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Dersin Bilgileri

Dersin Adı
Türkçe Diferansiyel Geometry
İngilizce Differantial Geometry
Dersin Kodu
MAT 342E Kredi Ders
Dönem 6
3 3 - -
Dersin Dili İngilizce
Dersin Koordinatörü Füsun Zengin
Dersin Amaçları 1. To give the student essentials of curves and surfaces in 3-dimension,
2. To reinforce their advanced calculus and linear algebra knowledge and to give an ability to apply this knowledge on geometry problems
Dersin Tanımı Differential geometry of curves; osculating plane, curvature and torsion, Frenet?s trihedral, Frenet?s formulas, osculating sphere. Helices, involutes and evolutes, Bertrand?s curves. Natural equations, the fundamental theorem of the theory of curves. Differential geometry of surfaces; first and second fundamental forms of a surface, normal curvature, the lines of curvature, asymptotic curves, Dupin indicatrix, Meunier?s theorem, mean curvature, Gaussian curvature. Gauss?s Theorema Egregium.
Dersin Çıktıları Students completing this course will be able to :
I. understand the definition of the regular curve, vector field along the curve, know how to derive the formula for the length of a curve, and be able to operate with parametric and nonparametric forms of a curve, parameterize a curve by arc length,
II. know the definitions tangent, normal, binormal vectors, spherical curves, tangent line, normal line, binormal line and the definitions of tangent plane, osculating plane and rectifying plane,
III. calculate the Frenet quantities for a given smooth curve in R^3 calculate curvature and torsion understand what these quantities say about the general shape of a curve and how they characterize certain classes of simple curves
IV. be familiar with the following concepts: Helices, involutes and evolutes, Bertrand?s curves and the fundamental theorem of curves,
V. understand the concept of a surface and their classification, calculate the first and second fundamental forms and calculates the principal directions at a point
VI. calculates various curvatures and lines of curvature of a surface understand the concepts of Mean and Gauss curvatures of a surface.
Gereken Olanaklar
Ders Kitabı
Diğer Referanslar
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