Best Calculus book for self-study

Bassir

I'm currently in high school and would like to get a better understanding of Physics as well as Calculus, as I have no experience with either precalculus or calculus, and I really want to self study it.

What books do you recommend for learning calculus on your own?

stewartcs

I would recommend studying Precalculus/Trigonometry before attempting Calculus.

However, I am a fan of James Stewart's Calculus books.

CS

Bassir

I'm currently taking trigonometry.

Do you have any books you can recommend for learning precalculus all the way up to calculus?

DarrenM

Trigonometry is Precalculus; or rather, it's part of it. Precalculus is part algebra and part trigonometry. For example, Georgia Tech's Precalculus course description says:

They use Precalculus,7th edition by Larson, Hostetler, Houghton-Mifflin. I can't speak to that, as I'm not familiar with the book. I used Stewart's Precalculus: Mathematics for Calculus, 5th edition, and I liked it quite a bit. I should point out that this is the same Stewart mentioned by stewartcs.

Bassir

Would 4th edition be adequate?

DarrenM

Yea, snagging old editions of textbooks can be a pretty cost-effective way of getting your hands on them. An old edition would probably suffice; just be aware that an older edition may have a few more errors than the most recent version. That's not a big deal, though. You'll just have to strike a balance between being determined enough not to give up when you encounter a tough problem and smart enough to realize that the book itself may be wrong.

Bassir

Also, does anyone have any recommendations for introductory physics textbooks with very minimal math skills, considering I've no exposure to calculus?

Something not too advanced, just high school AP physics/college freshman physics.

Feldoh

Halliday and Resnick fundamentals of physics.

Bassir

After being exposed to precalculus, what textbook do you recommend for learning calculus?

Calculus by James Stewert?

Sankaku

Stewart's Calculus is ok - the 5th edition can be found for very cheap. However, there are other books that may be a little better.

I like Swokowski for a good general book but I hear that Kline's book and Gootman's book are also popular for people new to the subject.

Once you have the basics, look for Spivak.

DarrenM

Yes, I like Stewart's Calculus quite a bit, but that may be because I'm comparing it to the book I've had to use. It's called University Calculus and it's a weird derivative of Thomas' book. Frankly, I'm not fond of it.

I have heard, but not seen for myself, that Spivak's book is very good. I haven't been able to find even an old edition that wasn't still a bit pricey.

DanP

From the series "Dover books on mathematics"

"Essential Calculus with applications" , Silverman
"Advanced calculus", Widder


Cant go wrong with them , even if you may have to look to a video lecture or two for some issues and explanations. (For example the analysis of trig functions is omitted )The price is excellent, ~25 USD for both, compare this with the price of today popular textbooks.

qspeechc

I am not familiar with Stewarts precalculus books, and I don'y know any such books I can recommend. However, I was forced to learn calculus with Stewart's book. In short, I hated it. Ok, you will learn everything you need to know about calculus from this book, so in that respect it is worth getting. I'm not singling out Stewart's book here, I think most calculus books at that level are mediocre.

I could write an essay on why I think Stewart and many other calc books are not worth your time or money. But I won't bore you. Let me instead present a list of books I think are worth your time, and they won't break the bank either. Btw, as others have said, you pre-calculus needs to be good before you start calculus. Here's the promised list (you need to do single-variable calculus before multi-variable calculus):

Calculus Made Easy by Thompson. Don't let the title or the price fool you. Calculus is really a simple subject, as Thompson skillfully shows here. It's so cheap, you should definitely get this book. The 2nd edition is the best. Only covers single-variable calculus.

A First Course in Calculus by Serge Lang. Ok, it's Lang, but don't be scared. To the point and well written. Only covers single-variable calculus. Can find it used for a good price.

Calculus of Several Variables by Serge Lang. The follow-up to the above book. This one covers multi-variable calculus. You can also find cheap copies of this one.

Vector Calculus by Marsden and Tromba. Multi-variable calculus book. A very difficult book if you have no background in proofs, but the best vector calculus book I have read. You might want to try the other calculus books by Marsden, but I've never read them.

Div, Grad, Curl and All That by Schey. Vector calculus book, very intuitive, and actually explains the things in vector calculus, which surprisingly, is rare in calculus books, e.g. Stewart. I strongly recommend this one.

Calculus by Gilbert Strang. The book is available for free online (it's legal):
http://ocw.mit.edu/ans7870/resources...strangtext.htm
I haven't myself read this book but:
1) It's written by Strang, so it's probably good (it has good reviews on amazon.com).
2) It covers both single- and multi- variable calculus, but it's not too long (Stewart is over 1100 pages!).
3) It's free!

**********************************
In short, I recommend:
Thompson, Schey, Strang.

n!kofeyn

Spivak's calculus is absolutely wonderful. You really shouldn't learn calculus from Stewart unless you have to, i.e. a course requiring you to use it. It is the same standard textbook that is 1000+ pages and has endless exercises that don't do anything but teach you computation and worthless applications. Plus, Spivak starts off by teaching you about the real numbers and precalculus. It is highly recommended. Some might say it is analysis book or too difficult (it's a thorough calculus text), but if you can get through the first 70 pages or so (the introductory precalculus material), then you'll be fine for the rest of the book. The payoff is huge if you learn calculus from this text.

jgens

I'll second n!kofeyn's recommendation. Spivak's Calculus is a great book and he presents the material in a way that's easy to understand. The problems in Spivak's calculus text are also considerably more difficult than those in Stewart's calculus text (I felt I was wasting my time by working the problems in Stewart's text whereas Spivak's problems are challenging and engaging).

Bassir

Wait, Spitvak's Calculus has precalclus in it?

Does that mean Precalclus by Stewert is unnecessary if I decide to go with Spitvak?