Calculus textbook

Question

I have a basic question concerning calculus. I'm soon going to teach myself calculus and I wondered which textbook should I take :

Spivak's calculus or Lang's A first course in calculus

Any suggestions ? Thank you !

score 2 · Answer 1 · answered Dec 01 '13 at 01:30

Spivak, Calculus: This is a book everyone should read. If you don't know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of bad-calculus-book “explanations”. The whole thing is the most coherently envisioned and explained treatment of one-variable calculus I've seen (you can see throughout that Spivak has a vision of what he's trying to teach).
The book has flaws, of course. The exercises get a little monotonous because Spivak has a few tricks he likes to use repeatedly, and perhaps too few of them deal with applications (but you can find that kind of exercise in any book). Also, he sometimes avoids sophistication at the expense of clarity, as in the proofs of Three Hard Theorems in chapter 8 (where a lot of epsilon-pushing takes the place of the words “compact” and “connected”). Nevertheless, this is the best calculus book overall, and I've seen it do a wonderful job of brain rectification on many people.

Other calculus books worthy of note, and why:

Spivak, The hitchhiker's guide to calculus: Just what the title says. I haven't read it, but a lot of 130s students love it.

Hardy, A course of pure mathematics: Courant, Differential and integral calculus These two are for “culture”. They are classic treatments of the calculus, from back when a math book was rigorous, period. Hardy focuses more on conceptual elegance and development (beginning by building up R). Courant goes further into applications than is usual (including as much about Fourier analysis as you can do without Lebesgue integration). They're old, and old books are hard to read, but usually worth it. (Remember what Abel said about reading the masters and not the pupils!)

Apostol, Calculus: This is “the other” modern rigorous calculus text. Reads like an upper-level text: lemma-theorem-proof-corollary. Dry but comprehensive (the second volume includes multivariable calculus).

Janusz, Calculus: The worst calculus book ever written. This was the 150s text in 1994–95; it tries to give a Spivak-style rigorous presentation in colorful mainstream-calculus-book format and reading level. Horrible. Take a look at it to see how badly written a mathematics book can be.

For more lists see: Chicago undergraduate mathematics bibliography

I just wanted to that Hardy's book is old but much better than the ones written by modern authors. Also it is much more inspiring and targeted for self-study. It covers almost everything which Spivak covers but in much less number of pages and the textual part is a literary masterpiece. Its an enjoyable read. Some terminology or notation may be outdated but the concepts are explained way better than any modern text. A review is available at http://paramanand.blogspot.in/2005/11/book-review-course-of-pure-mathematics.html — Paramanand Singh, Dec 01 '13 at 04:23

score 2 · Answer 2 · edited Apr 13 '17 at 12:19

Here is a similar post:

Looking for a Calculus Textbook

I think the book you pick is not essential. The essential part is to have a Q&A process in which you can work problems through, check your answers and find where it went wrong or better than official answers. This would help for your future math/science studies as well. I think a textbook with a guided solution manual or at least partial hints would be helpful.

The difference between book A and book B will not be significant, because for a lot concepts (like continuity, Hessian matrix) the student usually only has a refined understanding after he/she learned more advanced material in future. But the difference between struggling alone and working with some guidance would be significant. I think stackexchange, art of problem solving, etc might be helpful in this aspect.

Ahaan S. Rungta · Answer 3 · 2013-12-01T01:14:29.637

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This is a matter of opinion but, personally, I have neither but would recommend Spivak since it is used for a lot of undergraduate and AP courses, definitely more, as per my knowledge, than Lang.

If you ask my opinion, I'd use Calculus by David Patrick.

edited Dec 01 '13 at 01:14

answered Dec 01 '13 at 01:05

Ahaan S. Rungta

7,706

I've not read Patrick. Could you explain why you'd use it? – NicNic8 May 12 '21 at 21:37

score 0 · Answer 4 · answered Dec 01 '13 at 01:09

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I recommend Apostol's Calculus vol I and II

answered Dec 01 '13 at 01:09

Euler....IS_ALIVE

4,707

But the OP gave only two choices. – Ahaan S. Rungta Dec 01 '13 at 01:13
OP may have been mistaken in thus limiting the options. Particularly since one of the choices, Lang, is not mainstream. – André Nicolas Dec 01 '13 at 01:37

score -1 · Answer 5 · answered Dec 01 '13 at 01:55

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I would recommend Stewart's Calculus texts http://www.stewartcalculus.com/. Calc I, II, and III can all be done with one textbook and there's also a solutions manual for you to check your work.

answered Dec 01 '13 at 01:55

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Really? Stewart's Calculus? And what is Calc I, II and III? At my university, this is the text they use for the life science students. I took a glance at it once and it has, for example, a full chapter on directional derivatives. Now take Munkres which deals with them succinctly in one page. Stewart is for non-mathematicians and takes you about as far you can go on your mathematical journey without being exposed to the rigour necessary to pursue higher mathematics. Spivak is unequivocally better. – Christopher K Dec 01 '13 at 02:16
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If the OP is a beginner to Calculus then I don't think Stewart is a bad option. Calc I, II, and III are terms used in standard undergrad-level for courses in Calculus. But I realize that the OP has limited himself with two options, so apologies for the redundancy. – Dec 01 '13 at 03:42

Calculus textbook

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