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	2	3	-	-	-
Course Language		English
Course Coordinator		Aybike Özer
Course Objectives		1. To give students essentials of curves and surfaces in three dimensional Euclidean space. 2. To reinforce students’ multivariable calculus and linear algebra knowledge and to give them the ability to apply this knowledge on geometry problems.
Course Description		Differential Geometry of Curves: Parametrizations of regular curves in R^3 space, curvature, torsion, Frenet trihedral, Frenet-Serret equations. Spherical curves. Special curve families; helices, involutes and evolutes, Bertrand’s curves. Fundamental theorems of the theory of curves. Some applications of symbolic computation. Differential Geometry of Surfaces: Regular surfaces. The tanget plane. First fundamental form of a surface, Local geometry of Gauss map. Second fundamental form and shape operator. Normal curvature, principal curvatures and principal directions, Gausssian curvature, mean curvature. The lines of curvature, asymptotic curves, Dupin indicatrix, Meunier’s theorem. Special surface families. Some applications of symbolic computation. Theorema Egregium of Gauss.
Course Outcomes		a
Pre-requisite(s)		MAT232E MIN DD and MAT116E MIN DD
Required Facilities
Other
Textbook		Differential Geometry of Curves and Surfaces, Mafredo P. De Carmo, Prentice-Hall, 1976. Modern differential geometry of curves and surfaces with Mathematica, Alfred Gray, Elsa Abbena, and Simon Salamon, 2006.
Other References		Geometry From a Differentiable Viewpoint, John McCleary, 1997. Theory and Problems of Differential Geometry, Martin M. Lipschutz (Schaum’s Outline Series).

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