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Real Analysis through Modern Infinitesimals

2011-02-17 Mathematics
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Release : 2011-02-17
Genre : Mathematics
Kind : eBook
Book Rating : 017/5 ( reviews)

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Book Synopsis Real Analysis through Modern Infinitesimals by : Nader Vakil

Download or read book Real Analysis through Modern Infinitesimals written by Nader Vakil. This book was released on 2011-02-17. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses.

Real Analysis Through Modern Infinitesimals

2011-02-17 Mathematics
Download Real Analysis Through Modern Infinitesimals PDF Online Free

Author :
Release : 2011-02-17
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)

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Book Synopsis Real Analysis Through Modern Infinitesimals by : Nader Vakil

Download or read book Real Analysis Through Modern Infinitesimals written by Nader Vakil. This book was released on 2011-02-17. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.

A Primer of Infinitesimal Analysis

2008-04-07 Mathematics
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Release : 2008-04-07
Genre : Mathematics
Kind : eBook
Book Rating : 186/5 ( reviews)

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Book Synopsis A Primer of Infinitesimal Analysis by : John L. Bell

Download or read book A Primer of Infinitesimal Analysis written by John L. Bell. This book was released on 2008-04-07. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Modern Real Analysis

2017-11-30 Mathematics
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Release : 2017-11-30
Genre : Mathematics
Kind : eBook
Book Rating : 29X/5 ( reviews)

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Book Synopsis Modern Real Analysis by : William P. Ziemer

Download or read book Modern Real Analysis written by William P. Ziemer. This book was released on 2017-11-30. Available in PDF, EPUB and Kindle. Book excerpt: This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.

Infinitesimal

2014-07-03 Science
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Release : 2014-07-03
Genre : Science
Kind : eBook
Book Rating : 338/5 ( reviews)

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Book Synopsis Infinitesimal by : Amir Alexander

Download or read book Infinitesimal written by Amir Alexander. This book was released on 2014-07-03. 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.

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