000			03412nam a22003378i 4500
001			CR9780511619625
003			UkCbUP
005			20200124160255.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090915s2008||||enk o ||1 0|eng|d
020			_a9780511619625 (ebook)
020			_z9780521887182 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA299.82 _b.B45 2008
082	0	0	_a515 _222
100	1		_aBell, J. L. _q(John Lane), _eauthor.
245	1	2	_aA primer of infinitesimal analysis / _cJohn L. Bell.
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c2008.
300			_a1 online resource (xi, 124 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aBasic 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			_aOne 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	_aNonstandard mathematical analysis.
776	0	8	_iPrint version: _z9780521887182
856	4	0	_uhttps://doi.org/10.1017/CBO9780511619625
999			_c519830 _d519828