Course Information

Course Name	Turkish	Yüzeyler Teorisi
	English	Theory of Surfaces
Course Code	MAT 417E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Fatma Özdemir
Course Objectives		1. To provide students with basic knowledges on regular surface and the concepts of differential geometry of surfaces in 3-dimensional Euclidean space; 2. To introduce Gauss egregium theorem and the structure equations of surfaces such as Gauss equations, Mainardi-Codazzi equations. 3. To introduce geodesics of surfaces, the Gauss-Bonnet theorem and exponential map.
Course Description		Surfaces in 3-dimensional Euclidean space. First Fundamental Form. Mappings of surfaces. Geometry of the Gauss map. Ruled Surfaces. Minimal surfaces. Intrinsic properties. Theorema Egregium of Gauss. Geodesics. Gauss-Bonnet Theorem. Exponential map.
Course Outcomes		Students completing this course will be able to : I. understand how to describe surfaces in terms of parametric and level set descriptions;change between these descriptions locally for simple surfaces II. compute the Gauss curvature and mean curvature , III. understand minimal and ruled surfaces and decide whether a given surface is minimal IV. understand and use the concepts of isometric and conformal maps, V. calculate the Gauss curvature by using Gauss’s Theorema Egregium VI. decide whether a curve on a surface is a geodesic VII. understand the idea underlying the proof of the Gauss-Bonet theorem.
Pre-requisite(s)
Required Facilities
Other
Textbook		M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall.
Other References		A. Gray, E. Abbena and S. Salamon Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman & Hall/CRC M. Spivak, Differential Geometry, Vols. II & III

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