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

In summary, if you are looking for an easier alternative to Rudin's Principles of Mathematical Analysis chapters 8-12, some recommended books are Wendell Fleming's Functions of Several Variables and Hubbard and Spivak's The Unified Approach to Differential Calculus. These books cover topics such as analysis of functions of several variables, manifolds, and differential forms, making them useful for studying differential geometry and topology.
  • #1
bacte2013
398
47
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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  • #2
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.
 

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

1) What are alternative books to Rudin-PMA's chapters 8-12?

Some popular alternatives to Rudin-PMA's chapters 8-12 include "Real Analysis" by Royden and Fitzpatrick, "Principles of Mathematical Analysis" by Apostol, "Real Analysis" by Bartle and Sherbert, and "Introductory Real Analysis" by Kolmogorov and Fomin.

2) How do these alternative books differ from Rudin-PMA's chapters 8-12?

Each alternative book offers a unique perspective and approach to the material covered in Rudin-PMA's chapters 8-12. Some may have more thorough explanations, more examples and exercises, or a different organization of topics.

3) Are these alternative books suitable for self-study?

Yes, these alternative books are suitable for self-study as they provide clear explanations and a variety of practice problems for readers to work through on their own.

4) Are there any notable drawbacks to using alternative books instead of Rudin-PMA's chapters 8-12?

One potential drawback is that the alternative books may not cover all the same topics in the same depth as Rudin-PMA's chapters 8-12. It's important to carefully compare the table of contents and see if any important topics are missing.

5) Can these alternative books be used as a supplement to Rudin-PMA's chapters 8-12?

Yes, these alternative books can be used as a supplement to Rudin-PMA's chapters 8-12. They can provide additional explanations, examples, and practice problems to further enhance understanding of the material.

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