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Course Information
Course Unit Title : Differential Geometry II
Course Unit Code : MAT302
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 3
Semester : 6.Semester
Number of ECTS Credits Allocated : 7,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Recognition of hypersurfaces and manifolds, elementary calculations in hypersurfaces.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Manifolds: Riemann manifolds, hypersurfaces, geometry of hypersurfaces: Normal vector field, orientation, geodesics, shape operator, Gauss map and equation, fundamental forms, Euler theorem, Dupin indicatrix, Olinde-Rodrigues formulas.
Languages of Instruction : Turkish-English
Course Goals : Aim of this course is to present the basic items of manifolds and especially hypersurfaces, and to give some fundamental theorems with respect to theirs.
Course Aims : Aim of this course is to present the basic items of manifolds and especially hypersurfaces, and to give some fundamental theorems with respect to theirs.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook :
Additional Resources : 1) Hacısalihoğlu, H. H., Diferensiyel Geometri, 2000.
2) O?Neill, B., Elementary Differential Geometry, Academic Press, 1965.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
15 5 75  
Time Of Studying Out Of Class :
15 5 75  
Homeworks :
4 10 40  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 10 10  
Finals :
1 10 10  
Workload Hour (30) :
30  
Total Work Charge / Hour :
210  
Course's ECTS Credit :
7      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
0 0
Quiz :
0 0
Homework :
0 0
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
0
The ratio of the term to success :
0
The ratio of final to success :
0
TOTAL :
0
Weekly Detailed Course Content
Week Topics  
1 Manifolds: Riemann manifolds
 
2 Manifolds: Riemann manifolds
 
3 Manifolds: Riemann manifolds
 
4 Hypersurfaces, geometry of hypersurfaces
 
5 Hypersurfaces, geometry of hypersurfaces
 
6 Hypersurfaces, geometry of hypersurfaces
 
7 Normal vector field, orientation
 
8 Normal vector field, orientation
 
9 Geodesics, shape operator
 
10 Gauss map and equation
 
11 Fundamental forms
 
12 Euler theorem
 
13 Dupin indicatrix
 
14 Olinde-Rodrigues formulas