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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Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and application of non-standard analysis which grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. -- L'Enseignement Mathématique
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First Sentence:
Underlying the fundamental notions of the branch of mathematics known as Analysis is the concept of a limit. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standard positive number, stratified sentences, infinite natural number, finiteness principle, positive infinitesimal number, finite natural numbers, principal galaxy, lower predicate calculus, standard real number, same monad, infinitely large quantities, internal set, prenex normal form, limites données, finite positive integers, fine partition, finite roots, infinitely large numbers, infiniment petites, higher order theories, internal sequence, nonstandard analysis, same galaxy Key Phrases - Capitalized Phrases (CAPs): (learn more)
Non-standard Analysis, Lower Predicate Calculus, Dirac Delta, Nonstandard Analysis, Theory of Elasticity New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Underlying the fundamental notions of the branch of mathematics known as Analysis is the concept of a limit. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standard positive number, stratified sentences, infinite natural number, finiteness principle, positive infinitesimal number, finite natural numbers, principal galaxy, lower predicate calculus, standard real number, same monad, infinitely large quantities, internal set, prenex normal form, limites données, finite positive integers, fine partition, finite roots, infinitely large numbers, infiniment petites, higher order theories, internal sequence, nonstandard analysis, same galaxy Key Phrases - Capitalized Phrases (CAPs): (learn more)
Non-standard Analysis, Lower Predicate Calculus, Dirac Delta, Nonstandard Analysis, Theory of Elasticity New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 23
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79
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- Abraham Robinson by Joseph Warren Dauben in Front Matter
- An Essay Concerning Humane Understanding Volume I by John Locke in Back Matter
- Topology from the Differentiable Viewpoint by John Willard Milnor in Front Matter
- Angular Momentum in Quantum Mechanics (Investigations in Physics) by A. R. Edmonds in Front Matter
- Linear Programming and Extensions by George Dantzig in Front Matter
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- Developments in Nonstandard Mathematics (Chapman & Hall/CRC Research Notes in Mathematics Series) by Nigel J Cutland on 5 pages
- The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations (Foundations of Communication) by Javier Echeverria on page 221, page 222, and page 223
- A Brief History of Infinity by Paolo Zellini on page 122, and page 124
- Infinity and the Mind by Rudy Rucker in Back Matter (1), and Back Matter (2)
- Infinitesimal Analysis (Mathematics and Its Applications (closed)) by E.I. Gordon in Back Matter (1), and Back Matter (2)
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