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Course Information

Course Name
English Theory of Surfaces
Course Code
MAT 417E Credit Lecture
Semester 1
3 3 - -
Course Language English
Course Coordinator Elif Canfes
Course Objectives 1.To provide students with basic knowledges on regular surfaces 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 parametrizations compute the Gauss curvature and mean curvature ,ruled and minimal surfaces,
II. understand and use the concepts of isometric and conformal maps,
III. calculate the Gauss curvature by using Gauss’s Theorema Egregium,
IV. decide whether a curve on a surface is a geodesic,
V. understand the idea underlying the proof of the Gauss-Bonet Theorem.
Required Facilities
Textbook M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.
Other References 1.S. Lipschutz, Differential Geometry, Schaums Outline Series, McGraw-Hill.
2.A. Gray, E. Abbena and S. Salamon Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman & Hall/CRC
3.M. Spivak, Differential Geometry, Vols. II & III.
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