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I'm currently doing a course in Elementary Analysis (Intro to real analysis). My course focuses on the topics: sequences, limits of functions, continuity, uniform continuity and derivative/derivability of functions, all in R. I've studied on my own with the book "Elementary Analysis, the theory of calculus", which has proved to be an extremely useful book for someone with zero previous knowledge in analysis or calculus.

My question is whether anybody knows of any good books that have exercises in them, my textbook (mentioned above), has some exercises, but not a lot, and the vast majority of the exercises do not have solutions. I'm looking for a book that focuses mostly on proving, rather than strictly calculating limits and derivatives, all though preferably a book that does both.

Thanks in advance

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  • $\begingroup$ See Spivak's Calculus (which, as prefaces to later editions comment, would almost be better titled Introduction to Analysis). It has many exercises. $\endgroup$
    – Simon S
    Oct 17, 2015 at 18:58
  • $\begingroup$ Have you tried a Google search? Maybe "problem book analysis." It gives a list, you can use Google books for a preview. $\endgroup$
    – smokeypeat
    Jul 9, 2017 at 7:52

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Abbott's Understanding Analysis has good exercises, but no solutions. All exercises are proof-based.

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    $\begingroup$ I was going to recommend this book. It is a good introduction. $\endgroup$
    – abnry
    Jan 16, 2014 at 2:35
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  1. Advanced Calculus: G.B. Folland
  2. Principles of Mathematical analysis: W. Rudin
  3. Mathematical Analysis: An Introduction: A. Browder.

More extensive problem books:

Problems in Mathematical analysis by Kaczor and Nowak.

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A pretty one is "Elementary Classical Analysis" of Jerrold E. Marsden and Michael J. Hoffman

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