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FACULTY of SCIENCE / DEPARTMENT of MATHEMATICS

Course Catalog
http://www.ktu.edu.tr/matematik
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FACULTY of SCIENCE / DEPARTMENT of MATHEMATICS /
Katalog Ana Sayfa
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MAT3011DIFFERENTIAL GEOMETRY4+0+0ECTS:7
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Ömer PEKŞEN
Co-LecturerProf. Dr. Yasemin SAĞIROĞLU
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
Aim of the course is to introduce some of the main ideas of differential geometry of curves and surfaces in 3-dimensional space, to reinforce their advanced calculus and linear algebra knowledge giving a good opportunity to exhibit their interplay through application to geometry
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : familiar with the main ideas of differential geometry of curves and surfaces. 5,71,
LO - 2 : apply Frenet Formulas to find invariants of curves 5,71,
LO - 3 : use shape operator to evaluate curvatures of a surface 5,71,
LO - 4 : have a good opportunity to use their advance calculus and linear algebra knowledge to explore geometry 5,71,
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), LO : Learning Outcome

 
Contents of the Course
Euclidean Space; Tangent Vectors and Vector Fields in 3-dimensional Space, Directional Derivatives; Curves in 3-dimensional Space; 1-Forms; Differential Forms; Mappings Between Euclidean spaces; Dot Product; Curves; The Frenet Formulas; Arbitrary-Speed Curves; Covariant Derivatives; Frame Fields; Connection Forms; Surfaces3-dimensional Space; Patch Computations; Differentiable Functions and Tangent Vectors; The Shape Operator; Normal Curvature; Gaussian Curvature; Computational Techniques; Special Curves in a Surface; Surfaces of Revolution.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Euclidean Space
 Week 2Tangent Vectors, Directional Derivatives
 Week 3Curves in 3-dimensional space, 1-Forms
 Week 4Differential Forms, Mappings
 Week 5Dot Product, Curves
 Week 6The Frenet Formulas, Arbitrary-Speed Curves
 Week 7Covariant Derivatives, Frame Fields
 Week 8Connection Forms
 Week 9Mid-term exam
 Week 10Surfaces in 3-dimensional Space, Patch Computations
 Week 11Differentiable Functions and Tangent Vectors, The Shape Operator
 Week 12Normal Curvature, Gaussian Curvature
 Week 13Computational Techniques
 Week 14Special Curves in a Surface, Surfaces of Revolution
 Week 15Completion
 Week 16End-of-term exam
 
Textbook / Material
1O'Neill, B. 1966; Elementary Differential Geometry, Academic Press, New York and London
 
Recommended Reading
1Gray, A. 1999; Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press
2Hacısalihoğlu, H.H. 1983; Diferansiyel Geometri, İnönü Üniversitesi, Fen-Ed. Fakültesi Yayınları, No:2,
3Lipschutz, M.M. 1969; Theory and Problems of Differential Geometry, Schaum's Outline Series, McGraw-Hill Book Company.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 29/11/2023 2 30
Quiz 5
13		 01/11-27/12/2023 1 20
End-of-term exam 16 12/01/2022 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 4 14 56
Sınıf dışı çalışma 6 14 84
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 6 1 6
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 0 0 0
Proje 0 0 0
Kısa sınav 1 2 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 2 4
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load164