Cheap Calculus: Single and Multivariable : Course Advantage (Book) (Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum, David O. Lomen, David Lovelock) Price

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Customer Reviews of Calculus: Single and Multivariable : Course Advantage

The authors of _Calculus_ don't seem to have made up their minds regarding whether or not it is necessary to introduce the notion of mathematical justification in this book. On the one hand, the examples feature sound arguments for why a curve looks the way it does, or why a critical point is a maximum or minimum - but on the other hand, alongside Newton's Method and the Bisection Method for estimating roots, is a "Using the Zoom Function on Your Calculator" primer on how to estimate the zeroes of functions. Offhand remarks about "and you can use your graphing calculator for this and that" serve to seriously undermine any attempt to explain to first-year students the concept of mathematical argument - which is unfamiliar to many.

The organization of the chapters is also somewhat questionable. Differentiation is broken up into two sections: one dealing with the concept of a derivative (complete with pictures), and the other pertaining to computing them. While the idea of introducing differentiation through a concrete example - measuring instantaneous velocity given a displacement function - is a good one, by the time students actually get to work with derivatives, they're no longer focused on what they actually represent. Curve sketching is introduced vaguely at the end of the second chapter - before the shortcuts to differentiation are mentioned - and then revisited only in chapter 4.

The section on integration is even worse: again, it's introduced in a concrete manner - this time, by asking how displacement can be computed from a velocity function. But for some bizarre reason, the authors don't take this opportunity to explain that the area under a velocity curve - the integral - is that same displacement function whose derivative was the velocity. It's a perfect opportunity to do so, as it's an interesting and surprising (to the beginner) result, and one that's accessible at this point in the course. But instead, the Fundamental Theorem of Calculus is relegated to a later section, long after the "integral as an area" idea has been abandoned and students are just working with integrals as antiderivatives. (Even more curiously, there's a section entitled "The Second Fundamental Theorem of Calculus", but none called "The First Fundamental Theorem of Calculus".)

I'd highly recommend James Stewart's _Calculus_ instead of this text for a first-year calc course: the material is far better explained, and there's even a section on the inadequacies of graphing calculators (which are expensive, and which most first year students don't have the mathematical background to use properly).

Horrid
The book is a disaster. I had to suffer with it for 2 semesters. None of the other students in my Calc I and Calc II courses got anything from it either, as far as I can tell. I had to scramble and seek information from other calc books in order to understand what differentiation and integration was all about. The text in no way prepares one for the exercises. There's no connection between the text and the exercises. In the exercises there appear some inane, open-ended questions that seem to be trying to make some unfathomable point. This is not a book anyone can learn from. I would strongly advise any student who must use this book as their course textbook to CHANGE COLLEGES. There are many great calculus books out there, on all levels. For those who prefer a 'calculus reform' approach, I would recommend Calculus Lite, by Frank Morgan. For the more traditional approach, I got a lot out of Anton's classic.

A good reference book
When I took Multivariable Calculus, we used "Multivariable Calculus" by James Steward in class. I personal like Steward's book very much because it made me understand without the help of my professor. With a supplement of this book, I found I understand Multivariable Calculus in a more comprehensive way. All in all, I like this book a lot.