A primer of infinitesimal analysis:
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 so...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xi, 124 pages) |
| ISBN: | 9780511619625 |
| DOI: | 10.1017/CBO9780511619625 |
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|---|---|
| any_adam_object | |
| author | Bell, J. L. |
| author_facet | Bell, J. L. |
| author_role | aut |
| author_sort | Bell, J. L. |
| author_variant | j l b jl jlb |
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| bvnumber | BV043943427 |
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| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511619625 (OCoLC)850968706 (DE-599)BVBBV043943427 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511619625 |
| edition | Second edition |
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| institution | BVB |
| isbn | 9780511619625 |
| language | English |
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| spelling | Bell, J. L. Verfasser aut A primer of infinitesimal analysis John L. Bell Second edition Cambridge Cambridge University Press 2008 1 online resource (xi, 124 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Nonstandard mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-88718-2 https://doi.org/10.1017/CBO9780511619625 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bell, J. L. A primer of infinitesimal analysis 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 Nonstandard mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4072798-1 |
| title | A primer of infinitesimal analysis |
| title_auth | A primer of infinitesimal analysis |
| title_exact_search | A primer of infinitesimal analysis |
| title_full | A primer of infinitesimal analysis John L. Bell |
| title_fullStr | A primer of infinitesimal analysis John L. Bell |
| title_full_unstemmed | A primer of infinitesimal analysis John L. Bell |
| title_short | A primer of infinitesimal analysis |
| title_sort | a primer of infinitesimal analysis |
| topic | Nonstandard mathematical analysis Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Nonstandard mathematical analysis Infinitesimalrechnung |
| url | https://doi.org/10.1017/CBO9780511619625 |
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