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MAT 417E
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Course Information
Course Name
Turkish
YÜZEYLER TEORİSİ
English
Theory of Surfaces
Course Code
MAT 417E
Credit
Lecture
(hour/week)
Recitation
(hour/week)
Laboratory
(hour/week)
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 3dimensional Euclidean space.
2. To introduce Gauss Egregium theorem and the structure equations of surfaces such as Gauss equations, MainardiCodazzi equations.
3.To introduce geodesics of surfaces, the GaussBonnet theorem and exponential map
Course Description
Surfaces in 3dimensional Euclidean space. First Fundamental Form. Mappings of surfaces. Geometry of the Gauss map. Ruled Surfaces. Minimal surfaces. Intrinsic properties. Theorema Egregium of Gauss. Geodesics. GaussBonnet 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 GaussBonet Theorem.
Prerequisite(s)
Required Facilities
Other
Textbook
M. do Carmo, Differential Geometry of Curves and Surfaces, PrenticeHall, 1976.
Other References
1.S. Lipschutz, Differential Geometry, Schaums Outline Series, McGrawHill.
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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