SDU Education Information System
   Home   |  Login Türkçe  | English   
 
   
 
 


 
Course Information
Course Unit Title : Differential Geometry I
Course Unit Code : MAT301
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 3
Semester : 5.Semester
Number of ECTS Credits Allocated : 7,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Manifolds, elementary calculations in Euclidean space, the curves and their properties.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Topological Manifolds: Basic concepts and some examples. Analaysis on manifolds, tangent spaces in the Euclidean spaces, directional derivative, cotangent spaces and 1-forms, Lie operators, the differential of a map, submanifolds, the theory of curves, definitions, change of parameters, Serret-Frenet theorems, the curvature and the torsion of a curve.
Languages of Instruction : Turkish-English
Course Goals : To introduce basic concepts of the manifold theory, and explain the general nature of differentiations on manifolds.
Course Aims : To introduce basic concepts of the manifold theory, and explain the general nature of differentiations on manifolds.
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 Topological Manifolds: Basic concepts and some examples
 
2 Topological Manifolds: Basic concepts and some examples
 
3 Analaysis on manifolds
 
4 Analaysis on manifolds
 
5 Tangent spaces in the Euclidean spaces, directional derivative
 
6 Tangent spaces in the Euclidean spaces, directional derivative
 
7 Cotangent spaces and 1-forms
 
8 Cotangent spaces and 1-forms
 
9 Lie operators, the differential of a map
 
10 Submanifolds
 
11 Submanifolds
 
12 The theory of curves, definitions, change of parameters
 
13 Serret-Frenet theorems,
 
14 The curvature and the torsion of a curve.