Well, this question may seem silly and I fear it's even out of topic here. My motivation to ask that is to know the correct terminology when talking about that here in Math.SE. The point is, here in Brazil the topics covered in Spivak's Calculus on Manifolds and Munkres Analysis on Manifolds is called "Analysis in $\Bbb R^n$", but it seems that in english people just call this "analysis on manifolds". I feel that there should be another name, because "manifolds" is much more general than $\Bbb R^n$.
So, how do people call in english the set of topics covered in those books? Analysis in $\Bbb R^n$, analysis on manifolds, multivariable analysis or what?
Thanks very much in advance!