Prerequisite: Math 201
Text: Elementary Differential Geometry by Andrew Pressley.
Differential geometry studies geometries of various types by means of calculus. It is very helpful in understanding relativity, Hamiltonian and quantum mechanics. It is also useful in studies related to computer graphics. The course will concentrate on making you familiar with the language and computational aspects.
Curves in Euclidean space: Arc length, tangent normal and binormal vectors; curvature and torsion, Frenet formulae. Geometry of surfaces: the first and second fundamental form, geodesics, Gaussian and mean curvature; fundamental theorem of Gauss. Introduction to the non Euclidean geometries of the sphere and the unit disc.
Handouts and lecture notes: Here you will find handouts and other material supplementing the lectures. This is very important that you keep visiting (and refreshing) this link regularly as it would contain useful material to help your understanding of the lectures.
Solutions to home work: