Customer Reviews

Calculus: A New Horizon, Combined, 6th Edition

5 star:		(18)
4 star:		(3)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

I have taught Calculus at the University level for well over 20 years now. When I first arrived, the school had already adopted the 1st edition of Anton's Calculus, and the school (and myself) have liked it so much that we have stuck with Anton for 20 years, until 2000. For some reason, the Math Department has decided to change to Stewart's book. Let me tell you, Anton's book is most certainly the best. The examples actually explain the concept, the concepts are explained coherently in words before the mathematics is presented, graphs are abundant where necessary, and the book eases students into Calculus. I have found that deficiencies in trigonometry plague students through the calculus sequence. Mr. Anton provides a thorough review in Appendix 1, which clears up the problems. Also, Chapter 1 is a review of Algebra and Coordinate Geometry. This gets students into a mental framework necessary to learn Limits (Chap 2), Differentiation (Chaps 3-4), Integration (Chaps 5-6), Logs and Exponential Functions (Chap7), etc. My ONLY complaint about this book is the way Anton leaves logs and the number e out until Chap 7. Students are expected to learn it all at once, where I feel it would be better distributed throughout the exercise sets. But, again, that is my ONLY complaint. IF YOU WANT YOUR STUDENTS TO BE SUCCESSFUL IN CALCULUS, CHOOSE THIS TEXT. It truly beats the pants off Stewart's book!

To add a bit more information to the raw data of these reviews, I've mapped the universe of all possible readers of this book onto a set of x-y axes. Let the x-axis run from "non-Math-types" up through "Math-types." Let they y-axis go from "non-geniuses" up through "geniuses:"

- Quadrant I: genius Math-types will probably be both irritated and bored with this book. Their irritation will spring from the fact that not all of the pure-math proofs they'll be looking for are here. The book focuses more on explaining and doing calculus than on proving it. Most of the material is proven (properly: no missing steps), but the proofs that would get in the way of doing calculus are omitted. Quadrant Is will be bored because the author does his best to pound on a topic until practically everyone can understand it. Genius math-types, since they're inherently capable of grasping this material from proofs alone, will not be pleased by this repetition. For Quadrant Is, some version of Tom M. Apostol's Calculus books (ISBNs 9686708103, 842915003X, 8429150013, 0471000051, 0471503037, 0471000078, or 0471000086) would be a better text.

- Quadrant II: genius non-Math-types will probably prefer the fact that the author skipped some proofs in favor of applications. However, like the Quadrant Is, they'll probably be somewhat bored by the author's "slowness" in moving on after he introduces a topic. This book will be OK for them, but they'd probably prefer a more "terse" presentation. Unfortunately, I don't have any recommendations for such a book.

- Quadrant III: non-genius non-Math-types (i.e., "normal" people), will find this book just right. As noted above, the author's focus is on teaching and using calculus, not *necessarily* on proving it. If the proofs are complex enough that they'd distract from that mission, they're either relegated to Appendix G or omitted (though most proofs are present). Best of all, the author doesn't skip steps in his proofs: all the steps are there in their detailed glory. Later in the book, he will occasionally skip a simplification of an expression, but none of the "proof" material is missing. In the latter half of the book, he sometimes does the "proof is left as an exercise for the student" routine, but those are for non-essential proofs. After the author introduces a topic/theorem/method, he always gives multiple (at least three) examples. So, if the readers are having trouble with the equations and proofs, they'll have several chances to figure out what he means from the examples. Also, all the odd problems have answers in the back of the book. There are no steps included with the answers, but usually that's not a problem (since there are so many examples in the book). I also found the appendices giving explanations of pre-Calculus math facts very useful: it's been a long time since I've seen those things, so I needed the refresher.

- Quadrant IV: non-genius Math-types will join the Quadrant Is in disliking the skipping of several proofs, but, like the Quadrant IIIs, will be pleased with the thorough, step-by-step nature of the existing proofs. Not the best choice of a textbook for them, but for those who are having trouble with a "pure math" Calculus book, this is a good supplement.

Overall, this is an excellent book (I rate it 5 stars out of 5). The author did a wonderful job matching his material to his chosen audience (Quadrant III, "normal" people). For non-genius non-math-types, I highly recommend it. For genius non-math-types and non-genius math-types, it's OK. Genius math-types should avoid it and try something like Apostol's Calculus.

After taking differential calculus, integral calculus, and elementary differential equations, I took a year off of college. Then when I came back, I had forgotten alot of things concerning those courses. Well, I bought this book because it had the most pages and seemed to cover the most information. Well, it was a good buy! It covered ALL of the material that I had covered in those 3 previous courses. It was a great book for refreshing my memory. This would also be a great book for learning calc for the first time also.

Anton's Calculus textbook is the best I have ran across. It is a fantastic text, most of the proofs are worked out and for the most part easy to follow. His writing style is clear and extensive in which he avoids being dense which is a common pitfall in many math textbooks.. (Especially Calculus.) The problems are generally the right difficulty, and the examples are generally very good. He spends a lot of time concentrating on concepts over computational techniques. Paraphrasing, I completely agree with his preface in which its more important to understand the concepts. . . because every problem in the book has been computationally solved, understanding the concepts is the most important thing. This is especially true of the at times esoteric and difficult subject of vector calculus at the end of the text. Anton also integrates (no pun intended) the use of CAS and graphing calculators in his text.

The down side to the book is probably its price. It is a very expensive book!

As good as this book is, Calculus is a hard subject matter. the textbook alone is not enough. Supplement it with a great teacher and a lot of hard work and one should learn calculus very well.

Our school used this book for calc 3 and I'm very happy with the selection.
Our teacher taught the theory part of the material. He rarely taught how to do the work (he relied on the book to do that and it was very understandable and taught well). The teacher's theory helped to get the material to our long term memories so hopefully your teachers' are using the same method.

So if you need a book to show you how to work through the problems of Calc 3, buy this one, it'll do the job.

I thought I was terrible at math until I picked up this book for a college calculus course. In contrast to virtually every other math textbook I'd ever been forced to use, this book explained concepts clearly and simply, providing examples that increased gradually in complexity. I happened to have a good professor that semester, but whenever I didn't understand something in class, I taught myself from this textbook. It was a rare pleasure to feel I could learn such a difficult subject independently. I ended up getting an A in the class - and more importantly, I learned I wasn't bad at math at all.

THE GREATEST WEAKNESS STUDENTS BRING TO CALCULUS IS A POOR FOUNDATION IN ALGEBRA - ESPECIALLY THE STANDARD TOPICS OF PRECALCULUS. ANTON APPARENTLY AGREES BECAUSE THE PRECALCULUS REVIEW IN THE BACK OF THE BOOK AND THE SPRINKLINGS OF PRECALCULUS THROUGHOUT THE TEXT, WHICH SERVE AS A REVIEW AND INTRODUCTION TO CALCULUS TOPICS, ARE GREAT. TRULY, THIS CALCULUS TEXT CONTAINS A PRECALCULUS SUBTEXT THAT IS BETTER THAN A STANDARD PRECALCULUS COURSE. AS FOR THE CALCULUS, BRAVO, BRAVO, BRAVO. THIS IS THE BEST TEXT I HAVE EVER SEEN. THERE IS ANTON AND ALL OTHERS.

Anton's is the quintessential magnum opus of calculus. It is written with the struggling students in mind, and the advanced at heart; with its enlightening exposition yet perfectly rigorous derivations. The clear explanation goes unrivaled, and the beautifully told history of mathematicians simply entertains and inspires.

Anton apparently would not let any competition in the aesthetic department either. Not only are the illustrations visually appealing, but they speak the language of clarity no word can possibly capture. A true example of the intertwined worlds of mathematics and art.

In the Platonistic realm of Ideals, Anton's is The Book.

This is the most relevant calculus book to all specializations. Howard Anton clearly explains the mathematical ideas. It is excellent for those interested in mathematical modeling. You can also do mathematics during your leisure time with this book because the author gives some brief historical background of famous mathematicians.

If you are a serious student of Calculus, go get Anton's Calculus. I am a Math teacher in Malaysia and a long time user of Anton's Calculus since his 3rd edition. I teach Calculus the traditonal way because in my country we are still new to the computers. Prof Anton has written books in his previous editions in a lively and refreshing manner that I could read his book again and again without getting bored. I may be old-fashioned, but as a fan of Anton, reading his latest 6th editions is such a delight, and only recently I have just learned how to make use of software like Maple, I could see Anton's Calculus paving my way into new explorations, as his new book says, Calculus: A New Horizon indeed. Buy Anton's Calculus, I am sure you will not regret.