Non-standard Analysis (eBook)

Abraham Robinson (Autor)

eBook Download: PDF

2016
Princeton University Press (Verlag)
978-1-4008-8422-3 (ISBN)

Infos

RobinsonAbraham:

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.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.

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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.

Produkt-Details

• Erscheint lt. Verlag: 11.8.2016
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Addition • analytic function • associative property • Axiom • Axiom of choice • Big O notation • Binary Relation • Boolean algebra (structure) • Boundary value problem • bounded operator • Cartesian Product • Cauchy Sequence • Characterization (mathematics) • commutative property • compactness theorem • Compact operator • complex number • consistency • continuous function • Continuous function (set theory) • Dedekind cut • Diagram (category theory) • Dirac delta function • Dirichlet Integral • Dirichlet's principle • Division by zero • empty set • Equation • equicontinuity • equivalence class • equivalence relation • existential quantification • exponential function • First variation • Function (mathematics) • Function of a real variable • Hyperreal number • improper integral • Infimum and supremum • Infinitesimal • Limit point • Linear map • Logic • Logical conjunction • Logical connective • Logical disjunction • Mathematical Analysis • Mathematical Induction • Mathematics • Maximal Ideal • mean value theorem • Meromorphic Function • Method of exhaustion • Metric Space • Natural number • Neighbourhood (mathematics) • non-standard analysis • Non-standard model • Non-Standard Model of Arithmetic • Normal family • Order theory • Order type • partially ordered set • philosophy of mathematics • polynomial • Prenex normal form • Prime number • Product topology • Pure Mathematics • Quantifier (logic) • Quantity • real number • Reflexive relation • Riemann Mapping Theorem • Riemann sphere • Right inverse • Ring Extension • Self-adjoint • Sequence • Set (mathematics) • set theory • Sign (mathematics) • Special case • SUBGROUP • Subset • Summation • Taylor series • Theorem • theory • Topological space • transfinite • Type Theory • Ultrafilter • Ultraproduct • uniform continuity • Upper and lower bounds • Variable (mathematics) • Zermelo–Fraenkel set theory • Zero divisor • Zorn's lemma
• ISBN-10: 1-4008-8422-5 / 1400884225
• ISBN-13: 978-1-4008-8422-3 / 9781400884223