A primer of infinitesimal analysis
By: John L. Bell.
Edition: 2nd ed.
Publisher: Cambridge University Press
Published: 2008
Place of publication: Cambridge; New York
Language: eng
Number of pages: 124
ISBN-13: 9780521887182
Subjects: Nonstandard mathematical analysis
Notes: Includes bibliographical references (p. 121-122) and index.
Table of contents: title: Basic features of smooth worlds; title: Basic differential calculus; title: The derivative of a function; title: Stationary points of functions; title: Areas under curves and the constancy principle; title: The special functions; title: First applications of the differential calculus; title: Areas and volumes; title: Volumes of revolution; title: Arc length; surfaces of revolution; curvature; title: Application to physics; title: Moments of inertia; title: Centres of mass; title: Pappus' theorems; title: Centres of pressure; title: Stretching a spring; title: Flexure of beams; title: The catenary, the loaded chain, and the bollard-rope; title: The Kepler-Newton areal law of motion under a central force; title: Multivariable calculus and applications; title: Partial derivatives; title: Stationary values of functions; title: Theory of surfaces. Spacetime metrics; title: The heat equation; title: The basic equations of hydrodynamics; title: The wave equation; title: The Cauchy-Riemann equations for complex functions; title: The definite integral. Higher-order infinitesimals; title: The definite integral; title: Higher-order infinitesimals and Taylor's theorem; title: The three natural microneighbourhoods of zero; title: Synthetic differential geometry; title: Tangent vectors and tangent spaces; title: Vector fields; title: Differentials and directional derivatives; title: Smooth infinitesimal analysis as an axiomatic system; title: Natural numbers in smooth worlds; title: Nonstandard analysis.