(35 lectures : 8+11+11+5)
Preliminaries: linear algebra and topology
Lecture 1 : What is a curve ? Arc-length
Lecture 2 : Reparametrization
Lecture 3 : Level curves vs. parametrized curves
Lecture 4 : Curvature I
Lecture 5 : Curvature II
Lecture 6 : Plane curves
Lecture 7 : Space curves I
Lecture 8 : Space curves II
Lecture 9 : What is a surface ?
Lecture 10 : Smooth surfaces. Smooth maps
Lecture 11 : Tangents and derivatives I
Lecture 12 : Tangents and derivatives II
Lecture 13 : Level surfaces. Quadric surfaces
Lecture 14 : Ruled surfaces and surfaces of revolution
Lecture 15 : Normals (and orientability). Compact surfaces
Lecture 16 : Length of curves on surfaces
Lecture 17 : Isometries of surfaces I
Lecture 18 : Isometries of surfaces II
Lecture 19 : Conformal mappings on surfaces
Lecture 20 : The second fundamental form
Lecture 21: The Gauss and Weingarten maps
Lecture 22 : Normal and geodesic curvatures
Lecture 23 : Parallel transport and covariant derivative I
Lecture 24 : Parallel transport and covariant derivative II
Lecture 25 : Gaussian and mean curvatures
Lecture 26 : Principal curvatures of a surface I
Lecture 27 : Principal curvatures of a surface II
Lecture 28 : Flat surfaces
Lecture 29 : Surfaces of constant mean curvature
Lecture 30 : Gaussian curvature of compact surfaces
Lecture 31 : Definition and basic properties
Lecture 32 : Geodesic equations I
Lecture 33 : Geodesics equations II
Lecture 34 : Geodesics on surfaces of revolution
Lecture 35 : Geodesic as shortest paths
Last Modified: Wed, 22 Jul 2015 11:13:23 SAST