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What Is Calculus About? (New Mathematical Library) Paperback – January 1, 1962

ISBN-13: 978-0883856024 ISBN-10: 0883856026 Edition: Volume 2

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Product Details

  • Series: New Mathematical Library
  • Paperback: 118 pages
  • Publisher: Mathematical Association of America; Volume 2 edition (1962)
  • Language: English
  • ISBN-10: 0883856026
  • ISBN-13: 978-0883856024
  • Product Dimensions: 5.9 x 8.6 inches
  • Shipping Weight: 5.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #1,184,534 in Books (See Top 100 in Books)

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Customer Reviews

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Truly one of the greatest Mathematics teachers ever.
Southern Jameson West
W.W. Sawyer wrote several math books and this is one of his popular ones still sought after and very valuable today.
Criz Romero
Plenty with examples presented in a simple form that makes a very difficult subject possible to understand.
Thom Erik Johannessen

Most Helpful Customer Reviews

26 of 26 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on August 27, 2002
Format: Paperback
Whenever I teach calculus, my emphasis is always on the fact that the basic ideas of calculus can be understood by almost anyone. While I am not always successful in proving this to the students, Sawyer certainly would be. His explanations of the basics of a derivative are the clearest, most understandable that I have ever seen. There are many diagrams, and each one has a specific purpose and they are well integrated into the textual explanations.
This is not a book that you could use to teach a college calculus course. The mandatory epsilons and deltas that form the backbone of basic calculus are mentioned only as an incidental. Sawyer sets out to explain the foundation ideas of calculus in terms of everyday occurrences and for that reason it is better suited to someone who is curious about calculus. However, it could be used as a supplemental text in the foundations of science, as calculus is used in all areas of change, which describes almost all of nature.
While the notation of mathematics is concise, abstract and often appears esoteric, many of the ideas expressed in that notation are quite easy to follow. In this book, Sawyer explains what calculus is all about in terms that anyone who understands motion can follow. There needs to be more people like him writing books like this.
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15 of 17 people found the following review helpful By Southern Jameson West on March 30, 2009
Format: Paperback Verified Purchase
It all began one winter's night.

Forty years ago and one month on the February winter night of the lunar eclipse in North America in 1968 was the day I began to read W.W. Sawyer's "What is Calculus About?" And my life was forever changed.

I had never read a style of writing up to that point on any topic that exuded as much confidence, as much philosophy of learning and conveyed as much mystery, the mystery of how to handle infinity as that deceptively small book.

I had known about the concept of infinity but up to that point did not know that you could calculate with it. That is take limits. Take derivatives. Then work backwards. But when Sawyer explained it it was like watching a professional magician. There was it could be said a "fresh rebelliousness" in his attitude toward Mathematics understanding and its teaching. It was as if reading his words got you directly in contact with the minds of Newton and Leibnitz and other mathematicians of that "happy-go-lucky" era that Sawyer talks about in his book.

Everyone had warned me at the time that I wouldn't be able to learn Calculus on my own. That it was this mathematics that was so special that it was for many impossible to learn especially if you studied it by yourself. That is was somehow an unattainable goal. That I would somehow "ruin" my learning. It was amazing the degree of prejudice that at that time prevailed.

But they were all wrong. I ended up mastering it. And then the "fur really began to fly". I wasn't supposed to have understood it. I was as one science ( later to be my physics teacher) teacher said: "in way over my head...and if I didn't watch it I'd wind up ruining my career...life..you name it." It was the sixties, the 1960's and my parents generation were total reactionaries.
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14 of 17 people found the following review helpful By N. F. Taussig on August 20, 2004
Format: Paperback
Sawyer's text introduces the concept of the derivative to students who are preparing to take a calculus course. Since Sawyer assumes only a solid foundation in algebra and some experience with graphing functions, the text is accessible to the lay reader. He takes an inutitive approach; formal definitions and proofs are not provided.

Sawyer begins his study of the derivative by looking at velocity. He describes the difference between average and instanteous velocity. He shows that instanteous velocity, the derivative of the position function, can be obtained as the limit of the average velocities as the time interval approaches zero. Sawyer then defines the derivative as the slope of the tangent line to a curve at a point, provided it exists. He shows that this definition is equivalent to the first. To keep things simple, he confines his attention to polynomial functions and reciprocal powers of the variable.

Sawyer uses his results to show how the derivative can be used to describe acceleration, curvature, and the behavior of graphs. The final chapters describe, without going into detail, how (integral) calculus can be used to compute areas and volumes and how calculus can lead to nonintuitve results.

Sawyer employs many diagrams and well-chosen examples to show why the formulas that he derives are reasonable. However, I think that formal definitions and proofs would have made his arguments far more convincing. Sawyer stresses conceptual understanding of the derivative, but the exercises, for which answers are provided in the back of the text, consist mostly of repetitive applications of the formulas he derives in his exposition.

The material in this text is covered in good calculus texts, making this text superfluous for students taking calculus. It is best suited to students who want to understand the basic concepts of calculus without having to deal with the formal machinery of calculus.
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1 of 1 people found the following review helpful By Thom Erik Johannessen on October 29, 2012
Format: Paperback Verified Purchase
A very good book. Plenty with examples presented in a simple form that makes a very difficult subject possible to understand. I can recomend this book to any one who whish to learn what calculus is all about.
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2 of 3 people found the following review helpful By Roger Q. Callaway on February 18, 2013
Format: Paperback Verified Purchase
My 1st semester calculus prof said that I would either get calculus, or not. I didn't feel anything. Eventually I moved on to Geology, where I have; made sort of a living for 40 years, had some great times, met some great people, and generally developed a negative attitude towards engineers.

Finally, I bought this book which led me through a brilliant demonstration of the derivation of a limit. If you are beginning in calculus and feeling lost, buy this book. Once you grasp the basics of calculus, you can try something more honorable than engineering; maybe even geology.
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