# Spivak as first exposure to Calculus?

1. May 15, 2008

### Helical

Next year I'm going to begin studying physics as freshman and this summer I was thinking about studying Calculus on my own. Would Spivak be feasible as an introduction to calculus? I'm in Pre-Calculus right now and find it pretty easy (though I know that is not necessarily any indicator of calculus ability).

I want to study Spivak because I want to see the more theoretical side of math, something I have no experience with. If it's not really feasible though, what book would you recommend, something like Stewart? The university I'm going to next year uses Hughes-Hallet...the reviews on Amazon.com basically say it's one of the worst calculus textbooks; another reason I feel like studying over the summer is a good idea.

2. May 16, 2008

### uman

Get a copy at your favorite library and see for yourself.

Note: This is real advice, not just me being sarcastic.

3. May 16, 2008

### lurflurf

Pre-Calculus alone might be enough for Spivak if it was a theoretical couse, but most are not and some extra preparation may be needed. Can you prove simple results and derive new results from previous ones?

Hughes-Hallet is quite terible, I thought it was Hallet-Hughes maybe they switch the order of there names every edition, at least newer editions ha l'Hopitals rule. Stewart is o.k. as a representative of most calculus books, which are very much alike and very bad. Also Stewart is quite expensive.

Spivak is practical as a first book, but also could be frustrating if you don't have the right background, don't have some one experiance to guide you through it, or are not highly motivated. The advice of fliping through several books is quite good. You should be able to see at a glance is you have the background and like the writing style.

I suggest a three level approach.
Choose one book of each
-junk book like all the others (get cheapest available like an old edition \$10 maximum) just so you see the silly ways other books do things so you will not be confused if you see some poor wretch using such methods
Slokowski
Stewart
Anton

-nice basic (maybe intuitive) book
Lang
Thompson
Lax
Hamming
-nice book (maybe challenging)
Lang
Shilov
Apostle
Spivak
Courant

4. May 16, 2008

### CRGreathouse

Any opinions, while you're at it, on Leithold's calculus text?

5. May 16, 2008

### Helical

lurflurf, thanks for the response. As for your question about proving things, the only thing we have really covered as far as proofs go are trigonometric identities.

An example of what we did was as follows:
$$cos2\theta = cos^{2}\theta - sin^{2}\theta$$

$$tan(S-T) = \frac{tan(S) - tan(T)}{1+tan(S)tan(T)}$$

etc.

I don't have much experience with theory but maybe a bit (if that sort of proof is theoretical); What might a theoretical pre-calculus course cover?

By the way, it might well be Hallet-Hughes, I often confuse such things.

6. May 16, 2008

### uman

I learned calculus via self-study from Apostol.

I was skimming near the end because I was up against a time crunch preparing for the AP Calculus exam. But I got a lot out of the parts I did go through thoroughly. I recommend it a lot. You can get it dirt cheap used online.

7. May 16, 2008

### uman

Go through the first few pages with the Amazon preview feature. That should keep you occupied for quite a while if you actually do the exercises and such.

8. May 16, 2008

### rocomath

Helical, I was in a similar position as you last year. I am not sure how good or intuitive your math abilities are, but I can assure you Spivak is one bad mother! I was a tutor and already in Calculus II when I first heard of his book. I really loved Calculus, but what I studied/learned was "computing" Calculus and at times, theoretical in sense I proved simple things. I can tell you that Spivak's book is tough. You haven't taken Calculus yet, and I know for a fact that Precalculus isn't enough. Take your time! I am not sure what Precalculus text you are using, but I would say Precalculus by Cohen is IMO the best preparation to Calculus I, but to take on Spivak? I'm not quite sure, since I don't know you well enough.

I'm currently using Spivak's book now, it took me a while to get here, but now I'm loving it :)

btw, I'll be more than happy to scan the problem set for Chapter 1 to decide for yourself whether or not you're ready.

2 things can come from having Spivak as your first exposure to Calculus: You will learn Calculus the right way! And you'll know that you're smart enough to be a Math major :p

Last edited: May 16, 2008
9. May 16, 2008

### mathwonk

boo! ..... try it, it wont hurt you.

10. May 17, 2008

### LukeD

It could. People have been known to go insane after reading Spivak.

In all seriousness, I don't know Spivak at all, but if it's too much for you, try Apostle.

If you're trying to learn Calculus completely from Spivak, you might get confused because many things will seem unmotivated (I mean, you might not know why you are learning a certain topic at any time). In many books of the sort, ideas are presented without much if any indication as to why a person would want to know a topic or how to apply what it teaches. For instance, you will very rarely see practice problems worked out or be shown applications to engineering or anything of the sort. Often times you'll even be presented with something that is used to calculate things without being told that it's used to calculate things or shown how it could be used.

Even if that does not interest you much, it will be very useful to read a usual high school calculus text book in parallel with Spivak because knowing how to calculate things and knowing when to apply the tools is also extremely important for your mathematical maturity.

Also, reading a usual high school book could help you with intuition about the concepts and could clear up some things. One thing that you should be aware of is that Spivak is expecting his students to have already had some prior experience with Calculus through one of those usual high school books.

11. May 18, 2008

### mathwonk

forgive me but it is hard to stay straight after giving the same advice about a million times on here, please read the first couple pages of my thread " who wants to be a mathematician?".