GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
DIFFERENTIAL GEOMETRY II/MAT3006
Course Title: DIFFERENTIAL GEOMETRY II
Credits 4 ECTS 6
Semester 6 Compulsory/Elective Compulsory
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Assoc.Prof. Mustafa ÖZKAN
 -- WEB SITE(S) OF LECTURER(S)
  http://www.websitem.gazi.edu.tr/site/ozkanm
 -- EMAIL(S) OF LECTURER(S)
  ozkanm@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
He/she defines the concept of surface, exemplifies surface.
He/she defines the parameter curves of the surface.
He/she defines the tangent space of the surface.
He/she defines the shape operator of surface.
He/she understands the normal curvature, makes its applications.
He/she defines the concepts of Gaussian curvature, mean curvature, principal vectors, linear and umbilical point, basic forms.
He/she defines Gauss transformation,the knows the geometric meaning.
He/she understands the integral over the surface and Dupin indicatrix.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  There is no recommended optional programme component for this course.
 --COURSE CONTENT
1. Week  Surfaces
2. Week  Parameter curves of the surface, tangent space of the surface
3. Week  Differentiable functions, directional derivatives
4. Week  Vector fields, covariant derivatives
5. Week  Orientation, shape operator
6. Week  Normal curvature
7. Week  Gaussian curvature, mean curvature, principal vectors, linear and umbilical point, fundamental forms
8. Week  Midterm exam
9. Week  Gauss transformation, metric on the surface
10. Week  Integral on the surface , Dupin indicatrix
11. Week  Principal curve, asymptotic curve,geodesical curve
12. Week  Induced connection on the surface, the induced connection and geodesics
13. Week  Roundabouts, parallel and ruled surfaces
14. Week  Lie multiplication, the Riemann curvature tensor, sectional curvature
15. Week  Congruence surfaces
16. Week  Final exam
 -- RECOMMENDED OR REQUIRED READING
  Sabuncuoğlu, Arif. Diferensiyel Geometri, Nobel Yayınları, Ankara, 2001. Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri, Ankara Üniversitesi Fen Fakü
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
   Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  Not Applicable
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
0
0
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
3
42
 Practising Hours of Course Per Week
14
2
28
 Reading
10
1
10
 Searching in Internet and Library
5
1
5
 Designing and Applying Materials
5
2
10
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
6
2
12
 Final and Studying for Final
8
2
16
 Other
7
3
21
 TOTAL WORKLOAD: 
144
 TOTAL WORKLOAD / 25: 
5.76
 ECTS: 
6
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To train individuals who are equipped with enough mathematicsX
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing,X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial,X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods,X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information,X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector,X
9To gain substructure to be able to study at graduate level.X
10The skill to have professional and ethical responsibilityX