C.T.J. DodsonGeneral description: Differential geometry begins with the study of curves and surfaces in three-dimensional Euclidean space. Using vector calculus and moving frames of reference on curves embedded in surfaces we can define quantities such as Gaussian curvature that allow us to distinguish among surfaces. The extension of the theory to higher dimensions leads to the study of n-manifolds, 1-manifolds being curves and 2-manifolds being surfaces. A distance structure was provided by Riemann and so we study Riemannian n-manifolds, their curvature and curves in them. We consider geodesic (literally, `divide the Earth') curves, which give extremal paths in n-manifolds, generalizing lines in the plane and great circles on a sphere.
Notes On Making Mathematical Notes For Your Course (PDF format).
description: Tangent vectors, vector fields, differentiable maps;
curves, Frenet frames; surfaces, shape operator, Gaussian and mean
curvature; n-manifolds, metric, Riemann curvature and geodesics.
See the online documents relating to this course: 351 Background Notes , Curves , Surfaces
Tutorial Problems 1 Tutorial Problems 2 Tutorial Problems 3 Tutorial Problems 4
Mathematica Notebooks on curves and surfaces from 117----To use, download and open in Mathematica
Problems: Plane Curves,