Non-standard Analysis

Front Cover
Princeton University Press, 1974 - Mathematics - 293 pages

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

 

Contents

GENERAL INTRODUCTION
1
TOOLS FROM LOGIC
6
DIFFERENTIAL AND INTEGRAL CALCULUS
49
GENERAL TOPOLOGY
89
FUNCTIONS OF A REAL VARIABLE
123
FUNCTIONS OF A COMPLEX VARIABLE
147
LINEAR SPACES
177
TOPOLOGICAL GROUPS AND LIE GROUPS
202
SELECTED TOPICS
230
CONCERNING THE HISTORY OF THE CALCULUS
260
Copyright

Other editions - View all

Non-standard Analysis
Abraham Robinson
Limited preview - 2016
Non-standard Analysis
Abraham Robinson
Snippet view - 1974
Non-standard Analysis
Abraham Robinson
Snippet view - 1974
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Common terms and phrases

analytic arbitrary assumption atomic formulae axiom of choice belongs Calculus Cauchy compact completes the proof complex numbers conclude condition consider contains continuous corresponding defined definition denoted elements exists a positive exists a standard finite number follows function f(x given Hausdorff space Hence holds in Mx individual constants infiniment petite infinite natural number infinitely close infinitely small integral internal set Leibniz Let f linear mapping mathematical metric space monad n-tuples near-standard Non-standard Analysis non-standard model normal notion obtain open neighborhood open sets order theory polynomial positive infinitesimal positive standard pre-distribution prenex normal form proves the theorem R₁ relation symbols right hand side S-continuous S-interior S-open satisfied set of individuals set of points shows standard function standard number standard point standard positive number standard real number stratified subset Suppose THEOREM Standard theory topological group topological space ultraproduct values variable z₁ zero

References to this book

About the author (1974)

Abraham Robinson (1918-1974) was born in Prussia and taught mathematics at universities in Canada, Israel, and the United States. At the time of his death he was Sterling Professor of Mathematics at Yale University.

Bibliographic information

TitleNon-standard Analysis
Princeton landmarks in mathematics and physics
Princeton landmarks in mathematics
Princeton paperbacks
AuthorAbraham Robinson
Editionillustrated, revised
PublisherPrinceton University Press, 1974
ISBN0691044902, 9780691044903
Length293 pages
Subjects › 

Mathematics / Calculus
Mathematics / Complex Analysis
Mathematics / Logic
Mathematics / Mathematical Analysis
  
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