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Course Information

Course Name
Turkish Yüzeyler Teorisi
English Theory of Surfaces
Course Code
MAT 417E Credit Lecture
Semester 7
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 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
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