About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521624010

ISBN-139780521624015

eBay Product ID (ePID)1051717

Product Key Features

Number of Pages136 Pages

LanguageEnglish

Publication NamePrimer of Infinitesimal Analysis

Publication Year1998

SubjectTransformations, Logic, Mathematical Analysis

TypeTextbook

Subject AreaMathematics

AuthorJohn L. Bell

FormatHardcover

Dimensions

Item Height0.6 in

Item Weight12.2 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN97-041877

Reviews'The book will be of interest to philosophically orientated mathematicians and logicians.'European Mathematical Society, "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, Marion Cohen, University of the Sciences, Philadelphia, ‘The book will be of interest to philosophically orientated mathematicians and logicians.’European Mathematical Society, 'The book will be of interest to philosophically orientated mathematicians and logicians.' European Mathematical Society

Dewey Edition21

TitleLeadingA

IllustratedYes

Dewey Decimal515

Table Of Content1. Basic features of smooth worlds; 2. Basic differential calculus; 3. First applications of the differential calculus; 4. Applications to physics; 5. Multivariable calculus and applications; 6. The definite integral: Higher order infinitesimals; 7. Synthetic geometry; 8. Smooth infinitesimal analysis as an axiomatic system; Appendix; Models for smooth infinitesimal analysis.

SynopsisOne of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion that played an important role in the early development of the calculus and mathematical analysis. In this book, 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, literally, to zero. As the author shows, 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. The text also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an Appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible., One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion that played an important role in the early development of the calculus and mathematical analysis. In this book, 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, literally, to zero. As the author shows, 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. The text also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an Appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible., One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this book, 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, literally, to zero. As we show, 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. The book also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible., This book provides an approach to the calculus and its applications to physical problems using a concept of the infinitesimal - that is, of a quantity so small that, while not necessarily zero, it is nevertheless smaller than any finite quantity. This approach enables the calculus to be presented in a particularly straightforward way, avoiding the usual complication associated with the subject. This is the first elementary book to employ the so-called 'zero-square' infinitesimals, and so at the moment it really has no direct competition.

LC Classification NumberQA299.82 .B45 1998