Course Information

Course Name	Turkish	Diferansiyel Geometri
	English	Differantial Geometry
Course Code	MAT 342E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	2	3	3	-	-
Course Language		English
Course Coordinator		Elif Canfes
Course Objectives		1. To give the student essentials of curves and surfaces in 3-dimension, 2. To reinforce their advanced calculus and linear algebra knowledge and to give an ability to apply this knowledge on geometry problems
Course Description		Differential geometry of curves; osculating plane, curvature and torsion, Frenet’s trihedral, Frenet’s formulas, osculating sphere. Helices, involutes and evolutes, Bertrand’s curves. Natural equations, the fundamental theorem of the theory of curves. Differential geometry of surfaces; first and second fundamental forms of a surface, normal curvature, the lines of curvature, Dupin indicatrix, Meunier’s theorem, mean curvature, Gaussian curvature. Gauss’s Theorema Egregium, Mainardi-Codazzi and Weingarten equations. Asymptotic lines, geodesic lines. Euler’s, Ossian-Bonnet’s and Liouville’s formulas. The fundamental theorem of the theory of surfaces.
Course Outcomes
Pre-requisite(s)
Required Facilities
Other
Textbook		Differential Geometry Of Curves and Surfaces---Mafredo P. Do Carmo ,Prentice-Hall.
Other References