Calculus Review

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Calculus ReviewI 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.Calculus OverviewSuccess in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!
About This Edition
James Stewart's calculus texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of Calculus, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

New Features
Revised: For this edition, chapters 1 and 2 have been combined--and some material has been moved to an appendix--to streamline the presentation of these early topics.
Revised: Throughout the text, the author has revised the narrative as necessary to improve clarity and aid in student comprehension.
New: New examples, margin notes, applications, and projects have been added.
New: This edition has been updated with approximately 25% more exercises than the previous edition, giving students more opportunities to practice concepts they have learned.
New: "PS" icons denoting problem-solving margin notes are aimed at increasing instructors' awareness of this important aspect of Stewart's approach.
Updated: Tools for Enriching Calculus--a free, online, interactive resource that allows Calculus students to work with animations that deepen their understanding of key concepts by helping them visualize the concepts they are learning--has been updated with new problems and a new Flash design that is more visually appealing and engaging to students.
New: Collections of more challenging exercises called "Problems Plus" have been added to the end of every chapter. These sections reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.
Explore additional features of James Stewart's Calculus, Seventh Edition.

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