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I'm looking for a textbook (or website etc.) which contains challenging problems in calculus. Problem in Real Analysis by Titu Andreescu is good, but slightly too advanced for me. Spivak's Calculus is very good, but I need more. Can anyone give me any references?

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    $\begingroup$ Related: math.stackexchange.com/questions/9958/… $\endgroup$ – Jesse Madnick Nov 4 '11 at 9:52
  • $\begingroup$ In this question the poster also asked about challenging exercises in calculus. $\endgroup$ – Martin Sleziak Nov 4 '11 at 14:54
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    $\begingroup$ Spivak's text must have more than 1000 problems, most of which are indeed challenging. You say you like these problems but "need more". Could you explain why you need more than 1000 problems? $\endgroup$ – Pete L. Clark Nov 4 '11 at 17:13
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There is a problem book:

  • Problems in Calculus of One Variable by I.A. Maron

You can always see the entrance question papers of the IIT - JEE exam. They do contain challenging calculus problems.

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The Harvard-MIT Math Tournaments always feature some interesting calculus problems. Both problems and solutions from previous contests are archived.

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If you haven't already considered it (it's a well-known classic), I suggest looking at

Introduction to Calculus and Analysis by Richard Courant and Fritz John.

http://www.amazon.com/dp/354065058X

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I'll be dating myself with this answer, but I always found the miscellaneous problems at the end of some of the chapters of Thomas (3rd) to be a good source of challenges. I'd also consider looking in Apostol's Calculus.

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The Art of Problem Solving has textbooks for middle school through calculus. The description for the calculus book includes:

The book includes hundreds of problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the Putnam Competition and the Harvard-MIT Math Tournament. Many of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual.

It's relatively inexpensive and you can get a full solutions manual, which is also relatively inexpensive. This is a full textbook for single variable calculus.

http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus

The point of these Art of Problem Solving books is that you learn problem solving and not just the basic rules/techniques.

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I also suggest the AOPS Calculus book. The problems are challenging, but they often have hints you can choose to look up, and clear solutions in a separate book. Very informative. My Calc professor had us buy it instead of a regular college textbook, and it's been much more challenging, but much more rewarding, too.

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