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I'm looking for a calculus book that (1) is comprehensive and rigorous enough for Calculus I-III (but pre-Spivak/Apostol in terms of rigor -- they can come later perhaps) (2) has only a small number of exercises (say, about 10 per section, where a section is along the lines of a section in the standard brick textbooks of Stewart/Anton/etc.).

Every so often I attempt a cover-to-cover completion of a calculus book but end up getting bogged down in tedious, repetitious exercises whose answers I get right. Even supposedly pared-down books -- e.g., Stewart's ESSENTIAL CALCULUS -- have way too many exercises.

Now, you may wonder why I can't take one of the standard books and focus on, say, only the odd-numbered exercises. I've tried that. There's still too much tedium and repetition. I come away thinking I could've learned just as much with a tiny set of well-chosen exercises. As for other schemes, I really don't want to spend half my time examining dozens and dozens of exercises just to pick out a custom exercise set.

Help.

Edit: I just discovered that Serge Lang has a book called CALCULUS OF SEVERAL VARIABLES. I wrote off Lang's A FIRST COURSE IN CALCULUS because it's weak on Calc III and may not even be all that comprehensive for Calc I and Calc II -- but, on the other hand, it seems to have just the right number of exercises for my needs. Does anyone have any comments on using these two books for Calc I-III? Are there better alternatives? (I don't mind if it's not the same author for Calc I+II and Calc III.)

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    $\begingroup$ The artofproblemsolving.com Calculus textbook is really good and has a challenging problem set (not too big as you request and definitely not repetitive). The only problem would be that it does not go up to multivariable calculus. $\endgroup$ – Robert Cardona Apr 9 '14 at 20:18
  • $\begingroup$ You could just do the homework problems for one of the Calculus courses on MIT Opencourseware. $\endgroup$ – littleO Apr 9 '14 at 20:28
  • $\begingroup$ Robert -- thanks. I'll check it out. $\endgroup$ – TimeEffectiveMathPlease Apr 9 '14 at 20:33
  • $\begingroup$ littleO -- yeah, using the assigned problems from some course notes on an .edu is an option, I suppose. $\endgroup$ – TimeEffectiveMathPlease Apr 9 '14 at 20:33
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I've worked with Thomas' "Calculus", I have the 11th Edition -- which is pretty bloated but the quality is good, I also have earlier editions. There are many exercises, but the quality is high. It is not up to the level of Apostol or Spivak but if you are okay with that it's excellent.

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  • $\begingroup$ I have Stewart and Anton but have heard good things about Thomas. These books are a bit too bulky for my tastes, but I guess it's good to have a book to refer to when more details/exercises are called for. Cheers. $\endgroup$ – TimeEffectiveMathPlease Apr 9 '14 at 20:37
  • $\begingroup$ I was going to say it's "luggable". $\endgroup$ – Alan Apr 9 '14 at 20:38
  • $\begingroup$ Hah! That gave me a chuckle. $\endgroup$ – TimeEffectiveMathPlease Apr 9 '14 at 20:43
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You might take a look at Calculus Lite by Frank Morgan.

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  • $\begingroup$ Hadn't heard of it. Thanks. I'll give it a look. $\endgroup$ – TimeEffectiveMathPlease Apr 9 '14 at 20:34

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