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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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MATI7262Differential Geometry of Curves3+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
LecturerProf. Dr. Ömer PEKŞEN
Co-LecturerDoç.Dr. İdris ÖREN
Language of instruction
Professional practise ( internship ) None
 
The aim of the course:
The aim is to investigate the curves in the 2-dimensional Euclidean space by invariant theory and Frenet approach.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : Learn some information about curve2,4
PO - 2 : Get some information about local and global invariants of curves2,4
PO - 3 : Learn existence and uniqueness theorems of curves2,4
PO - 4 : Learn solution of equivalence problems of curves2,4
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
Vectors, vector functions of a real variable, concept of a curve, curvature and torsion, the fundamental existence and uniqueness theorem of curves in the two and three dimensional Euclidean space, the local invariants of curves and its applications,orthogonal transformations and Euclidean group, the global invariants of a path and a curve, the rigidity, existence and equivalence theorems of curves.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Vectors
 Week 2Vector functions of a real variable
 Week 3Concept of a curve
 Week 4Concept of curvature of a curve
 Week 5Concept of torsion of a curve
 Week 6The fundamental existence and uniqueness theorem of curves : Frenet approach
 Week 7The fundamental existence and uniqueness theorem of curves : Frenet approach
 Week 8The local invariants of curves and its applications
 Week 9Midterm
 Week 10Two and three dimensional Euclidean space and Euclidean motions group
 Week 11Global invariants of a path in the two dimensional Euclidean space
 Week 12Global invariants of a curve in the two dimensional Euclidean space
 Week 13Equivalence problem of the paths : Invariant theory approach
 Week 14Existence and uniqueness theorem of curves : Invariant theory approach
 Week 15Existence and uniqueness theorem of curves : Invariant theory approach
 Week 16Final exam
 
Textbook / Material
1Lipschutz, M.M. 1969; Theory and Problems of Differential Geometry, McGraw-Hill, New York
 
Recommended Reading
1Carmo, M. P. do, 1976; Differentil Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, New Jersey
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 08042020 2 25
In-term studies (second mid-term exam) 5 12032020 2 25
End-of-term exam 17 03062020 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 5 14 70
Arasınav için hazırlık 6 1 6
Arasınav 2 1 2
Kısa sınav 2 1 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Total work load134