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

Course Objectives 
1. To provide students with basic knowledges on regular surface 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 
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 GaussBonet theorem and exponential map. 
Prerequisite(s) 
None 
Required Facilities 

Other 

Textbook 

Other References 
