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
MAT534	MOTION GEOMETRY II	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

The aim of this course is to give basic concepts and theorems of MOTION GEOMETRY II.

Name of Lecturer(s)

Doç.Dr.Murat BABAARSLAN

Learning Outcomes

1	Knows Lie groups
2	Knows Matrix Lie groups
3	Knows operators
4	Knows the concept of invariant
5	Knows the concept of 1-forms

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Lie Groups and differentials, group, topology, topological space, topological group, topological sub-groups, Lie groups, Lie sub-group, Lie algebra, Lie sub-algebra definitions. Matrix Lie groups and the roof beams: the parallel motion, and the group paralelism, group homomorphism, the core, the normal sub-group, parallel to the motion, exponential transform, theorems, parallelism, matrix Lie group G on the left of the group parallelism, theorems. Stars operator: Right and left-invariant vector fields, the theorems. Vector evaluation function, theorems, Transportation function. Adjoint transformation: Definition and theorems. Left-invariant p-forms, right-invariant p-forms: Definitions (1-form vector space of 1-forms, 0-form, p-form, left invariant 1-forms, and asset-uniqueness of the integral curve, parallel to the vector space, the identity transformation), theorems, Reduced- Euclidean metric, theorems. Real quaternions, algebra of real quaternions, basic operations on real quaternions, matrix representation, symplectic geometry, dual quaternions, basic operations on dual quaternions, line quaternion, complex number operator, quaternion operator, rotation operator, shear operator, screw operator, screw movement, combination of screw movements, Euler angles

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Lie Groups
2	Lie sub-roup
3	Lie algebra
4	Matrix Lie groups and the roof beams
5	Theorems
6	Matrix Lie group G on the left of the group paralelism
7	Stars operator
8	Mid-Term Exam
9	Transportation function.
10	Adjoint transformation: Definition and theorems
11	Left-invariant p-forms, right-invariant p-forms
12	Definitions (1-form vector space of 1-forms, 0-form, p-form, left invariant 1-forms, and asset-uniqueness of the integral curve, parallel to the vector space, the identity transformation)
13	Reduced- Euclidean metric
14	Theorems
15	Theorems
16	Final -Exam

Recommended or Required Reading

Hareket Geometrisi ve Kuaterniyonlar Teorisi Prof. Dr. H. Hilmi Hacısalihoğlu Eylül 1983 / 1. Baskı / 338 Syf.

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	80	80
Final Examination	1	70	70
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