Infinitesimal
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Infinitesimal Calculus
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Author : James M. Henle
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
Infinitesimal Calculus written by James M. Henle and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
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 Analysis
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Author : E.I. Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Infinitesimal Analysis written by E.I. Gordon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
The Continuous And The Infinitesimal In Mathematics And Philosophy
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Author : John Lane Bell
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2005
The Continuous And The Infinitesimal In Mathematics And Philosophy written by John Lane Bell and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Infinitesimal
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Author : Amir Alexander
language : en
Publisher: Simon and Schuster
Release Date : 2014-07-03
Infinitesimal written by Amir Alexander and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Science categories.
On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
A Primer Of Infinitesimal Analysis
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Author : John Lane Bell
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-28
A Primer Of Infinitesimal Analysis written by John Lane Bell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-28 with Mathematics categories.
This is the first elementary book to employ the concept of infinitesimals.
The Nature Of Infinitesimals
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Author : Peter F. Erickson
language : en
Publisher: Xlibris Corporation
Release Date : 2006-05-05
The Nature Of Infinitesimals written by Peter F. Erickson and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-05 with Mathematics categories.
Erickson explores and explains the infinite and the infinitesimal with application to absolute space, time and motion, as well as absolute zero temperature in this thoughtful treatise. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson delves into the history of these concepts and how people learn and understand them. He regards the infinitesimal as the key to understanding much of the scientific basis of the universe, and intertwines mathematical examples and historical context from Aristotle, Kant, Euler, Newton and more with his deductions-resulting in a readable treatment of complex topics. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. At the heart of Ericksons work is the veritable number system, in which positive and negative numbers are incompatible for the basic mathematical operations of addition, subtraction, multiplication, division, roots and ratios. This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions. In the case of non-Euclidean geometry, the author determines that its inconsistent with the infinitesimal. Erickson supplies illustrative examples both in words and images-he clearly defines new notation as needed for concepts such as eternity, the infinitesimal, the instant and an unlimited quantity. In the final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. While explaining his deductions and thoughts on these complex topics, he raises new questions for his readers to contemplate, such as the origin of memory. A weighty tome for devotees of mathematics and physics that raises interesting questions.
Foundations Of Infinitesimal Stochastic Analysis
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Author : K.D. Stroyan
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Foundations Of Infinitesimal Stochastic Analysis written by K.D. Stroyan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Computers categories.
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
The Origins Of Infinitesimal Calculus
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Author : Margaret E. Baron
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Origins Of Infinitesimal Calculus written by Margaret E. Baron and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
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.
The Metaphysical Principles Of The Infinitesimal Calculus
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Author : René Guénon
language : en
Publisher: Sophia Perennis
Release Date : 2003
The Metaphysical Principles Of The Infinitesimal Calculus written by René Guénon and has been published by Sophia Perennis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
René Guénon (1886-1951) is undoubtedly one of the luminaries of the twentieth century, whose critique of the modern world has stood fast against the shifting sands of recent philosophies. His oeuvre of 26 volumes is providential for the modern seeker: pointing ceaselessly to the perennial wisdom found in past cultures ranging from the Shamanistic to the Indian and Chinese, the Hellenic and Judaic, the Christian and Islamic, and including also Alchemy, Hermeticism, and other esoteric currents, at the same time it directs the reader to the deepest level of religious praxis, emphasizing the need for affiliation with a revealed tradition even while acknowledging the final identity of all spiritual paths as they approach the summit of spiritual realization. Guénon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet threat throughout his doctrinal studies. In this late text published just five years before his death, Guénon devotes an entire volume to questions regarding the nature of limits and the infinite, both with respect to the calculus as a mathematical discipline, and to the symbolism of the initiatic path. This book therefore extends and complements the geometrical symbolism Guénon employs in several of his other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. A sampling of chapter titles will convey some sense of this remarkable work: 'Infinite and Indefinite', 'Degrees of Infinity', 'Zero is not a Number', 'The Law of Continuity', 'Vanishing Quantities', 'Various Orders of Indefinitude', 'The Arguments of Zeno of Elea', 'The True Conception of Passage to the Limit'. The Collected Works of René Guénon brings together the writings of one of the greatest prophets of our time, whose voice is even more important today than when he was alive. Huston Smith, author of The World's Religions, etc.
Infinitesimal Differences
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Author : Ursula Goldenbaum
language : en
Publisher: Walter de Gruyter
Release Date : 2008-11-03
Infinitesimal Differences written by Ursula Goldenbaum and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-03 with Philosophy categories.
The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.