# Introductory Calculus

1. Feb 12, 2014

What introductory calculus textbook do you recommend? Is Spivak's book good or is it too hard? What about Ron Larson's?

2. Feb 12, 2014

### jgens

Spivak is an excellent intro book. Depending on your interests it might be more theory-oriented than you care for, but regardless it contains most of the important information.

3. Feb 12, 2014

The 4th edition is the best one, correct? Also, does it explain the information thoroughly?
Larson's seems a bit watered down so I guess I'm probably getting Spivak.

edit: Apostol's seems good. Should I get it or stay with Spivak?

4. Feb 12, 2014

### jgens

Any edition is probably fine. Which one is best is honestly more a matter of accessibility, cost, etc.

Yes. It essentially starts from first principles, taking the existence of a Dedekind-complete ordered field for granted, and then proves everything systematically from there.

Either is fine.

5. Feb 12, 2014

If I don't know what a Dedekind-ordered field is, should I go for an easier book?

6. Feb 12, 2014

### jgens

No. He never uses that terminology. Instead he simply lists all the properties we want our real numbers to have. Since the only Dedekind-complete ordered field is the real numbers you can read my statement as "It essentially starts from first principles, taking the existence of the reals numbers for granted, and then proves everything systematically from there" which is honestly what I should have written in the first place.

Edit: Since I am generally against giving overly complicated answers my previous response deserves some defense. The reason I opted for "Dedekind-complete ordered field" instead of "real numbers" initially was that I wanted to emphasize how Spivak gives a functional definition of the real numbers (i.e. in terms of their abstract properties) instead of a concrete one like the decimals. In retrospect, given the OPs background, this was a poor choice and I apologize for that.

Last edited: Feb 12, 2014
7. Feb 12, 2014

Alright, thanks a lot for the help! Looks like I'm going for Spivak.

8. Feb 12, 2014

### mathwonk

Spivak is a very hard, very abstract book, suitable mostly for those who already know a lot of math and who are very motivated and strong theoretically. For the right audience it is superb, but it helps to have a teacher.

I personally think it is not at all an introductory book, but you will find out by reading it. I say all this only so that you are not discouraged if it is not right for you. Many other books are much easier and more appropriate for most people to begin with.

I like Cruse and Granberg for instance, but it is hard to find.

9. Feb 12, 2014