S.E advisers,
I have been hearing that the chapters on multi-varaible analysis in Rudin's PMA are almost nothing like previous insightful chapters in the single-variable analysis, and I verified myself too (very difficult to read). I would like to receive your suggestions on alternative books to learn the analysis in R^n, manifolds, and differential forms. Do I need to read a book in differential geometry/topology?
Unfortunately, I forgot most of concepts from the multivariable calculus...
Zorich, "Mathematical Analysis". Intuitive explanations, physical connections; in short, a ``human touch'' of a caring teacher.