Contents

Tensor Manifolds Vector bundles Affine connections on manifolds Integration on manifolds Distributions Riemann Metric Curvature Differentiable operators Integration on Riemannian manifolds Reduced connection and the second basic form of submanifold

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Tensor
2	Manifolds
3	Vector bundles
4	Affine connections on manifolds
5	Integration on manifolds
6	Distributions
7	Applications
8	Midterm
9	Riemann Metric
10	Curvature
11	Differentiable operators
12	Riemann manifoldları üzerinde integrasyon
13	Reduced connection and the second basic form of submanifold
14	Applications
15	final exam

Recommended or Required Reading

Lecture Notes

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		50
End Of Term (or Year) Learning Activities		50
SUM		100

Language of Instruction

Turkish

Work Placement(s)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1	1
Final Examination	1	2	2
Attending Lectures	14	3	42
Question-Answer	14	3	42
Individual Study for Mid term Examination	1	50	50
Individual Study for Final Examination	1	50	50
TOTAL WORKLOAD (hours)			187

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO1	5	5	5	5	5	5	5	5	5	5	5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High