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I have noticed that a lot of other reviewers here have mixed feelings about this text. It would help if they stated their background which should be taken into account. I am a junior computer science/mathematics double major who does well in both subjects and is not afraid of reading through a long proof or spending time on advanced problems. Thus, my perspective is that of an advanced student. I noticed that the other students in my class were not all mathematics majors and there were a lot of physics/chemistry majors in the group. These people are probably learning from a pragmatic perspective and could probably care less about proofs, so as long as they pass they are happy.
The chapters from the book that I read in detail (12-19) I found to be full of great illustrations and examples and were presented in a clear logical manner without superfluous material/examples. Starting with the basic tools needed for multivariable calculus (multivariable functions, vector algebra), I found myself grasping topics and ideas very quickly (I aced the course). The exercises were not too difficult and could be solved in a few minutes using the information from the section. The problems require more time and sometimes ideas from other sections/subjects, but none are too difficult. Mostly every topic was given a algebraic and geometric explaination. The book provides a great introduction for beginners while the scope of topics covered appeals to advanced students as well.
In comparison to my old calculus text (Stewart) I found this book to have a lot more material in general that wasn't in Stewart, such as trig sub and fourier series. There is also a chapter on differential equations, which I should probably read before my class starts next semester ;D .
In summary, this review is from the perspective of a young mathematician, and I felt that it was perfect for me to learn from. I liked it enough to keep it. If you are in the same category you will find this to be a wonderful text. It is hard to say whether or not it should be recommended for beginners/non-math students, since I am not one, but from the other reviews on here it seems like some people have had trouble. If that's the case you might want to find a supplement (Standard Deviant's or Cliff's Notes). Learning calculus for the non-math student is not easy, so the best way is to just work harder.
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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).
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In my opinion, unless theory is ingrained in students' heads from the start, they will never even attempt to understand it. After all, the book gives the theory second priority, so why should students pay any attention to it?
Moreover, in the introduction, the book promises to have problem sets that a student "cannot just look for a similar example to solve... you will have to think." However, after working with this book's homework problems, I've found them to be the exact opposite of this! There are plenty of similar examples for any given problem, and as a result the teacher's role becomes trivial, while at the same time students don't really understand anything they're doing. Not only this, but the problems are overly MUNDANE, and there is too much practice for a single concept. If a student has taken calculus, he can do derivatives, so he should not need 31 exercises to learn how to do partial derivatives.
Capping all this off, there are no truly challenging problems at all in this book. All of them focus on mechanical methods rather than clever application of known theory. The biggest challenge in this book, in fact, is keeping your hand intact as you take 50 partial derivatives, and then hit a problem that says "repeat for the second partial derivatives."
Meanwhile, your fine motor skills deteriorate quickly as you overwork them drawing or re-drawing a graph or table every other problem.
Bravo, Debbie Hughes, you can use Mathematica's graphing capabilities to their fullest. We're all proud of you. Now can you keep them out of your textbook? No one wants to see a billion tables staring them in the face, and then have to copy and change a billion more for homework. That's not a way to learn. This whole textbook is just a way to pretend you're learning.
Waiting to really learn anything from this book is like waiting for Richard Simmons to get married. Trust me, it's not gonna happen, folks.
kubkhan
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Unfortunately, Amazon does not offer any way to properly rate this waste of money.
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