A Primer of Infinitesimal Analysis 2nd Edition

by John L. Bell (Author)

11 customer reviews

ISBN-13: 978-0521887182

ISBN-10: 0521887186

Why is ISBN important?

Have one to sell? Sell on Amazon

Added to

Unable to add item to List. Please try again.

Buy new

$50.44

Only 2 left in stock (more on the way).

Ships from and sold by Amazon.com.

This item ships to France. Want it Friday, Aug. 31? Order within and choose AmazonGlobal Priority Shipping at checkout. Learn more

List Price: $79.99
Save: $29.55 (37%)

9 New from $50.44

Deliver to

Turn on 1-Click ordering

More Buying Choices

9 New from $50.44 11 Used from $30.60

20 used & new from $30.60

See All Buying Options

Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student

One of the most remarkable recent occurrences in mathematics is the re-founding, on a rigorous basis, the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new and updated edition, basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the "infinitesimal" methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.

Customers who bought this item also bought

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

James M. Henle

30

Paperback
$13.25
Alain M. Robert
Paperback
$14.95
Thomas L. Heath

17

Paperback
$12.60
Thomas L. Heath

13

Paperback
$17.95
Øystein Linnebo

2

Hardcover
$21.33
J. L. Bell

3

Paperback
$16.95

Customers who viewed this item also viewed

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

James M. Henle

30

Paperback
$13.25
Alain M. Robert
Paperback
$14.95

Editorial Reviews

Review

'This might turn out to be a boring, shallow book review: I merely LOVED the book...the explanations are so clear, so considerate; the author must have taught the subject many times, since he anticipates virtually every potential question, concern, and misconception in a student's or reader's mind.' MAA Reviews

'John Bell has done a first rate job in presenting an elementary introduction to this fascinating subject ... I recommend it highly.' J. P. Mayberry, British Journal for the Philosophy of Science

Book Description

In this new edition basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal. This edition also contains an expanded historical and philosophical introduction.

See all Editorial Reviews

Product details

Hardcover: 140 pages
Publisher: Cambridge University Press; 2 edition (April 7, 2008)
Language: English
ISBN-10: 0521887186
ISBN-13: 978-0521887182
Product Dimensions: 6 x 0.6 x 9 inches
Shipping Weight: 11.2 ounces (View shipping rates and policies)
Average Customer Review: 11 customer reviews
Amazon Best Sellers Rank: #2,631,834 in Books (See Top 100 in Books)
- #503 in Books > Science & Math > Mathematics > Pure Mathematics > Combinatorics
- #1210 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #2045 in Books > Science & Math > Mathematics > Mathematical Analysis

Would you like to tell us about a lower price?
If you are a seller for this product, would you like to suggest updates through seller support?

Be the first video

Your name here

Try the Kindle edition and experience these great reading features:

See Kindle Edition

Customer reviews

4.1 out of 5 stars

5 star

4 star

3 star (0%)

2 star (0%)

1 star

Write a customer review

See all 11 customer reviews

Read reviews that mention

Top customer reviews

There was a problem filtering reviews right now. Please try again later.

Colin McLarty

Engaging, novel approach

March 27, 2000

Format: HardcoverVerified Purchase

A recently developed approach to calculus lets Bell go very quickly from the basic definitions up to several interesting applications in geometry and mechanics. This version of calculus bypasses a lot of technical details to focus on the geometric meaning. If you have had analytic geometry then in principle you could read this book. It would be better if you have had some exposure to calculus but you do not need to remember much of it, and this book can quickly take you farther.
Readers who want to get to the applications can skim through much of the first chapter, on historical and philosophic motivations for the approach.
But a word for specialists: the book is also valuable as an exploration of this approach, called "synthetic differential geometry". This was created to make calculus more accessible but most people writing about it have focussed on theoretical investigations, as it involves a number of very new ideas. By writing on the introductory level, with rather advanced geometric applications, Bell has brought out novel aspects of the approach. Logicians and mathematicians interested in this foundation for geometry, or in elementary topos theory, should see what he has done.

32 people found this helpful

Helpful

Not Helpful

Comment

Bruce R. Gilson

An unusual but very interesting book.

September 26, 2003

Format: HardcoverVerified Purchase

I have to compare this book with another one which I recently bought: "Infinitesimal Calculus" by James M. Henle and Eugene M. Kleinberg. Both books are basically the same in that they use the concept of infinitesimals to provide a more intuitively satisfying basis for the concepts of calculus than the common, "delta/epsilon" limit approach. Yet the two could not be more different in the way they go about it.
Henle and Kleinberg's book uses a concept of infinitesimals developed by Abraham Robinson, known as "nonstandard analysis." In this system, an expanded number system, the "hyperreal number system," is created, which obeys almost all the same rules as the real number system but includes infinitesimals (numbers different from zero but smaller in absolute value than any other real number), as well as infinite numbers (larger than any real number) and finite but nonstandard numbers. By contrast, the "smooth infinitesimal analysis" used in this book has no infinite numbers, and does not obey the normal laws of logic (in particular, the law of the excluded middle). Bell is well aware of the difference between these two approaches, and gives detailed and valuable comparisons between them in this book.
Oddly, nothing could be further than infinitesimals from the ideas of the intuitionist mathematicians like L. E. J. Brouwer, yet Bell's logical system is based on the modifications to logic which Brouwer had to make so that his intuitionistic program could work. And Bell refers to his logical system as intuitionistic.
My own personal feeling is that nonstandard analysis has the merits of the logic being familiar and of its being based on the extension of the real number system in a compatible manner, but smooth infinitesimal analysis makes the mathematics easier to _do_ (as, in nonstandard analysis, it is continually necessary to extract the standard part of a nonstandard number, and a corresponding step is unnecessary in smooth infinitesimal analysis). So both have their merit.
Another contrast with Henle & Kleinberg's book is that the other book ignores applications, while this book is strongly oriented toward the use of calculus in physical applications.
I was tempted to give this book 5 stars, but I find the mathematics in some places rather dense and hard to follow, which was my reason for deducting one star. But I am glad to own both of the two books, this one and Henle & Kleinberg's.

50 people found this helpful

Helpful

Not Helpful

Comment

Freethinker

Nilpotent infinitesimals

January 1, 2015

Format: HardcoverVerified Purchase

Extremely interesting read! Definitely not for beginners. This is smooth infinitesimal analysis involving nilpotent non-invertible infinitesimals. These are non-zero infinitesimals whose "squares" are zero that are used in synthetic differential geometry. These are very unlike the infinitesimals used in Keisler's and Henle's books. Historically they are more like Nieuwentijdt's infinitesimals than Leibnitz infinitesimals. Highly recommended for those with some mathematical logic and set theory background,

One person found this helpful

Comment

December 18, 2013

Format: Kindle EditionVerified Purchase

Description: Elementary infinitesimal analysis of non-invertible infinitesimals. This is not about non-standard analysis.

Pros:
1. Reads well and quickly.
2. Author starts at foundation and works well through to the principles.
3. Clearly works out problems and shows application.

Cons:
1. Does not actually outline the proofs of principles step-by-step and makes some small syntactic mistakes.

Helpful

Not Helpful

Comment

Most recent customer reviews

Jason Dowd

Highly Recommended for Physics Students

Physics students face a serious problem in that physics books are littered with calculations involving infinitesimals while math books are essentially devoid of them.Read more

Published on May 6, 2012

David Karapetyan

Another perspective on infinitesimals

A bit philosophically heavy at times and initially the loss of the law of the excluded middle is a little disconcerting but one gets used to the new logic quickly enough.

Published on May 17, 2009

aethr

Calculus Done Right

Or maybe just a very good introduction to a variation on infinitesimal analysis. As someone who disliked limits the first time I came across them, and having watched students I...Read more

Published on July 20, 2006

Sam

Important Book

What lurks behind the approach taken in this

important and finely-rendered book is not widely

appreciated. Why so slow everyone?Read more

Published on January 24, 2005

jeremy.jae@cell.matrix.cn

A Mathematical Jewel of the Nile and the Stone of Philosophy

I originally came accross this beautiful text in 98 at a bookstore when it was first released. I purchased another copy recently when I could not locate my original.Read more

Published on September 6, 2003

Jeffrey Marshall Albert

Apology

Having read Dr. Bell's book again (at a somewhat more leisurely pace than at first) and having explored some of his sources (primarily Kock and Moerdijk) I must apologize for my...Read more

Published on May 23, 2000

Set up an Amazon Giveaway

Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway

This item: A Primer of Infinitesimal Analysis

Set up a giveaway