Yozgat Bozok 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
MAT525	ELEMANTARY DIFFERANTIAL GEOMETRY I	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

The aim of this course is to give basic concepts and theorems of ELEMENTARY DIFFERENTIAL GEOMETRY I.

Name of Lecturer(s)

Doç. Dr. Murat BABAARSLAN

Learning Outcomes

1	Knowing the concepts of affine space and Euclidean space
2	Knows the concept of a topological manifold
3	Interpreting Tangent and cotangent vector and the concepts of space
4	Knows Lie bracket operator
5	Dominate the tensor and tensor spaces

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Affine spaces and affine transformations, topological manifolds, differentiable manifolds, Euclidean spaces, tangent spaces and tangent vectors, 1-forms, Lie operator, Gradient, Divergence and Rotational functions, transformations, the coordinate functions.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Affine Spaces
2	Euclidean Spaces
3	Topological Manifolds
4	Differentiable Manifolds
5	Tangent Vectors and Tangent Spaces
6	Covariant Derivative
7	Lie Bracket Operation
8	MID-TERM EXAM
9	Cotangent Vectors and Cotangent Spaces
10	1-forms
11	Gradient and Divergent Functions
12	Differential of a Map
13	Submanifolds
14	Tensors and Tensor Spaces, Exterior Product
15	Tensors and Tensor Spaces, Exterior Product
16	FINAL EXAM

Recommended or Required Reading

Prof. Dr. H. H. Hacısalihoğlu, Diferensiyel Geometri, İnönü Üniversitesi Fen Ed. Fak. Yayınları Mat. No 2 1983. B. O'Neill, Semi Riemannian Geometry-With Applications to Relativity, New York, Academic Press Inc. (1983). M. Berger and B. Gostiaux, Differential geometry: Manifolds, Curves and Surfaces, Springer-Verlag New York 1987. M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall (1976).

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		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	70	70
Final Examination	1	80	80
Makeup Examination	1	40	40
TOTAL WORKLOAD (hours)			190

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

LO4

LO5

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