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

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SUMMARY

Alternative resources to Rudin's Principles of Mathematical Analysis Chapters 8-11 include Wendell Fleming's "Functions of Several Variables" and the combined works of Hubbard and Spivak. These texts provide a more accessible approach to the analysis of functions of several variables, manifolds, and differential forms. The discussion emphasizes the need for easier alternatives to Rudin's later chapters, which are perceived as less effective for foundational understanding.

PREREQUISITES
  • Understanding of basic calculus and real analysis concepts.
  • Familiarity with differential geometry and topology fundamentals.
  • Knowledge of functions of several variables.
  • Experience with mathematical proofs and rigorous reasoning.
NEXT STEPS
  • Explore Wendell Fleming's "Functions of Several Variables" for foundational concepts.
  • Study the combined texts of Hubbard and Spivak for a comprehensive understanding of differential forms.
  • Research differential geometry and topology to prepare for advanced studies.
  • Investigate additional resources that simplify complex mathematical theories.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on analysis, differential geometry, and topology, will benefit from this discussion. It is also valuable for anyone seeking alternative learning materials to Rudin's work.

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.
 

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