Analysis on manifolds without analysis on $\mathbb{R}^n$ I wonder if there are any texts that treat analysis on manifolds as a separate topic requiring no knowledge of analysis on $\mathbb{R}^n$
One might say it's a bad idea but i don't see why it shouldn't be an existing alternative when we have the same with linear algebra and algebra nowadays. Math students study abstract theory first, special cases of which they learn when they need them.
Anyway, it is not a discussion of whether it's right or no. I'm only interested in whether such alternatives exist.

Try "Introduction to Differentiable Manifolds" by Serge Lang. 
