Information Package / Course Catalogue
Introduction to Motion Geometry
Course Code: MAT331
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 purpose of this course is to give fundamental informations about dual numbers and quaternions along to undergraduate and master period student needs.

Course Content

Dual numbers, dual vector spaces, dual module, real quaternions, dual quaternions, rotation, translation and skew operators

Name of Lecturer(s)
Lec. Dilek AÇIKGÖZ KAYA
Learning Outcomes
1.To be able to learn dual number system and its properties.
2.To be able to learn basic concepts on D-module.
3.To be able to define basis concept about real quaternions.
4.To be able to define basis concept about dual quaternions.
5.To be able to examine motion geometry with the help of dual quaternions.
Recommended or Required Reading
1.Motion Geometry and Quaternions Theory, Prof. Dr. H. Hilmi Hacısalihoğlu
2.Numbers and Geometry, Salim Yüce
3.Hareket Geometrisine Giriş, Cumali Ekici, H. Hilmi Hacısalihoğlu
Weekly Detailed Course Contents
Week 1 - Theoretical
Introduction of the course and reflection, translation and rotation motion
Week 2 - Theoretical
Transformations and Systems of dual numbers
Week 3 - Theoretical
Systems of dual numbers
Week 4 - Theoretical
Matrix representation of dual numbers, dual matrix and dual determinant
Week 5 - Theoretical
D-module, inner product and norm definition on D-module
Week 6 - Theoretical
E.Study mapping and dual angle
Week 7 - Theoretical
E.Study mapping and dual angle
Week 8 - Theoretical
Problem solving (Midterm exam )
Week 9 - Theoretical
Exterior derivative, scalar triple product and basis concept on dual vectors
Week 10 - Theoretical
Dual isometries on D-module
Week 11 - Theoretical
Real quaternions algebra and matrix representation of real quaternions
Week 12 - Theoretical
Dual quaternions and basic operations on dual quaternions
Week 13 - Theoretical
Dual quaternions and basic operations on dual quaternions
Week 14 - Theoretical
Line quaternions
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work140456
Midterm Examination120222
Final Examination128230
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
3
3
4
3
OÇ-2
3
3
3
3
OÇ-3
3
3
5
3
OÇ-4
3
3
3
3
OÇ-5
3
3
3
3
Adnan Menderes University - Information Package / Course Catalogue
2026