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I have background in calculus, linear algebra, single variable analysis, topology, ode and some abstract algebra.

So I've decided to study multivariable analysis before/alongside Lee's smooth manifolds. But since I have had trouble with Rudin and Spivak, I have done some research to find different textbook.

After some researching, I have narrowed down to 3 books: Zorich, Hubbard, and Callahan's book. However, I have some question regarding Callahan's book.

Is the book rigorous enough to be used in a multivariable analysis course or should it be used as a supplement instead of main textbook?

Thanks in advance.

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  • $\begingroup$ Also, if you think there are better alternatives, feel free to suggest. $\endgroup$
    – Mark Noel
    Commented Mar 30, 2022 at 15:18
  • $\begingroup$ same boat here. self-study as well. Ideally need a book that has solution easy to access. Many options but not sure which one to pick. $\endgroup$
    – Roy Huang
    Commented Aug 22, 2022 at 6:33

1 Answer 1

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My favorite book on Advanced Calculus is:

Angus E. Taylor and W. Robert Mann: Advanced Calculus

(John Wiley & Sons, third edition, 1983)

ISBN-13: 978-0471025665

ISBN-10: 0471025666

It is a well-written book and I refer to this book often..

https://www.amazon.com/Advanced-Calculus-Angus-Taylor/dp/0471025666

[Advanced Calculus - Taylor & Mann 1

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  • $\begingroup$ Thank you for your suggestion I will definitely check it out. $\endgroup$
    – Mark Noel
    Commented Mar 30, 2022 at 15:40

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