A primer of infinitesimal analysis [EBook] / John L. Bell.
A primer of infinitesimal analysis [EBook] / John L. Bell.
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...
Personal Name(s):  Bell, J. L., (author) 

Edition: 
Second edition. 
Imprint: 
Cambridge :
Cambridge University Press,
2008

Physical Description: 
1 online resource (xi, 124 pages) 
Note: 
englisch 
ISBN: 
9780511619625 9780521887182 
Subject (LOC):  
Full Text 
Table of 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 bollardrope
 The KeplerNewton 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 CauchyRiemann equations for complex functions
 The definite integral. Higherorder infinitesimals
 The definite integral
 Higherorder 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.