Calculus (with Tools for Enriching Calculus Video CD-ROM, Ilrn Homework, and Vmentor) with CDROM [Hardcover]

Let's face it, the book is dry. It breaks down concepts into steps and recalls the number of the particular step, rather than the concept of the step (hope I didn't confuse anybody). Expanded explanations of algebraic manipulation/tricks would have been helpful. Because of the previous statement, I have gone through the whole book and still sometimes wonder how he got from point A to point B.

Positives:

Forces ones mind to expand beyond the terrible habit of memorization (in most chapters). If one knows all the algebra that the book composes of, then that one is an algebraic god (not kidding). Don't excpect to get much out of this book without alot of time.

o Text: The text is pretty clearly written, with no errors I know of, but makes some conceptual leaps periodically.

o Layout: The layout is excellent. It makes great use of consistent color coding and typographical conventions to identify classes of concepts. (I.e., It's always easy to spot and distinguish Examples, Proofs, Rules, and New Sections.)

However, there are some algebraic manipulations that are sometimes combined into one line that should probably be expanded out and explained better. Even though students are expected to understand the algebra at this point, it's often crucial to explain _why_ certain algebraic manipulations are being done. Usually there is a certain form of an expression or equation that is useful or desirable for a specific reason. Such reasons need to be explicated side-by-side with the steps to reach the desired form, instead of just skipping to the desired form (as sometimes is done).

o Terminology: In some places Stewart talks about "constants" when what he really means are "scalars." There is a distinction between these two concepts that is important in other fields of math that could be confused. He also uses different letters to identify "any real number" or "a particular real number" than is standard in many other texts. This also could lead to confusion.

o Graphics: The integration (pun intended :) of graphs and diagrams to supplement functions, step-by-step processes, and proof descriptions in this text is frequent, helpful, and very well done.

o Exercises: The exercises for each section start off easy and in close step with the concepts and example problems that have been demonstrated in the preceding section. However, Stewart's problems ramp up in difficulty quickly. Exercises in the the middle or near the end of a set often have no direct prototypes in the preceding text for students to lean on. Some instructors might consider this an asset, but when assigned carelessly can be a frustration to students. One improvement from Fourth Edition to Fifth Edition was the "red flagging" of many exercises of especial difficulty.

o Proofs: Simple theorems and rules are proved in the text as they are introduced. More complicated proofs are provided in appendices in the back. The text is pretty thorough about proofs.

o Worst section: I think the hardest section for students to understand (and unfortunately one of the most important in Calculus) is the section titled "The Precise Definition of a Limit". Stewart has a habit in this section, when manipulating an absolute value of epsilon expression, to abbreviate it all on one line without explaining _why_ he is performing the operations that he is. He should expand these out to multiple algrebraic lines, possibly with some text explaining that he is trying to get the epsilon expression to match the delta expression. It is impossible to be too verbose, explicit, and careful with this section. And certainly more of each of these could be used in Stewart's rendition.

Other reviewers mentioned the sections on the Chain Rule, Integration by Substitution, and Integration by Parts -- all of which could be improved. Substitution and Parts could be improved by drawing the little grids of what u and du represent (that many instructors write underneath these kind of exercises before substituting).

To summarize, if you're good at math this is probably a good text for you. If you (or your students) have weaknesses, stick with something simpler -- Larson's Calculus text is excellent and good to compare against this one.