MAT 342E  Differantial Geometry
Course Objectives
1. To give the student essentials of curves and surfaces in 3dimension,
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, MainardiCodazzi and Weingarten equations. Asymptotic lines, geodesic lines. Euler’s, OssianBonnet’s and Liouville’s formulas. The fundamental theorem of the theory of surfaces.


Course Coordinator
Fatma Özdemir
Course Language
English


