steps:
- 1-variable calculus
  analytic
- multi-variable calculus R^n -> R^m
  matrices; understanding a bit the geometry of paths and functionals
- generalizations:
  + measure spaces for domains
  + top.vect.spaces for targets
  + ...also -manifolds- as bases
    ...and more generally, calc on manifolds
    (which can and should be motivated by concrete issues like
    Gauss-Bonnet)
