Here's why you should consider buying this book
10/21/2005
As you browse books in Amazon, you might think: "oh, yet another Calculus book."
First, let me begin by putting this book in its proper context: it is a Calculus 2 book, but not an Advanced Calculus book.
But this book has some qualities that set it apart from the heap of Calculus books. First of all, it is the fruition of a Harvard-based consortium with a grant from the National Science Foundation to write a "new" Calculus book. What's new about it? Well, it is based on an "old" philosophy, that I'll paraphrase from the Preface: Calculus was invented to solve problems! So, using Calculus, you can reduce complicated problems to simple ones. Central to this unified, application-oriented approach, every topic is presented numerically, geometrically, and algebraically. Every time, every topic: numerically, geometrically, and algebraically. Now, all contemporary authors of Calculus text would claim to be doing the same. But this way of approaching the subjects is here by design, as a very core characteristic of the text. The result is that you begin to look at the problems as something more than nuisances to be solved by rote learning (gone are the days students got to read Apostol at their first iteration through Calculus...really learning, instead of having dumbed down explanations that, in fact, make learning *harder* - I wasn't one of the lucky ones...) Somehow the authors were very precise and sensitive in identifying "gotchas" in the student's first iteration through multivariable calculus.
I discovered this book a bit too late in my Calculus 2 class. But this is a cheaper book than the ones that cost over $100. You should buy it, even as a supplement. Again, keep in mind this is not Advanced Calculus and neither was it meant to be.
And insofar as "mathematical rigor" is concerned _at this level_ it is the same - and IMHO even a little better - than some other very popular books.
Sometimes Helpful, Frequently Not
2/15/2006
The idea of a solutions manual is fantastic. It's a quick, convenient way to see how to solve problems.
Unfortunately, this book falls short in several ways.
First, only EVERY OTHER ODD problem is covered. That means, in a typical chapter, only 5-10 problems are covered. For a course as difficult as Multivariable Calculus, this is woefully inadequate.
Second, many of the "solutions" are NOT solutions. They are answers. You will frequently find just the answer given with no explanation of how the solution was derived. In the back of the actual textbook is the answer to EVERY odd numbered problem. So to reprint just the answer in a new book is a waste of paper. Why spend $34 on a solutions manual that gives the same info that the back of the text has?
Third, for the solutions that are explained, they aren't explained very well. You will frequently find a sequence of algebraic operations, but nothing saying how they went from one step to the next. The authors apparently expect you to know, but if you did, why would you need a solutions manual?
This solutions manual CAN be helpful, but just be aware that your $34 isn't going to get you very much help.