Differential Geometry (MAT 314)




Linear algebra, Advanced calculus.  (Some exposure to geometry would be advantageous.)


Roughly speaking, differential geometry is concerned with understanding shapes and their properties in terms of (differential and integral) calculus. Differential geometry is a subject with a long and wonderful history, but also a subject which has found new relevance in many areas ranging from machinery design to gravitation and cosmology to the study of DNA.

An elementary course on differential geometry provides a perfect transition to higher mathematics and its applications. It is a subject which allows students to see mathematics for what it is - a unified whole mixing together geometry, calculus, linear algebra, differential equations, complex variables, calculus of variations and topology.


Curves (in the plane and in the space),  curvature,  surfaces, the first fundamental form, isometries, the second fundamental form, the normal and principal curvatures, the Gaussian and mean curvatures, the Gauss map, geodesics.


"Elementary Differential Geometry"(2E) by A. Pressley (Springer-Verlag, 2010).


ONE tutorial per week.


TWO class tests and ONE final examination.

Last Modified: Fri, 24 Jul 2015 12:31:10 SAST