GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
DIFFERENTIAL GEOMETRY/MAT305A
Course Title: DIFFERENTIAL GEOMETRY
Credits 3 ECTS 7
Semester 5 Compulsory/Elective Compulsory
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Prof. Dr. Hasan Hüseyin UĞURLU
 -- WEB SITE(S) OF LECTURER(S)
  w3.gazi.edu.tr/~hugurlu
 -- EMAIL(S) OF LECTURER(S)
  hugurlu@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
Students know the Frenet frame of curves, Frenet derivative formulas, planes related to this frame, circles and spheres.
Students identify some special curves.
Students learn surface concept, normal vector and the tangent plane.
Students know ruled surfaces and their properties.





 -- 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
  Mat 203A and Mat 204A lessons
 --COURSE CONTENT
1. Week  Introduction to the theory of curves
2. Week  Arclenght parameter curves and parameter transformation
3. Week  The curvature function, radius of curvature and curvature circle of a curve
4. Week  Torsion function, geometric representation and applications
5. Week  Osculator, rectified and normal planes at any point of a curve
6. Week  Contact theory, sphere of curvature and axis of curvature
7. Week  Midterm
8. Week  Frenet formulas for curves with arbitrary parameters
9. Week  Geometrical representations of curves and applications,
10. Week  The Helix curve and spherical curves
11. Week  Bertrand curves, involute and evolute curves
12. Week  Introduction to differential surfaces
13. Week  Parameter curves, normal vector and tangent plane on surfaces
14. Week  Forms of linear surfaces and examples
15. Week  
16. Week  
 -- RECOMMENDED OR REQUIRED READING
  M. P. Do Carmo Differential Geometry of Curvers and Surfaces, Prentice-Hall, New-Jersey, 1976. B. O’Neill Differential Geometry, Academic Pres, New
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  -
 -- 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
2
28
 Practising Hours of Course Per Week
14
2
28
 Reading
0
 Searching in Internet and Library
12
2
24
 Designing and Applying Materials
12
2
24
 Preparing Reports
0
 Preparing Presentation
12
3
36
 Presentation
0
 Mid-Term and Studying for Mid-Term
0
 Final and Studying for Final
12
2
24
 Other
0
 TOTAL WORKLOAD: 
164
 TOTAL WORKLOAD / 25: 
6.56
 ECTS: 
7
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1Acquisition of scientific thinking skillsX
2Making research and investigation independentlyX
3Acquisition of carefully observing and analytically thinking skillsX
4Acquisition of learning and teaching mathematics problemsX
5Comprehending, applying and explaining the importance of mathematical conceptsX
6Developing the thinking, producing, argumenting and probing abilitiesX
7Having the algorithm and sotftware writing abilities for solving computer supported problemsX
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technologyX
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.X