Calculus: A New Horizon

by Howard Anton

The new Sixth Edition of Anton's Calculus is a contemporary text that incorporates the best features of calculus reform, yet preserves the main structure of an established, traditional calculus text. This book is intended for those who want to move slowly into the reform movement. The new edition retains its accessible writing style and a high standard of mathematical precision.

Genres: Mathematics, Nonfiction

1312 pages, Hardcover

First published January 1, 1992

About the author

Howard Anton obtained his B.A. from Lehigh University, his M.A. from the University of Illinois, and his Ph.D. from the Polytechnic University of Brooklyn, all in mathematics. In the early 1960's he worked for Burroughs Corporation and Avco Corporation at Cape Canaveral, Florida, where he was involved with the manned space program. In 1968 he joined the Mathematics Department at Drexel University, where he taught full time until 1983. Since that time he has been an adjunct professor at Drexel and has devoted the majority of his time to textbook writing and activities for mathematical associations. Dr. Anton was president of the EPADEL Section of the Mathematical Association of America (MAA), Served on the board of Governors of that organization, and guided the creation of the Student Chapters of the MAA. He has published numerous research papers in functional analysis, approximation theory, and topology, as well as pedagogical papers. He is best known for his textbooks in mathematics, which are among the most widely used in the world. There are currently more than one hundred versions of his books, including translations into Spanish, Arabic, Portuguese, Italian, Indonesian, French, Japanese, Chinese, Hebrew, and German. For relaxation, Dr. Anton enjoys traveling and photography.

Reviews

[astaliegurec · Rating 5 out of 5]

5.0 out of 5 stars
Excellent Calculus Book for "Normal" People
January 21, 2005

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.

[Astrila · Rating 5 out of 5]

Anton rocks da house :)

[AbdElsatar · Rating 4 out of 5]

It is a great reference for calculus students
it covers a wide range of topics, including:
Limits and continuity
Differentiation (derivatives)
Integration (integrals)
Applications of differentiation and integration
Infinite series
Vectors and multivariable calculus