Prerequisite: MAA202
The course “Topics in Differential Geometry”
introduces basic and important
objects which are widely used in mathematics
and physics: vector fields and differential
forms.
Firstly, we propose a geometric point of
view on differential equations using the
langage of vector fields, their integral
curves and their flows. Secondly, we
define differential forms and the exterior
differentiation of such forms.
Many formulas used in physics (Gauss-
Green-Riemann-Ostrogradski-Stokes)
are naturally expressed and unified in
those terms and will illustrate the course.