Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MOTION GEOMETRY I MAT 530 0 3 + 0 3 6
 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 Dual number systems and dual number rings , D-module, inner product and norm on D-module, E. Study mappings and dual angle , Dual isometries on D-module , Real quaternion algebra, matrix representation of real quaternions , Dual quaternion, Line quaternion , Screw operators and screw motions,lines geometry.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She defines the basic concepts of dual numbers ring, 1 - 2 - 3 - 8 - 15 - A - C - 2 - He/She proves and interprets the theorems related to dual numbers ring, 1 - 2 - 3 - 8 - 15 - A - C - 3 - He/She compares systems of dual numbers with systems of real and complex numbers, 1 - 2 - 3 - 8 - 15 - A - C - 4 - He/She defines the basic concepts of D-Modul, 1 - 2 - 3 - 8 - 15 - A - C - 5 - He/She proves and interprets the theorems related to D-Modul, 1 - 2 - 3 - 8 - 15 - A - C - 6 - He/She defines dual variable functions similar to complex variable functions, 1 - 2 - 3 - 8 - 15 - A - C - 7 - He/She defines the basic concepts of real quaternions, 1 - 2 - 3 - 8 - 15 - A - C - 8 - He/She compares real quaternions with systems of real numbers, 1 - 2 - 3 - 8 - 15 - A - C - 9 - He/She defines the basic concepts of dual quaternion, 1 - 2 - 3 - 8 - 15 - A - C - 10 - He/She compares real quaternions with dual quaternion, 1 - 2 - 3 - 8 - 15 - A - C - 11 - He/She defines and formulates quaternion operator and other operator similar to complex number operator, 1 - 2 - 3 - 8 - 15 - A - C - 12 - He/She calculates algebraic invariants of ruled surfaces in lines geometry. 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 Dual number systems and dual number rings
2 Matrix representations of dual numbers and dual vector spaces,
3 D-module, inner product and norm on D-module,
4 E. Study mappings and dual angle
5 Exterior product, mixed product on D-module and the concept of bases in dual vector,
6 Dual isometries on D-module
7 Taylor series of dual valuable functions and dual integral
8 Real quaternion algebra and matrix representation of real quaternions
9 Midterm
10 Symplectic geometry, dual quaternion, fundamental process on dual quaternion
11 Line quaternion, Quaternion operators, rotation and translation operators, Screw operators
12 Lines geometry
13 Ruled surfaces
14 Dual acceleration, canonical system.

#### 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 Student follows the current journals in his/her field and puts forward problems. X
2 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 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
7 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
8 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
9 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
10 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
11 Student follows the current journals in his/her field and puts forward problems. X
12 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
13 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
14 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
15 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
16 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
17 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
18 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
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 10 10
Final examination 1 25 25
Toplam İş Yükü 151
Toplam İş Yükü /25(s) 6.04
Dersin AKTS Kredisi 6.04
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