Visualize some geometric shapes of three-dimensional space in the mind. Examine the properties of curves in three-dimensional Euclidien space by means of differential and integral calculus.
-C.E.Weathherburn; çev. Asuman Ilgaz, 3 Boyutlu Diferansiyel Geometri, 1984.
Dirk J.Struik, Lectures on Classical Differential Geometry, Addison-Wesley Pub.Co., 2nd ed.1961.Ferruh Şemin, Diferansiyel Geometri I, Eğriler, İstanbul Üniversitesi, 1983.
Manfredo P.do Carmo, Differential Geometry of Curves and Surface, Prentice-Hall,1976.
Martin M. Lipschutz, Differential Geometry, Schaum’s Outline Series, McGraw-Hill,1969.
Mustafa Şenatalar, Diferansiyel Geometri ( Eğriler ve Yüzeyler Teorisi), 1978.
Theodore Shifrin, Differential Geometry, A First Course in Curves and Surfaces, (2010)
Course Schedules
Week
Contents
Learning Methods
1. Week
Vector Functions of a Real Variable.
Oral and written presentation
2. Week
Concept of a Curve.
Oral and written presentation
3. Week
Regular Representations, Regular Curves.
Oral and written presentation
4. Week
Implicit representations of Curves.
Oral and written presentation
5. Week
Arc Length.
Oral and written presentation
6. Week
Unit Tangent Vector, Tangent Line and Normal Plane.
Oral and written presentation
7. Week
Principal Normal Vector, Principal Normal Line and Osculating Plane, Curvature.
Oral and written presentation
8. Week
Religious Holiday.
9. Week
Midterm Examination.
Written
10. Week
Binormal, Binormal Line and Rectifying Plane, Torsion.
Oral and written presentation
11. Week
Spherical Indicatrices, Frenet Equations.
Oral and written presentation
12. Week
Intrinsic Equations.
Oral and written presentation
13. Week
The Fundamental Existence and Uniqueness Theorem.
Oral and written presentation
14. Week
Involutes, Evolutes.
Oral and written presentation
15. Week
Final Examinations.
Written
16. Week
Final Examinations.
Written
17. Week
Final Examinations.
Written
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
45
Quizzes
2
0
Homework / Term Projects / Presentations
3
0
Attendance
21
5
Final Exam
1
50
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Know the basic concepts such as limits, continuity, differentiability of vector functions of a variable.
LO-2
Know the parametric equations of some special curves.
LO-3
Know the concept of regular curves, and determine whether an arc in parametric equations is rectifiable, and find the natural representations of curves.
LO-4
Know the concepts of curvature and torsion, and interpret these information.
LO-5
Find the moving trihedron of a given regular curve.
LO-6
Find the frenet equations, the intrinsic equations of a given curve.
LO-7
Prove The Fundamental Existence and Uniqueness Theorem, and determine the plane curves by using its intrinsic equations.
LO-8
Find the equation of Involute and Evolute of a given curve.
