129 of 138 people found the following review helpful
Excellent but Dense: A comparative Review
Jan. 24 2006
By
R. Markham
- Published on Amazon.com
Format: Hardcover
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.