I'm looking for a problem book in early math analysis, proof based, one single variable calculus problems, limit, continuity, derivative, integral, Taylor theorem, power series, convergence, divergence, elementary transcendental functions, least upper bounds, intermediate and extreme value theorems.

I find Kaczor problems in math analysis three volume, it seems cover same area that I'm looking for. however, this book has very few reviews, and I don't know if it's worthy to buy them.

Any advice?


1) The books are by Kaczor and Nowak.
2) The exercises are very difficult: I don't think there are many universities in the world where students learning analysis could tackle them unhelped.
3) They form one of the best collections of exercises ever.
Another contender for "best collection ever" is the famed two-volume work Problems and theorems in analysis by Pólya-Szegő.
That justly celebrated work contains, despite the title, much algebra and was at the research level, many exercises being extracted from papers published in prestigious journals.
Kaczor-Nowak is not so advanced.
4) Volume III covers integration and seems less relevant to what you want.
5) My advice: browse volume II. Buy it if you like it: it costs about 51 dollars in the US . Repeat the procedure for volume I and for volume III, in that order.

Some economists believe that the price of a Big Mac is a better indicator for purchasing power than currencies.
A Big Mac costs \$4.62 in the US and here is the price in other countries .
If you live in the US for example, you will have to decide if you want to sacrifice eleven Big Macs for volume II.

  • $\begingroup$ Thx for reply, I found that kaczor books seem lack of exercises in infinite series,sequence and uniform convergence and power series, Taylor theorem, Do you think where I can get good exercise book (proof based) in this area? $\endgroup$
    – ElleryL
    May 6 '14 at 18:28
  • $\begingroup$ And also I'm using spivak calculus 4th edition, do u think kaczor books is good complement exercise book? Or any else that you recommend? $\endgroup$
    – ElleryL
    May 6 '14 at 18:32
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    $\begingroup$ I wouldn't call the exercises "very difficult". They're challenging at best. Compare with Makarov's Selected problems in real analysis, you'll get a real taste of "very difficult". $\endgroup$ Jan 23 '17 at 7:09
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    $\begingroup$ @LeGrandDODOM I find your comment quite condescending. I consider these exercises very difficult and if you are so good at Analysis that you think the opposite (as your comment is meant to convey), why don't you tell us your name and your achievements in real life, like articles published in good research journals? $\endgroup$ Jan 23 '17 at 9:23
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    $\begingroup$ @GeorgesElencwajg you don't need to make this personal. Just have a look at the book I mentioned and see for yourself. $\endgroup$ Jan 23 '17 at 9:54

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