This is an extremely conventional calculus book. Its claims to fame are that it has especially clear explanations, and that, because of thorough checking, it has few errors.
Because this text is so conventional it generally does not respond to any of the criticisms of the calculus reform movement. There is quite a lot of attention to symbolic integration techniques. Technology (graphing calculators and computer algebra systems) appears only in the exercises and not in the body. There are no student projects or writing exercises. The applications are all conventional, although many of them are improved by what appears to be real numerical data (there are no sources given for the data, so it's realistic but I'm not certain it's real).
The book does appear to be exceptionally error-free for a first printing. Richard Feynman's name is consistently misspelled. One of the infinite series exercises has an incorrect exponent. The book is generally very careful in its proofs. Most books give incorrect proofs of the chain rule, forgetting that there may be a division by zero in the process. This book gives a correct proof (although only in the exercises). On the other hand it falls down on the Bolzano-Weierstrass theorem and the least upper bound property — the given proofs are incorrect.
Some terminology is used in a non-standard way. To most people, f << g means the same as f=O(g), but here it means f=o(g). The book speaks of a "root" of a function (most people speak of roots of equations and zeroes of functions). Several exercises ask students to "prove" something using a numerical calculation in a CAS. These exercises treat the CAS as an oracle, not mentioning that numerical results are approximate, and that CASs, like other computer programs, sometimes make mistakes.
I like the numerous Assumptions Matter sections that explore what happens if the hypotheses are not satisfied. There are Historical Perspective sections scattered through the book; these don't really advance the exposition but they're interesting and may capture the student's attention.
But now we come to the key question: Given that there are already thousands of calculus books in print, is it valuable to have a new calculus book that is just like nearly all of them, except that it is has clearer explanations and fewer errors? It's hard to make this sound exciting, and in fact I am not excited by it. Most calculus books are deadly dull, and even though this one has lots of pretty pictures and interesting sidebars I still had a hard time getting through it. I would have liked it much better if it had addressed some of the issues raised by the reform movement. Still, the present book is very well done, and if you love traditional calculus books or for some reason you are prohibited from making any innovations in your calculus course, this may be the book for you!
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.