GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
Elective Course-3 (Differential Geometry)/MTÖ309
Course Title: Elective Course-3 (Differential Geometry)
Credits 2 ECTS 4
Course Semester 5 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
Explain the basic concepts of differential geometry.
Explain concepts of tangent space, directional derivative and vector area and prove theorems related to them.
Define the curve; calculate the arc length of the parametric curve for the given interval and find arc length function.
Recognize concepts of derivative of a vector area through curve, covariant derivative and Lie parenthesis operator, explain them, and make applications related to them.
Distinguish unit speed and non-unit speed curves; determine Frenet formulas, functions of curvature and torsion for these curves; explain geometric interpretations for the curvature and torsion functions.
Explain concepts of osculator, rectifian and normal plane and make applications related to them.
Identify curvature radius, curvative circle and curvative sphere of a curve at a Point , explain them, and make applications related to them.
Have general information about surfaces.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face.
 --WEEKLY SCHEDULE
1. Week  Limit, continuity and derivatives of single scalar variable functions
2. Week  Basic notions (scaler product, norm, determinant, vector product, limit, derivative)
3. Week  Tangent space, directional derivative
4. Week  Vector area
5. Week  Theory of curves
6. Week  Parametric and cartesian equations of space curves
7. Week  Parametric and cartesian equations of space curves
8. Week  Mid-term Exam
9. Week  Derivative of a vector area through curve and covariant derivative
10. Week  Lie parenthesis operator
11. Week  Frenet formulas, Curvature and tortion
12. Week  Osculator, rectifian and normal plane
13. Week  Curvature radius, curvative circle; curvative sphere
14. Week  General information on Surfaces
15. Week  Final Exam
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
40
 Assignment
0
0
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
2
28
 Weekly Tutorial Hours
0
 Reading Tasks
10
3
30
 Searching in Internet and Library
10
3
30
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
2
3
6
 Final Exam and Preperation for Final Exam
2
3
6
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
100
 TOTAL WORKLOAD / 25: 
4
 Course Credit (ECTS): 
4
 -- 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 problems
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technology
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.
 -- NAME OF LECTURER(S)
   (Related Instructor)
 -- WEB SITE(S) OF LECTURER(S)
   (.)
 -- EMAIL(S) OF LECTURER(S)
   (.)