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I would like recommendations for a good calculus book that isn't as math centered as Spivak, nor as dumb as Stweart, that has decent theory and challenging PRACTICAL problems (less "Prove that...").

Edit: I don't want something with too much focus on axiomatic treating and theorem proving. I'm looking for a less mathematical book, focused on applying techiniques to solve uncommon limits, derivatives and integrals, as well as applications to science and engineering.

Otávio Rapôso
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3 Answers3

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I recommend Zorich's mathematical analysis. It is clear and contains lots of examples.

confuser12
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  • It's actually a book on analysis, with too much focus on axiomatic treating and theorem proving. I'm looking for a less mathematical book, focused on applying techiniques to solve uncommon limits, derivatives and integrals, as well as applications to science and engineering. – Otávio Rapôso Nov 25 '16 at 23:14
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    @OtávioRapôso Why don't you write that in your question? – Eff Nov 26 '16 at 00:15
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You might look at Adam's Calculus. I didn't think it was the best book for the class I was teaching, but I considered it harder than Stewart or Anton. There are more-than-average number of applications. It's a Canadian text, so you have to put up with bizarre spellings of words like "center" and "liter". And all word problems are in a a deviate measuring system called "metric". Otherwise, it might be what you're looking for.

B. Goddard
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  • I'm brazilian, so metric system is my native system. – Otávio Rapôso Nov 25 '16 at 21:08
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    "It's a Canadian text, so you have to put up with bizarre spellings of words like "center" and "liter". And all word problems are in a a deviate measuring system called "metric". Otherwise, it might be what you're looking for."

    Is this a joke?

     – Eff Nov 26 '16 at 00:16
  • @Eff Umm....yes. (Although I can make a pretty good argument that the metric system is inferior.) – B. Goddard Nov 26 '16 at 00:48
  • How is the metric system inferior if everything is smoothly based upon base 10? – Otávio Rapôso Nov 26 '16 at 14:11
  • @OtávioRapôso 1. The units aren't sized to match things we really encounter. 2. No one ever does these supposed easy conversions. 3. It's boring, like a trailer park. The English system is interesting, like the Shire. 4. 10 is second worst base we could use. It's not "smooth" when you have to divide something into 3rd's or 4th's. – B. Goddard Nov 26 '16 at 14:29
  • Only british people and americans use this crazy roller coaster system of units, with no internal logic or pattern. It's evident that there's cultural bias here.

    Also, there's smootheness in the metric system because the multiples and submultiples are all powers of the same number, 10, which is in turn the numerical base used by virtually everyone in representing real numbers, as well as the most natural and easy to learn (since we start learning to count using the fingers of hands).

    "It's boring" is subjective and not a "pretty good argument".

     – Otávio Rapôso Nov 26 '16 at 15:48
  • No, there is internal logic and pattern. Yes, I know why people like metric: "It's easier." But it's only easier if you want to convert kilometers to meters, (which no one ever does.) It's harder if you want to measure anything in the real world or divide things evenly into a small number of piles. And there were 4 arguments, not just the "boring" one. – B. Goddard Nov 26 '16 at 17:03
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If you think Steward's Calculus is dumb, you might be interested in Multivariable Mathematics by Ted Shifrin. It is not introductory but contains a lot of examples.

Henricus V.
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