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	3	-	-
Course Language		English
Course Coordinator		Fatma Özdemir
Course Objectives		Differential geometry of curves; osculating plane, curvature and torsion, Frenet curves in the Euclid space E^n and Frenet formulae, Curves in S^2 nd S^3, Curves with constant Frenet curvatures. Natural equations, the fundamental theorem of theory of 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.
Course Description		1. To give the student essentials of curves and surfaces in Euclid spaces, 2. To reinforce their advanced calculus and linear algebra knowledge and to give an ability to apply this knowledge on geometry problems
Course Outcomes		Students completing this course will be able to : I.Determine several geometrical properties of regular curves, II.Determine tangent, normal and binormal vector fields and compute curvature(s) and spherical cuvature(s) of a given curve, III.Obtain Frenet frame of a given Frenet curve in arbitrary dimensional Euclid space, IV.Comprehend basic theorems in theory of curves and surfaces V.Determine geometrical properties of given families of curves, VI.Understand the concept of a surface and their classification, calculate the first and second fundamental forms and calculates the principal directions at a point VII.Calculates various curvatures and lines of curvature of a surface understand the concepts of curvatures of a surface.
Pre-requisite(s)		MAT232 MIN DD /MAT232E MIN DD /MAT201 MIN DD /MAT201E MIN DD
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