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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
DIFERENTIAL GEOMETRY III MAT 451 7 2 + 0 2 5
Ön Koşul Dersleri Students are assumed to be familiar with Differential Geometry I and Differential Geometry II
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Lisans
Dersin Türü SECMELI
Dersin Koordinatörü Prof.Dr. MEHMET ALİ GÜNGÖR
Dersi Verenler
Dersin Yardımcıları Research assistants of geometry
Dersin Kategorisi
Dersin Amacı
The aim of this lesson is to give students the fundamental concepts concerning with differential geometry which they need during their undergraduate educations and to get them to comprehend a different way at the solution of the applied problems. To study integration theory for differential geometry of manifolds.
Dersin İçeriği
Riemannian manifolds and submanifolds, Connections, Integration and differential geometry.
Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - He/She defines the notions of Euclidean space on Riemanian manifolds, 1 - 2 - 3 - A - C -
2 - He/She compares affine connection with Riemannian connection, 1 - 2 - 3 - A - C -
3 - He/She interprets the known notions of hypersurfaces for any dimensional submanifolds, 1 - 2 - 3 - A - C -
4 - He/She defines and examines connections generally, 1 - 2 - 3 - A - C -
5 - He/She knows connections and Cartan structure equations, 1 - 2 - 3 - 4 - A - C -
6 - He/She remembers ordinary integrals of vectors, 1 - 2 - 3 - 4 - A - C -
7 - He/She defines line, surface and volume integrals, 1 - 2 - 3 - A - C -
8 - He/She explains and proves the Stokes Theorem. 1 - 2 - 3 - 4 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Distance and distance function Riemannian connection and curvature [1] Page1-5
2 Curves on Riemannian manifolds and the Frenet vectors and Frenet formulae of these curves [1] Page5-19
3 Submanifolds of Riemannian manifolds [1] Page19-21
4 Algebric invariants of generalized Weingarten map [1] Page21-34
5 (n-1)-dimensional submanifolds of n-dimensional Riemannian manifolds (Hypersurfaces) [1] Page34-42
6 Connections and its invariants [1] Page42-47
7 Torsion tensor of a connection, connection and Cartan equations [1] Page47-58
8 Difference tensor of two connection [1] Page58-69
9 Some appplications of exercises and Midterm
10 Integration on vectors, line integral, surface integral, volume integral [1] Page69-75
11 Fundamental notions for Integration theory [1] Page75-88
12 Integration on manifolds [1] Page143-150
13 Stokes Theorem on manifolds [1] Page150-156
14 Classical Stokes type theorems [1] Page156-174

Kaynaklar

Ders Notu [1] Hacısalihoğlu, H. H., Diferensiyel Geometri, Cilt III, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1994.
Ders Kaynakları [2] Hacısalihoğlu, H. H., Çözümlü Diferensiyel Geometri Problemleri, Cilt II, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1996.
[3] ONeill, B., Elementary Differential Geometry, Academic Press, New York, 1966.
[4] Lipschutz, M. M., Theory and problems of Differential Geometry, Schaums Outline Series, McGraw-Hill, New York, 1969.

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them.
8 He/ she uses the ability of abstract thinking. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
KisaSinav 2 10
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 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 10 10
Quiz 2 7 14
Assignment 1 8 8
Final examination 1 15 15
Toplam İş Yükü 111
Toplam İş Yükü /25(s) 4.44
Dersin AKTS Kredisi 4.44
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