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Author : K. D. Stroyan
Publisher :
ISBN 13 : 9780126741506
Total Pages : 326 pages
Book Rating : 4.7/5 (415 download)
Download or read book Introduction to the Theory of Infinitesimals written by K. D. Stroyan and published by . This book was released on 1976-01-01 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John L. Bell
Publisher : Cambridge University Press
ISBN 13 : 0521887186
Total Pages : 7 pages
Book Rating : 4.5/5 (218 download)
Download or read book A Primer of Infinitesimal Analysis written by John L. Bell and published by Cambridge University Press. This book was released on 2008-04-07 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author : K. D. Stroyan
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (856 download)
Download or read book Introduction to the Theory of Infinitesimals: Infinitesimals in functional analysis written by K. D. Stroyan and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K. D. Stroyan
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (856 download)
Download or read book Introduction to the Theory of Infinitesimals: Infinitesimals in functional analysis written by K. D. Stroyan and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 9780080873886
Total Pages : 323 pages
Book Rating : 4.8/5 (738 download)
Download or read book Introduction to the Theory of Infiniteseimals written by and published by Academic Press. This book was released on 1977-01-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Infiniteseimals
Author : Amir Alexander
Publisher : Simon and Schuster
ISBN 13 : 1780745338
Total Pages : 368 pages
Book Rating : 4.7/5 (87 download)
Download or read book Infinitesimal written by Amir Alexander and published by Simon and Schuster. This book was released on 2014-07-03 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Oswald Veblen
Publisher :
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.:/5 (5 download)
Download or read book Introduction to Infinitesimal Analysis written by Oswald Veblen and published by . This book was released on 1907 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Margaret E. Baron
Publisher : Elsevier
ISBN 13 : 1483280926
Total Pages : 312 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Origins of Infinitesimal Calculus written by Margaret E. Baron and published by Elsevier. This book was released on 2014-05-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nader Vakil
Publisher : Cambridge University Press
ISBN 13 : 1107002028
Total Pages : 587 pages
Book Rating : 4.1/5 (7 download)
Download or read book Real Analysis Through Modern Infinitesimals written by Nader Vakil and published by Cambridge University Press. This book was released on 2011-02-17 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Author : N J Lennes
Publisher :
ISBN 13 : 9781659154320
Total Pages : 236 pages
Book Rating : 4.1/5 (543 download)
Download or read book Introduction to Infinitesimal Analysis written by N J Lennes and published by . This book was released on 2020-01-11 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner is now recognized as an essential part of the training of a mathematician. It appears in the curriculum of nearly every university and is taken by students as "Advanced Calculus" in their last collegiate year, or as part of "Theory of Functions" in the first year of graduate work. This little volume is designed as a convenient reference book for such courses; the examples which may be considered necessary being supplied from other sources. The book may also be used as a basis for a rather short theoretical course on real functions, such as is now given from time to time in some of our universities.The general aim has been to obtain rigor of logic with a minimum of elaborate machinery. It is hoped that the systematic use of the Heine-Borel theorem has helped materially toward this end since by means of this theorem it is possible to avoid almost entirely the sequential division or "pinching" process so common in discussions of this kind. The definition of a limit by means of the notion "value approached" has simplified the proofs of theorems, such as those giving necessary and sufficient conditions for the existence of limits...
Author : James M. Henle
Publisher : Courier Corporation
ISBN 13 : 0486151018
Total Pages : 144 pages
Book Rating : 4.4/5 (861 download)
Download or read book Infinitesimal Calculus written by James M. Henle and published by Courier Corporation. This book was released on 2014-01-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Oswald Veblen
Publisher :
ISBN 13 : 9781689926751
Total Pages : 190 pages
Book Rating : 4.9/5 (267 download)
Download or read book Introduction to Infinitesimal Analysis Functions of One Real Variable written by Oswald Veblen and published by . This book was released on 2019-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: A course dealing with the fundamental theorems of infinitesimal calculus in a rigorousmanner is now recognized as an essential part of the training of a mathematician. Itappears in the curriculum of nearly every university, and is taken by students as "AdvancedCalculus" in their last collegiate year, or as part of "Theory of Functions" in the firstyear of graduate work. This little volume is designed as a convenient reference book forsuch courses; the examples which may be considered necessary being supplied from othersources. The book may also be used as a basis for a rather short theoretical course on realfunctions, such as is now given from time to time in some of our universities.
Author : Detlef Laugwitz
Publisher :
ISBN 13 : 9788821803413
Total Pages : 110 pages
Book Rating : 4.8/5 (34 download)
Download or read book The theory of infinitesimals. An introduction to nonstandard analysis written by Detlef Laugwitz and published by . This book was released on 1980 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Oswald Veblen
Publisher :
ISBN 13 : 9781537085425
Total Pages : 212 pages
Book Rating : 4.0/5 (854 download)
Download or read book Introduction to Infinitesimal Analysis written by Oswald Veblen and published by . This book was released on 2016-08-13 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: A course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner is now recognized as an essential part of the training of a mathematician. It appears in the curriculum of nearly every university, and is taken by students as "Advanced Calculus" in their last collegiate year, or as part of "Theory of Functions" in the first year of graduate work. This little volume is designed as a convenient reference book for such courses; the examples which may be considered necessary being supplied from other sources. The book may also be used as a basis for a rather short theoretical course on real functions, such as is now given from time to time in some of our universities.The general aim has been to obtain rigor of logic with a minimum of elaborate machinery. It is hoped that the systematic use of the Heine-Borel theorem has helped materially toward this end, since by means of this theorem it is possible to avoid almost entirely the sequential division or "pinching" process so common in discussions of this kind.
Author : Eric Schechter
Publisher : Academic Press
ISBN 13 : 0080532993
Total Pages : 907 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of Analysis and Its Foundations written by Eric Schechter and published by Academic Press. This book was released on 1996-10-24 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Author : Abraham Robinson
Publisher : Princeton University Press
ISBN 13 : 1400884225
Total Pages : 308 pages
Book Rating : 4.4/5 (8 download)
Download or read book Non-standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Frederik S. Herzberg
Publisher : Springer
ISBN 13 : 3642331491
Total Pages : 112 pages
Book Rating : 4.6/5 (423 download)
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-06 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
