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

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