GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
DIFFERENTIAL GEOMETRY I/5431305
Course Title: DIFFERENTIAL GEOMETRY I
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Understands the concept of manifolds in all aspects and learns the differences between them
Understands the manifold types.
Learns the subtleties of the concept of tangent space, differentiation and directional derivative.
 -- MODE OF DELIVERY
  The mode of delivery of this course is face to face.
 --WEEKLY SCHEDULE
1. Week  Parametrized manifolds, embedded parametrizations,
2. Week  Curves, surfaces,
3. Week  The coordinate map of a chart, transition maps
4. Week  Abstract manifolds,
5. Week  Product manifolds,
6. Week  Smooth maps in Euclidean spaces,
7. Week  Smooth maps between abstract manifolds,
8. Week  countable atlas, Whitney’s theorem,
9. Week  The tangent space of a parametrized manifold
10. Week  The tangent space of a manifold in Rn
11. Week  The abstract tangent space,
12. Week  Directional derivative,
13. Week  The differential of a smooth map,
14. Week  The standard basis, orientation
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
20
 Assignment
4
15
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
2
15
 Percent of In-term Studies  
50
 Percentage of Final Exam to Total Score  
50
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
0
 Reading Tasks
0
 Searching in Internet and Library
6
15
90
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
20
20
 Final Exam and Preperation for Final Exam
1
30
30
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
182
 TOTAL WORKLOAD / 25: 
7.28
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1X
2X
3X
4X
5X
6X
7
8X
9X
10
11
12X
 -- NAME OF LECTURER(S)
   (Prof.Dr. AyseL VANLI)
 -- WEB SITE(S) OF LECTURER(S)
   (http://websitem.gazi.edu.tr/site/avanli)
 -- EMAIL(S) OF LECTURER(S)
   (avanli@gazi.edu.tr)