Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
DIFFERENTIAL GEOMETRY II MAT 304 6 3 + 1 4 7
Ön Koşul Dersleri Students are assumed to be familiar with Calculus, Analytic Geometry, Linear Algebra and Differential Geometry I
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü ZORUNLU Dersin Koordinatörü Prof.Dr. MEHMET ALİ GÜNGÖR Dersi Verenler Dersin Yardımcıları Research assistant related to geometry Dersin Kategorisi Dersin Amacı This courses aim is to giving the fundamental concepts of the differential geometry and getting students to comprehend curve and surface theory.. Dersin İçeriği Definition of surface, Shape operator of surface, Gauss map, Normal curvature of surface, Principal curvatures, mean curvature and Gaussian curvature, Hyperplane, Hypersphere, Hypercylinder, Hypersurfaces of revolution, Torus.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/ She defines surfaces and hypersurfaces, 1 - 2 - 3 - A - C - 2 - He/She calculates algebraic invariants of the surface, 2 - 3 - 4 - 15 - A - C - 3 - He/She designs and solves applied problems in discipline of differential geometry. 2 - 3 - 4 - 15 - A - C - 4 - He/She defines the hypersurfaces, 1 - 2 - 3 - A - C - 5 - He/She illustrates hypersurfaces, 3 - 4 - 6 - 15 - A - C - 6 - He/She calculates algebraic invariants of the hyperplane, 2 - 3 - 4 - 15 - A - C - 7 - He/She calculates algebraic invariants of the hypersphere, 2 - 3 - 4 - 15 - A - C - 8 - He/She calculates algebraic invariants of the hypercylinder, 2 - 3 - 4 - 15 - A - C - 9 - He/She calculates algebraic invariants of the Hypersurfaces of revolution 2 - 3 - 4 - 15 - A - C - 10 - He/She calculates invariants of the torus surface 2 - 3 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 15:Problem Solving 6:Motivations to Show Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Manifolds
2 Hypersurfaces, Geodesics on the hypersurfaces
3 Shape Operator and Gauss map
4 Fundamental Forms and algebraic invariants of the shape operator
5 Properties of the second fundamental form
6 Euler Theorem for the hypersurfaces and conclusions
7 Hyperplane and shape operator, umbilical points
8 Fundamental forms for the hyperplane
9 Midterm
10 Hypersphere
11 Fundamental forms for the hypersphere
12 Hypercylinder
13 Fundamental forms on the -cylinder
14 Hypersurfaces of revolution, Torus

#### Kaynaklar

Ders Notu 1. Hacısalihoğlu, H. H., Diferensiyel Geometri, Cilt II, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1994.
2. Hacısalihoğlu, H. H., Çözümlü Diferensiyel Geometri Problemleri, Cilt II, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1996
3. Hacısalihoğlu, H. H., Diferensiyel Geometri, Cilt I, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1998.
4. Hacısalihoğlu, H. H., Çözümlü Diferensiyel Geometri Problemleri, Cilt I, Ankara Üniversitesi, Fen Fakültesi Matematik Bölümü, 1995.
Ders Kaynakları 1. ONeill, B., Elementary Differential Geometry, Academic Press, New York, 1966.
2. Lipschutz, M. M., Theory and problems of Differential Geometry, Schaums Outline Series, McGraw-Hill, New York, 1969.

#### 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. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
KisaSinav 3 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 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 2 10 20
Assignment 1 10 10
Final examination 1 25 25
Toplam İş Yükü 187
Toplam İş Yükü /25(s) 7.48
Dersin AKTS Kredisi 7.48
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