Courses

Curves in the plane and in space, tangent of a normal (smooth) curve, arc length - physical parameter, Frenet's accompanying trihedron, curvature and torsion, first, generalized helices, fundamental theorem of curves, total theory of curves, the isoperimetric inequality, regular surfaces, construction of surfaces via the entangled function theorem, tangent plane, first and second fundamental form, surface area, Gaussian map, shape operator (Weingarten map), perpendicular curvature, principal curvatures, Euler's formula, Gaussian curvature, mean curvature, the Wonderful Theorem (Theorema Egregium). Information: Renaming of the Course "Differential Geometry" in the Academic Year 2015-16.