Alternative Books to Rudin-PMA's Chp. 8-12

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bacte2013
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Hello!

What books are excellent choice to reaplace Rudin-PMA's Chapters 8-12? I am specifically interested in the easier books than Rudin that treat the analysis of functions of several variables, manifolds, and differential forms; my next goal is to study the differential geometry/topology.

I heard Rudin's later chapters are not good as first seven chapters.
 
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I don't think you're talking about the same book I interpreted you to be. I thought you were referring to Rudin's Principles of Mathematical Analysis, but the most recent edition of that book doesn't have a chapter 12.

However, assuming that you meant Rudin's Principles of Mathematical Analysis chapters 8-11, my current favorite text on those topics is Wendell Fleming's Functions of Several Variables.