Syllabus
A. INTRODUCTION
1. Motivation. The Euclidean space and its properties.
2. Differentiation in R^n. Tangent space, differential of a mapping. B. CURVES
3. Definition and basic properties. Curvature and torsion. The Frenet frame, Frenet formulae and its applications.
4. Curves in plane and space. C. SURFACES
5. Definition and basic properties. The first fundamental form.
6. Second fundamental form, Weingarten's mapping.
7. Curves on a surface, principal curvatures, Gauss and mean curvature.
8. Principal and asymptotic directions and curves, isometric surfaces.
9. Intrinsic geometry of a surface, geodetic curves.
10. Introduction to hyperbolic geometry.
Annotation
Lecture on Differential geometry for students of General Mathematics.
Surfaces in the three dimensional Euclidean space, the first and second fundamental forms, main curvatures of surface, Gauss and mean curvature, geodesics, geodesic curvature.