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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
Katalog Ana Sayfa
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MAT7303Motion Geometry and Theory of Kuaternions3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 3 hours of lectures per week
LecturerDoç. Dr. Gül TUĞ
Co-LecturerProf. Dr. Djavvat Khadjiev
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The course aims to study spatial motions and line geometry base on D-Module and quaternions
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : be familiar with the notion of dual numbers and dual vectors. 2,41,3
PO - 2 : generalize dual vectors to dual quaternions 2,31,3
PO - 3 : understand the relation between spatial motions and line geometry and quaternions. 2,31,3
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

 
Contents of the Course
Dual numbers, Dual vectors, Real and Dual quaternions, Spatial motion
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Dual numbers and D-modul
 Week 2Dual numbers and D-modul
 Week 3Dual numbers and D-modul
 Week 4Geometry of lines
 Week 5Geometry of lines
 Week 6Geometry of lines
 Week 7Trajectory surfaces
 Week 8Mid-term exam
 Week 9Trajectory surfaces
 Week 10Real and Dual quaternions
 Week 11Real and Dual quaternions
 Week 12Real and Dual quaternions
 Week 13 Spatial motion
 Week 14Spatial motion
 Week 15Spatial motion
 Week 16End-of-term exam
 
Textbook / Material
1Hacısalihoğlu, H. H. 1983; Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Yayınları, No 30, Ankara
 
Recommended Reading
1Müller, H. R. 1963; Kinematik Dersleri, Ankara Üniversitesi Fen Fakültesi Yayınları, Ankara
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 8 30-MAR-10 2 30
In-term studies (second mid-term exam) 12 30-APR-10 2 10
Homework/Assignment/Term-paper 14 10-MAY-10 2 10
End-of-term exam 16 30-MAY-10 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 10 14 140
Arasınav için hazırlık 5 1 5
Arasınav 2 1 2
Ödev 2 1 2
Dönem sonu sınavı için hazırlık 7 1 7
Dönem sonu sınavı 2 1 2
Total work load200