An account of the essentials of calculus, presented in a style that is designed to be both readable and mathematically precise. Concepts and central ideas are emphasized throughout. Physical examples and interpretations play a leading role, and alternative approaches to fundamental ways of thinking are provided to help the student develop the intuitive understanding so important in science and engineering. Many questions and problems, with detailed solutions, are offered to encourage active reading and independent thought. The volume can either be used as a basic classroom text, as a self-study text, or as a supplement that will give the reader a grasp of calculus as a whole.
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"The author succeeds well in giving an excellent intuitive introduction while ultimately maintaining a healthy respect for rigor." -- Zentralblatt MATH, 2003
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36 of 36 people found the following review helpful
5.0 out of 5 stars
One of the best books I've seen, though untraditionally organized
October 31, 2007
Format:Paperback|Amazon Verified Purchase
I am at this time familiar with four other books which use infinitesimals in whole or in part to explain the calculus, an approach which was ruled out in the 19th century but has more recently been shown (by Abraham Robinson) to be mathematically justified, and an approach that is closer to the way most scientists USE calculus than the rigorously (epsilon/delta) defined limits of traditional calculus texts. One of those four, by H. J. Keisler (who edited Robinson's papers) is now out of print, though I have been informed that it is available by download on the Internet (of course, printing a book of over 1000 pages will add to your costs!). The other three have been earlier reviewed by me. Henle and Kleinberg's book, "Infinitesimal Calculus," is a slim book, which explains the concepts well, but does not go much into the applications or techniques. I gave it 4 stars, because what it does, it does well, but it doesn't do everything one might want in a calculus text. Bell's book, "A Primer of Infinitesimal Analysis," is harder going but covers more in the way of applications. Neither of the two provides a lot of practice in techniques. Sparks' book, "Calculus Without Limits: Almost," is a very intuitive approach, geared very much to the prospective working scientist, but short on the kind of proofs that mathematicians would insist on. Of the three, I think Sparks' book was, up to now, the best for teaching that I've seen. But after looking at Comenetz' book, I prefer it, provided that you are teaching relatively good students.
If your students just barely got through algebra, they would find this book a little rough going. Sparks' more intuitive approach might be better. But for a prospective physicist or engineer who is not too weak in math to see (and try his hand at) some proofs, I would recommend this book. One of the strong points is that Comenetz never strays far from the idea that calculus is not just slopes and areas, but can be applied to a lot of types of problems (though almost exclusively taking physics-related ones). Many people think of a derivative as a slope or an integral as an area, and fail to see that anything that can be thought of as a rate of change or the accumulation of small bits is an example of the type of things calculus handles. Comenetz tries to dispel this attitude.
As I said, this is a harder book than Sparks' book (though easier, I think, than Bell's!) But if you want to understand things on a more fundamental basis, I think this book is the best of the lot. The other three books which I reviewed all got four stars from me; this gets five. So this should clue you into the fact that I think this the best one of the bunch.
If your students just barely got through algebra, they would find this book a little rough going. Sparks' more intuitive approach might be better. But for a prospective physicist or engineer who is not too weak in math to see (and try his hand at) some proofs, I would recommend this book. One of the strong points is that Comenetz never strays far from the idea that calculus is not just slopes and areas, but can be applied to a lot of types of problems (though almost exclusively taking physics-related ones). Many people think of a derivative as a slope or an integral as an area, and fail to see that anything that can be thought of as a rate of change or the accumulation of small bits is an example of the type of things calculus handles. Comenetz tries to dispel this attitude.
As I said, this is a harder book than Sparks' book (though easier, I think, than Bell's!) But if you want to understand things on a more fundamental basis, I think this book is the best of the lot. The other three books which I reviewed all got four stars from me; this gets five. So this should clue you into the fact that I think this the best one of the bunch.
30 of 31 people found the following review helpful
Format:Paperback
It's no secret to anybody that knows me that I am Calculus illiterate. I've taken three courses, failing once and just passing the other two times. I entered into the Master's program in Hydrology and soon began realizing that I would actually need to understand the principles of Calculus in order to successfully complete my coursework and thesis research.
I picked up a copy of Michael Comenetz' book "Calculus: The Elements" and began reading it, hoping that by some cosmic chance I might understand something that he had written. I'd done this with several other Calculus texts, only to find that I was still clueless.
Dr. Comenetz' book was the answer to my problems. He lays out fundamental concepts in easy to understand format. For the first time in my entire life, I understand the basics of Calculus and it's all thanks to this book!
I highly recommend this book if you're a "math illiterate" like myself but need to understand the complex subject of Calculus. Other texts that I've encountered simply have not been sufficient. THIS particular text has changed my entire mindset on the subject. Before the book, I thought "There's no reason to ever use this subject, and I'll never understand it anyway." After reading it, I'm understanding Calculus and actually considering taking an advanced course in the subject.
Thanks Dr. Comenetz!
I picked up a copy of Michael Comenetz' book "Calculus: The Elements" and began reading it, hoping that by some cosmic chance I might understand something that he had written. I'd done this with several other Calculus texts, only to find that I was still clueless.
Dr. Comenetz' book was the answer to my problems. He lays out fundamental concepts in easy to understand format. For the first time in my entire life, I understand the basics of Calculus and it's all thanks to this book!
I highly recommend this book if you're a "math illiterate" like myself but need to understand the complex subject of Calculus. Other texts that I've encountered simply have not been sufficient. THIS particular text has changed my entire mindset on the subject. Before the book, I thought "There's no reason to ever use this subject, and I'll never understand it anyway." After reading it, I'm understanding Calculus and actually considering taking an advanced course in the subject.
Thanks Dr. Comenetz!
19 of 19 people found the following review helpful
Format:Hardcover
This book presents all of the key topical areas to provide a basis for understanding calculus. It begins with the most basic or fundamental building blocks (this is the hardpart for most of us)and leads to a complete development of the topic. The fundamentals are presented and all you have to do is put forth the time and effort to stay with the material. You will be rewarded. Those who are also interested in proofs will be provided all of the details. The liberal use of technical examples help the reader grasp the fundamentals.
Most Recent Customer Reviews
5.0 out of 5 stars
Integrated approach
In high school I kept trying to puzzle out _why_ analysis works the way it does, trying, in other words, to translate math into the sort of verbal propositions I was already... Read more
Published on August 3, 2009 by Chris C. Hill
5.0 out of 5 stars
Best Textbook on Calculus--Concise & Fun to Read & Comprehensive
It's no doubt that Stewart's book is the most popuplar textbook on Calculus. It's comprehensive and standard. Read more
Published on November 21, 2008 by Physicsmind
5.0 out of 5 stars
Grasp the fundamentals
This is by far the book to have to grasp and retain the fundamentals of calculus. It starts a topic by building from the most basic(the part that is the hardest for most) and... Read more
Published on February 27, 2004 by Michael S. Krupka
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