My College Calculus professor uses this book as a suppliment to provide examples for the class use. Everyone hates the problems as they are vague and lack any explanation on how to solve the problem or even where to begin. It appears to me that someone wrote a book simply to create problems that cannot be solved by the book's explanations. Calculus requires a working understanding of the ideas and concepts of the base math before an sort of obscure application should be used. I would not recommend this book to anyone, unless they already have a good understanding of calculus and wish to delve further into the application of the math to the real world. In that case, buy the book. For the other 95% that are just wanting to learn calculus; go buy a different book that teaches you something first.

In my experience with this text, students either love it or hate it. They hate it because it does not offer a brief overview of the topics, like many more popular calculus text books. Instead "Calculus: Single Variable" requires that a student throughly read many examples as it explains rules and laws along the way. Those who love the text do so because the examples offer a firmer understanding of the concepts at hand, instead of just covering enough material to answer the questions at the end of each section. Although this is a very good text book, it definitely requires patience on behalf of the reader, and may not be the book for students who just want to slide by.

This book was used for my Fall 2002 Calculus III (multivariable) class. We used the last section of the book, chapters 12-19. I was able to review old concepts when needed from the earlier chapters, which were presented nicely.

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.

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.

Teaching with this text - which I've been doing for the past two semesters - is an uphill battle, to say the least. It's a text designed for non-majors; I teach business and social science students. Instructors of these sorts of students need to convince their pupils that they DO need to know how to reason mathematically, and that math IS relevant to their life plans - they can't just rely on their calculators to do all their work for them. When the textbook seems to disagree, our job is all the more difficult.

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).

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.

Besides the picture on the front, this book is horrible! I've learned more by personal derivation and experimenting than through this book. The explanations are overly bloated, and include so many approximations and tables that the theory behind this book's ramblings is lost completely. Instead of focusing on theoretical multivariable calculus while introducing, as a short diversion an approximating method, this book builds around a foundation of approximations, which clouds the actual mathematics in the process.

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

"This innovative book is the product of an NSF funded calculus consortium based at Harvard University and was developed as part of the calculus reform movement" Beware of Harvard, i.e. reform Calculus. Instead of teaching people about maxima and minima, you show them how to use a calculator to guess. What a load of junk. Nobody learns what anything means, just how to apply formulas, etc. It is a shame what books and authors like these are doing to college mathematics. This book is particularly bad, a whole bunch of fluff, not a damn ounce of substance.

I have to disagree with my fellow Californians and unfortunately agree with someone from New York. This is an excellent foundation overview without the clutter of Anton's and Stewart's books. I found it to be a conveniently carried paperback and an enjoyable read.

Skipped around leaving some odd problems out of book. Only explained a few problems in total detail. This is by far the worst solutions manual on the market. Bring it back for a refund before its to late.

This is, without a doubt, the most incredibly worthless book I have come across in my college experience. I am getting an A in Calculus in spite of, and NOT because of this book. The so-called "Harvard Method" leaves the student with the concepts of calculus, but with none of the tools to actually perform the operations. If you get stuck with this as a required text, I strongly recommend you also purchase a traditional calculus text to actually learn from.

I used this book about three years ago for all my three calculus classes, and most of my classmates liked it. We found this book to be very challenging because it made us think all semester long. We also liked it because our professor explained every single example of the book; most of all, they were very explained by our professor. Now I am looking forward to see the new edition of the book.

This "solutions manual" only offers answers for every fourth question. The most painful part is that the so-called solutions are merely the answers from the back of the text book put into complete sentences; there is NO additional instruction.

Unfortunately, Amazon does not offer any way to properly rate this waste of money.

This book is so pathetically minimal that I award it...1/10 of a star. (It may be useful in starting a fire in your fireplace...maybe). DO NOT WASTE YOUR MONEY ON THIS SOLUTION MANUAL! It only includes about every other odd solution, and most of the time, it shows just the (often incorrect) answer. The worst part is, that same answer is usually in the back of the textbook! It is definitely not worth even $5.00, so save your money!