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	7	3	3	-	-
Course Language		English
Course Coordinator		Fatma Özdemir 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		At the end of the course students will be able to : I.To define and parametrize surfaces. II.To calculate the Gauss curvature and mean curvature III. To know the ruled surfaces and minimal surfaces. IV. To learn the isometric and conforml maps. V. To calculate the Gauss curvature by knowing the first fundamental form via theTeorema Egregium of Gauss. VI. To find the geodesics of surfaces. VII. To learn the Gauss-Bonet theorem and exponential map.
Pre-requisite(s)		None
Required Facilities
Other
Textbook		M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall.
Other References		S. Lipschutz, Differential Geometry, Schaums Outline Series, McGraw-Hill. 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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