Course Information

Course Name	Turkish	Diferansiyel Geometri
	English	Differantial Geometry
Course Code	MAT 342E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	6	3	-	-	-
Course Language		English
Course Coordinator		Fatma Özdemir
Course Objectives		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
Course Description		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, Dupin indicatrix, Meunier’s theorem, mean curvature, Gaussian curvature. Gauss’s Theorema Egregium, Mainardi-Codazzi and Weingarten equations. Asymptotic lines, geodesic lines. Euler’s, Ossian-Bonnet’s and Liouville’s formulas. The fundamental theorem of the theory of surfaces.
Course Outcomes		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 various curvatures of a surface ,the principal directions at a point and the normal and geodesic curvatures of a curve on a surface VI. calculate asymptotic lines, geodesic lines understand Euler’s, Ossian-Bonnet’s and Liouville’s formulas understand the fundamental theorem of the theory of surfaces
Pre-requisite(s)		MAT232 / MAT201 or MAT232E / MAT201E
Required Facilities
Other
Textbook		Differential Geometry Of Curves and Surfaces, Mafredo P. Do Carmo, Prentice-Hall
Other References		Geometry From a Differentiable Viewpoint, John McCleary Theory and Problems of Differential Geometry, Martin M. Lipschutz(Schaum's Outline Series)

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