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Looking for a good problem book for PROOF-BASED integration

  1. Dec 24, 2007 #1
    Looking for a good book for PROOF-BASED integration

    Just to be clear, I'm not looking for a book that helps you to exercise calculating integrals, but more like problems that involve doing proofs involving integrals. Theoretical and abstract integration problems like the ones in this thread:


    Any good recommendation for these types of integration problems?
    Last edited: Dec 24, 2007
  2. jcsd
  3. Dec 24, 2007 #2
    Integration is usually around chapter 6. If you suddenly got the interest in a deeper understanding of the integral the bad news is that it is difficult for most people to skip the first 75% of undergraduate analysis to get to the good part.
    But the good news is that if you have a good motivation for studying analysis, the chances are better that you can get through the book (to chapter 6) more quickly. You should at least spend a month on it (and that would be a minimum in the case you are very good at it!).

    As for a book, Baby Rudin is the one I read, so that is the one I recommend.
  4. Jan 4, 2008 #3
    I use 'Integral Calculus' by P. Shanti Narayan. It has lots of exercises with each exercise succeeded by Illustrated examples and proof of the identities used in subsequent excercise.
  5. Jan 15, 2008 #4
    Riemann integration is fairly trivial once you build the machinery. The only interesting questions (in chapter 6 of rudin, at least) are just frustrating since they're much easier with the Lebesgue integral.
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