Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MOTION GEOMETRY MAT 531 0 3 + 0 3 6
Ön Koşul Dersleri Students are assumed to be Transformations and Geometries.
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. MEHMET ALİ GÜNGÖR Dersi Verenler Dersin Yardımcıları Research assistants of geometry Dersin Kategorisi Dersin Amacı The fundamental knowledge that are needed during students undergraduate and graduate education on motion geometry are taught. Furthermore, some different ways to solve the problems that they would come across on the subject are given. Dersin İçeriği Line-geometry, ruled surfaces, trajectory surfaces, one-parameter motions in line-space and ID- module, acceleration axes in Spatial motions, E. Study transformation of a circle.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She defines and calculates algebraic invariants of ruled surfaces in lines geometry. 1 - 2 - 3 - 8 - 15 - A - C - 2 - He/She constructs frame of trajectory surface, 1 - 2 - 3 - 8 - 15 - A - C - 3 - He/She defines 1-parameter dual spherical motion, 1 - 2 - 3 - 8 - 15 - A - C - 4 - He/She calculates algebraic invariants of 1-parameter dual spherical motion, 1 - 2 - 3 - 8 - 15 - A - C - 5 - He/She constructs Canonical Relative System of dual spherical motions. 1 - 2 - 3 - 8 - 15 - A - C - 6 - He/She generalizations Holditch and Steiner theorems for 1-parameter dual spherical motions, 1 - 2 - 3 - 8 - 15 - A - C - 7 - He/She defines closed ruled surfaces, 1 - 2 - 3 - 8 - 15 - A - C - 8 - He/She calculates velocities and acceleration in spatial motion, 1 - 2 - 3 - 8 - 15 - A - C - 9 - He/She formulates Bresse and inflection congruences of spatial motion. 1 - 2 - 3 - 8 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 8:Group Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Line-geometry
2 Ruled surfaces
3 Elements of trajectory and Pol tangent of a dual point
4 Principal Normal of the pol of a dual point and Using of Canonic Relative System
5 One-parameter motions in line-space and ID- module
6 Unit dual spherical motion and ruled surface theory
7 Generalizations of the Holditch theorem
8 Generalizations of the Steiner theorem
9 Midterm
10 The pitch of a closed ruled surface
11 Accelerations axes in spatial kinematics
12 Accelerations axes in spatial kinematics
13 Bresse and inflection congruences
14 Study map of a circle

#### Kaynaklar

Ders Notu [1] Hacısalihoğlu, H.H., Hareket geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi yayınlar Mat. No.2,1983.
Ders Kaynakları [2] Hacısalihoğlu, H. H., Yüksek Boyutlu Uzaylarda Dönüşümler ve Geometriler, İnönü Üniversitesi, Temel Bilimler Fakültesi Yayınları, Mat. No.1, 1980.
[3] Hacısalihoğlu, H.H., Dönüşümler ve Geometriler, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,1998.
[4] Müller H. R., Kinematik dersleri, Ankara Üniv. Fen-fakültesi yayınları, Ankara
[5] Blaschke W., Zur Bewegungsgeometrie auf. Der kugel, S. B. Heildelberger. Wiss. Math. Nat. KI. No.2(1948)

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student follows the current journals in his/her field and puts forward problems. X
4 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
5 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
6 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
7 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
8 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
9 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
10 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
11 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
12 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
13 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
14 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
15 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
16 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
17 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
18 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
19 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
20 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 1 15 15
Final examination 1 25 25
Toplam İş Yükü 156
Toplam İş Yükü /25(s) 6.24
Dersin AKTS Kredisi 6.24
; ;