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Excellent but Dense: A comparative Review
Posted by R. Markham on 1/25/2006
I took calculus over 20 years ago using a book by Howard Anton. Wanting to brush up on my skills, I recently took a Calc II and Calc III course for review. The book I used this time around was Stewart's "Calculus", 5th edition. I thought it would be a breeze, but trust me, after 20 years, it wasn't. Thinking there might be a more helpful calculus book out there I decided to see what else might be available. In my search I came across several other excellent calculus books, but after all was said and done, I have to say that the Stewart textbook is really one of the best.
One of the of the calculus books that almost always received a lot of praise was "Calculus With Analytic Geometry", by Ron Larson. In fact it received such high praises, I found a good deal on a used copy of the seventh edition and bought it to supplement the Stewart text. And I have to admit, I found the layout in the Larson text to be much better than the Stewart text. With Stewart, I was constantly having to highlight things and draw in boxes or add notes to show where examples ended and text began, or what an example was supposed to be teaching, or what specific step in an example was key. In the Larson text, all of this is nicely laid out. Each example is labeled to indicate what it is about, and colored text, annotations, arrows, etc. are used to clearly show where the important points are. When it came to explanations though, I did not find the Larson text to give any better explanations than the Stewart text. In fact, I often felt the Stewart text provided slightly better explanations. I would read the Stewart text and then read the Larson text and think, "Gee, I'm glad Stewart pointed this or that out". Overall though, the differences were minor. In fact, sometimes it seemed that the text was almost identical, and it was only after careful reading that the differences could be noted.
In at least one case, Larson presents material I haven't seen anywhere else that really simplifies some integrals, and that is the tablature method, which is just a short hand way of doing multiple integration by parts, but it can really save you a lot of time.
As a main text for a multi-semester course in calculus, either the Stewart or the Larson text would be excellent. I found the Stewart text to be less inviting and slightly more difficult to read, but generally, (with a few exceptions), a little more thorough overall.
Another excellent book to supplement any calculus text is "The Calculus Tutoring Book" by Carol and Robert Ash. This book covers most of the material covered in a standard text like Stewart's or Larson's, but in a much friendlier style. It strips away a lot of the formalism found in a standard text so that what you are left with is a practical guide to doing calculus problems. It is not packaged with a bunch of computer generated graphs and figures. Instead everything is hand sketched. At first this may seem like a drawback, but once you get used to it, you realize how much you can do with your own pencil and paper. In my opinion, this is one of the best supplemental calculus texts you can buy. It would even serve as an excellent review book in its own right.
One other calculus text that I came across and really liked was "Calculus: An Intuitive and Physical Approach" by Morris Kline. It does not follow along quite as nicely with a standard calculus sequence and so isn't quite as easy to use as a supplement, but when I did use this book, I found the explanations to be very clear and useful.
So there it is. Stewart's Calculus, 5th edition, is an excellent text even though it is a little difficult to read sometimes. Larson's "Calculus With Analytic Geometry", seventh edition, runs a very close second, with some advantages not found in the Stewart text. Since both of these are very formal calculus texts though, "The Calculus Tutoring Book" by Carol and Robert Ash is an excellent supplemental book to consider as it offers a friendlier, more practical perspective. And if you still haven't had enough, "Calculus: An Intuitive and Physical Approach" by Morris Kline is well written and provides additional insight and perspective.
As a footnote, though I imagine the review about the cover of Stewart's text was meant to be tongue in cheek, I personally like the cover and find that it works well on several levels. Although the f-hole of a violin and the integration symbol of calculus have nothing to do with each other, it is a nice visual image, and if one thinks of the violin as an instrument used in performing some of the greatest works in the world of music, calculus may be thought of as an instrument used in performing some of the greatest calculations in the world of math. Finally, the image was mathematically generated, so all in all, I don't think it's a bad choice for the cover of this text.
Excellent college calculus text
Posted by Corey on 1/7/2004
Contrary to what some reviewers have written, I feel that Stewart's Calculus book is easily the best textbook I have encountered so far in college. In my opinion, the best indication of a textbook's worth is having to learn the material solely through the text, instead in addition to a lecturer; this book passed that test with flying colors.
Of course I had calculus lecturers, but every one of them was horrible. For Calc I (single variable), the professor spoke in a thick Russian accent; in Calc II (advanced integration/series, sequences), the professor was simply inadequate and didn't know how to explain anything; in Calc III (multivariable), the professor was a crazy Polish guy bent on teaching us calculus using his own weird linear algebra/advanced math methods (you'd think Berkeley might assign some better math professors...). In every case, I ended up shunning the lectures and learning everything straight from Stewart. Every chapter was teeming with great example problems, and wasn't saturated with unnecessary proofs (read the Principia or other advanced books if you're interested in that sort of thing). Perhaps the homework problems weren't always as challenging as other books, but I'd rather understand the problems than sit around staring an unsolvable puzzle for 3 hours.
Again I say, best college text I've had so far. I highly recommend it.
The best there is - and I'm familiar with the others
Posted by Stan Vernooy on 5/13/2000
I was one of the pre-publication reviewers for the second edition of this book. I have not been shy about telling a publisher that their book stinks if that's my opinion. But the Stewart book was then, and remains now, IMHO, the best introductory calculus text available. Please note that the majority of negative reviews came from people who have seen exactly one calculus book, and they clearly don't like calculus! But I have taught from three of the most popular books, and I've read most of the others. There may be other books which take a radically entertaining, non-traditional, and more superficial approach to the subject, and those books may meet with approval from people who really don't want to learn calculus. But of those (many) books which cover the traditional topics in an introductory calculus course, no other author has written a text as learnable as Stewart's. On every topic, Stewart is clearly conscious of the fact that his reader doesn't already know the subject, and he has given some thought to exactly what has to be explained in order for the student to learn successfully. Remember, most textbooks are not written for students: they are written for the professors who are going to choose the books. Professors are not generally impressed with a book which spends a half page clearly describing the meaning of a theorem which can be written with a one-line equation. But students will appreciate the effort Stewart has exerted to help them learn. Stewart does not sugar-coat or resort to gimmicks or superficiality in order to make the material learnable. All the material is there, it's just presented with an awareness that the reader is trying to learn calculus for the first time. If you are taking a calculus course with any other book, try to get a cheap used copy of the Stewart to use as a supplement. It will help!
Posted by Joey Pittman on 5/11/2006
If you need to buy one calculus book... buy this one. It's got everything you will need for learning basic calculus. I was referring to this book constantly, both while taking basic math, and in more advanced courses in physics and engineering, when I would need to go back and re-learn how to integrate a particular type of problem. I was actually quite shocked to see that the last several reviews rated this book quite poorly... everyone who took math with me using this book loved it. Then again, we were all engineers, so we wanted to be doing this kind of stuff.