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Infinitesimal Calculus

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Size: 31.25 MB
Format: PDF
View: 1990
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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Infinitesimal Calculus

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Size: 32.57 MB
Format: PDF, Kindle
View: 1037
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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Elementary Calculus

Author: H. Jerome Keisler
Publisher: Courier Corporation
ISBN: 0486484521
Size: 52.46 MB
Format: PDF, Mobi
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This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

The Origins Of Infinitesimal Calculus

Author: Margaret E. Baron
Publisher: Elsevier
ISBN: 1483280926
Size: 46.29 MB
Format: PDF
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The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

A Primer Of Infinitesimal Analysis

Author: John L. Bell
Publisher: Cambridge University Press
ISBN: 0521887186
Size: 19.63 MB
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A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Applied Nonstandard Analysis

Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486152340
Size: 75.38 MB
Format: PDF, Mobi
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This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

A Concept Of Limits

Author: Donald W. Hight
Publisher: Courier Corporation
ISBN: 0486153126
Size: 56.87 MB
Format: PDF, Mobi
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An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.

Nonstandard Analysis

Author: Alain Robert
Publisher: Courier Corporation
ISBN: 9780486432793
Size: 49.67 MB
Format: PDF, Kindle
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This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.

Non Standard Analysis

Author: Abraham Robinson
Publisher: Princeton University Press
ISBN: 1400884225
Size: 53.76 MB
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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.

Lectures On The Hyperreals

Author: Robert Goldblatt
Publisher: Springer Science & Business Media
ISBN: 1461206154
Size: 69.68 MB
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An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.