Non-standard Analysis

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Princeton University Press, 1974 - Mathematics - 293 pages
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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.

  

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User Review  - chemacortes - LibraryThing

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 ... Read full review

LibraryThing Review

User Review  - fpagan - LibraryThing

From the horse's mouth -- the discoverer of nonstandard analysis himself (1918-1974) wrote this rigorous exposition, noted for its difficult logic-theoretic starting point. Pretty impenetrable, but I ... Read full review

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
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About the author (1974)

Abraham Robinson (1918-1974) was Sterling Professor of Mathematics at Yale University.

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