00000cam a22000003i 4500 UP-1685594773861725562 Buklod 20090728084421.0 j|||||||||||||| | ta 180201s2008 nyua rb |||1 u|eng d 9780521887182 (hardback) (iLib)UPBAG-00006174898 BC-57704 Forefornt Php3,780.00 DLC BAG rda eng QA 299.82 B44 2008 Bell, J. L. (John Lane) author. A primer of infinitesimal analysis John L. Bell. Second edition. New York, NY Cambridge University Press 2008. xi, 124 pages illustrations 24 cm Includes bibliographical references (pages 121-122) and index. 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. FO UPBAG UPBAG-MAIN QA 299.82 B44 2008 Book