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I want fo learn (Real) calculus and I've seem those books are very recommended, now I know why, I've given them a look and I think they are worth their reputation.

I'm talking about

  1. Calculus by Michael Spivak
  2. Calculus by Tom Apostol
  3. Introduction to Calculus and Analysis by Fritz John and Richard Courant

I want to read them all, but I have to chose: what should I pick and why? are there any sustactial difference? if I have to read them all, in what order should I read them?

joseph morrison
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1 Answers1

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I'm about halfway through Spivak and it's great. I haven't gone through Courant or Apostol. Spivak is known for uniquely interesting and difficult problems, and a tone that's widely considered more playful than is typical for a math textbook (though subtly so; it's not Mad Magazine).

Spivak also includes answers to about half of the exercises, and an Answer Book for the others is available for purchase.

I strongly encourage you to buy the Answer Book if you're going the Spivak route, as the problems are difficult.

You should expect to get stuck, often. You will likely be unable to do many of the problems without at least some hints from the book. There have been occasions in which it took me a few days to even understand the published solution to a problem I looked up.

Don't be discouraged when you get stuck. Take some time. Do something else. Maybe try thinking about it away from the book and your paper. Go for a walk. This is how learning math works. Not everything is immediately comprehensible. Some things take a little while to crystalize in you mind. Once they do its wildly gratifying.

Another Spivak tip: do every problem. Spivak often puts important results in the problems, and they typically build off each other in a very purposeful way.

Some disadvantages of Spivak are

  1. It's single variable only. Apostol and Courant each cover single variable calculus, multivariable calculus, and some linear algebra and other material.
  2. Spivak doesn't have many easy problems. You're not going to get practice doing a thousand rote calculations the way you might with a more standard (and mediocre) text like Stewart.
  3. Spivak doesn't focus much on applications. IIRC Courant and Apostol have more examples from Physics and other fields, and those things are cool and can help with your intuition and ability to picture what's going on.

It should be noted, Spivak is also a single volume. Those others are each two volume collections IIRC. I imagine (hope!) it's feasible to use Spivak for single variable, and then hop over to part II of either Apostol or Courant to tackle multivariable stuff.

Whatever you decide, don't be put off by "getting stuck"!

Ben
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