A primer of infinitesimal analysis / (Record no. 519830)
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| 000 -LEADER | |
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| fixed length control field | 03412nam a22003378i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511619625 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160255.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090915s2008||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511619625 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521887182 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA299.82 |
| Item number | .B45 2008 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Bell, J. L. |
| Fuller form of name | (John Lane), |
| Relator term | author. |
| 245 12 - TITLE STATEMENT | |
| Title | A primer of infinitesimal analysis / |
| Statement of responsibility, etc | John L. Bell. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | Second edition. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2008. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xi, 124 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Basic features of smooth worlds -- Basic differential calculus -- The derivative of a function -- Stationary points of functions -- Areas under curves and the constancy principle -- The special functions -- First applications of the differential calculus -- Areas and volumes -- Volumes of revolution -- Arc length; surfaces of revolution; curvature -- Application to physics -- Moments of inertia -- Centres of mass -- Pappus' theorems -- Centres of pressure -- Stretching a spring -- Flexure of beams -- The catenary, the loaded chain, and the bollard-rope -- The Kepler-Newton areal law of motion under a central force -- Multivariable calculus and applications -- Partial derivatives -- Stationary values of functions -- Theory of surfaces. Spacetime metrics -- The heat equation -- The basic equations of hydrodynamics -- The wave equation -- The Cauchy-Riemann equations for complex functions -- The definite integral. Higher-order infinitesimals -- The definite integral -- Higher-order infinitesimals and Taylor's theorem -- The three natural microneighbourhoods of zero -- Synthetic differential geometry -- Tangent vectors and tangent spaces -- Vector fields -- Differentials and directional derivatives -- Smooth infinitesimal analysis as an axiomatic system -- Natural numbers in smooth worlds -- Nonstandard analysis. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 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 - that is, a quantity so small that its square and all higher powers can be set, literally, 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Nonstandard mathematical analysis. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521887182 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511619625">https://doi.org/10.1017/CBO9780511619625</a> |
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