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Non-standard Analysis

Abraham Robinson

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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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Schlagwörter

Zermelo–Fraenkel set theory, Meromorphic function, Zero divisor, Equivalence class, Neighbourhood (mathematics), Riemann mapping theorem, Set (mathematics), Infimum and supremum, Logical connective, Upper and lower bounds, Big O notation, Riemann sphere, Commutative property, Dirac delta function, Logical disjunction, Quantifier (logic), Ultraproduct, Exponential function, Order type, Polynomial, Linear map, Theorem, Infinitesimal, Theory, Cauchy sequence, Sequence, Function of a real variable, Non-standard model of arithmetic, Philosophy of mathematics, Topological space, Existential quantification, Bounded operator, Normal family, Addition, Mathematics, Equicontinuity, Mathematical induction, Subgroup, Division by zero, Axiom, Natural number, Reflexive relation, Binary relation, Dedekind cut, Compact operator, Sign (mathematics), Complex number, Real number, Non-standard analysis, Prenex normal form, Characterization (mathematics), Zorn's lemma, Boolean algebra (structure), Mean value theorem, Improper integral, Ultrafilter, Method of exhaustion, Metric space, Continuous function (set theory), Analytic function, Special case, Subset, Prime number, Non-standard model, Associative property, Quantity, Axiom of choice, Set theory, Variable (mathematics), Order theory