Last edited by Faucage
Tuesday, August 4, 2020 | History

2 edition of Revitalization of nonstandard calculus found in the catalog.

Revitalization of nonstandard calculus

Iris B. Fetta

Revitalization of nonstandard calculus

project dates: September 8, 1992 - September 8, 1995

by Iris B. Fetta

  • 160 Want to read
  • 7 Currently reading

Published by U.S. Dept. of Education, Office of Educational Research and Improvement, Educational Resources Information Center in [Washington, DC] .
Written in English

    Subjects:
  • Clemson University -- Curricula.,
  • Calculus -- Study and teaching (Higher) -- South Carolina -- Clemson.

  • Edition Notes

    Statementprepared by Iris B. Fetta.
    ContributionsEducational Resources Information Center (U.S.)
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17129532M

    Many students find it difficult to solve calculus problems. That doesn't need to be you - download our free textbooks! Our authors have contributed textbooks for all levels.   This book can be considered a sequel of sorts to the author’s previous Methods of Solving Complex Geometry Problems (CGP).Like CGP, this is a problem book, but now the subject of the problems is not geometry but primary focus is on polynomial and trigonometric equations, but other kinds (including differential equations) make an appearance as well.

    A calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now. The explanations of new concepts is clear, written for someone who does not yet know calculus. ( views) Calculus: Early Transcendentals by David Guichard - Lyryx, Model theory, Nonstandard analysis Publications. Free Online Calculus Book (PDF files), updated Sepember Printed Third Edition of Calculus Book (Dover ) Foundations of Infinitesimal Calculus () Books ; Papers, updated February, Downloadable Papers (since ), updated May Ph.D. Students.

    the author of this book strongly suggests the reader to take the ap-proximately half an hour needed in order to read it with some care. During the last nearly four decades, since the first systematic presenta-tion of Nonstandard Analysis in the book of Abraham Robinson, quite a few excellent treaties have been published on the subject, a.   Probably the part of calculus that has changed the most from antiquity to the present is the handling of infinity and limits, and this book is especially careful in presenting those changes. Archimedes actually had nearly all the ingredients of 17th-century calculus, including the sum of a finite geometric progression.


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Revitalization of nonstandard calculus by Iris B. Fetta Download PDF EPUB FB2

Nonstandard calculus uses infinitesimals for computing limits and derivative. Following severe criticism, infinitesimals and infinite numbers were effectively banned from calculus at the end of the nineteenth century, favoring the epsilon and delta approach popularized by Karl Weierstrass.

It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert by: In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus.

It provides a rigorous justification that were previously considered merely heuristic. Non-rigorous calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the -definition of limit starting in the s.

For almost one. 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 inand it. THE TEACHING OF ELEMENTARY CALCULUS USING THE NONSTANDARD ANALYSIS APPROACH KATHLEEN SULLIVAN In the 's a mathematical logician, Abraham Robinson, found a way to make rigorous the intuitively attractive infinitesimal calculus of Newton and Leibniz, beginning a branch of mathematics called nonstandard Size: KB.

63 Responses to “Non-nonstandard Calculus, I” John Armstrong Says: Aug at am | Reply. Actually, it reminds me of something Louis Kauffman has on his door. It’s all of integral and differential calculus on two pages, and the only difference is he uses a Author: Mnoonan.

Calculus Online Textbook Toc Author: Gilbert Strang Created Date: 9/7/ PM. Textbook Instructor's Manual Study Guide Download Resource Materials; Published in by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike.

It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. Calculus. This is the free digital calculus text by David R. Guichard and others. It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years.

The book is in use at Whitman College and is occasionally updated to correct errors and add new material. The latest versions may be found by. Calculus I or needing a refresher in some of the early topics in calculus.

I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of theFile Size: 2MB. Get this from a library. Revitalization of nonstandard calculus: project dates: September 8, - September 8, [Iris B Fetta; Educational Resources Information Center (U.S.)].

Advanced Calculus Explored equips readers with the tools they need for success in their STEM courses and provides a multitude of nonstandard problems to engage the mathematically curious reader, enabling the reader to achieve their academic goals. Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions.

Of course, people had tried to use infinitesimals in calculus before; in fact, Calculus originally used infinitesimals. The problem was that it did not have a rigorous foundation, which is why mathematicians started using the epsilon-delta definitions instead, although they.

The usual approach to nonstandard (or infinitesimal) calculus (based on Abraham Robinson's work, Non-standard Analysis, ) does indeed depend on ultrafilters and the Axiom of Choice, and is usually reserved for third year university level or even post graduate courses.

This is a shame, because everything one needs to establish a rigorous "hyperreal" extension of the real. I got this book at a used bookstore for $10 as my first calculus book, I read the entire thing over a week long vacation.

It was sweeter than candy, I have not read a better non-fiction book in my entire (18 year old) life.

retro64 on Welcome to HN. I feel hopeful when I see passionate comments like this from newly minted adults:). LECTURE NOTES ON NONSTANDARD ANALYSIS 3 Since its origins, nonstandard analysis has become a powerful mathemat-ical tool, not only for yielding easier de nitions for standard concepts and providing slick proofs of well-known mathematical theorems, but for also providing mathematicians with amazing new tools to prove theorems, Size: KB.

My foreign book on calculus is more than pages long and it doesn’t cover analytic geometry or differential equations. So, calculus book are already compacted to an insane level, targeting mostly applications and cutting down on rigor and explanations, on the logic behind the scenes.

PART III. Advanced and Comprehensive Books on Calculus. Well this page is not about Keisler's book, there are several books on non-standard calculus and Hrbacek's article mentions a few of them. It seems out of place to discuss Keisler specifically in this context.

Thenub19 December (UTC) Great. All of those books provide definitions at standard points without epsilons. This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.5/5(2).

Abstract. In this paper we give an introduction to nonstandard analysis, starting with an ultrapower construction of the hyperreals. We then demon-strate how theorems in standard analysis \transfer over" to nonstandard anal-ysis, and how theorems in standard analysis can be proven using theorems in nonstandard analysis.

IntroductionFile Size: KB. It's true that calculus was initially developed using a vague concept of infinitesimals, and it's also true that modern nonstandard analysis allows us to formalize the idea of an infinitesimal.

But the modern formalization of nonstandard analysis.Finding this book was vindicating in that respect. This book provides a very clear and intuitive description of infinitesimal calculus, which falls within the domain of Non-standard analysis; which, by the way, has been shown to be logically equivalent to Real analysis.4/5.I highly recommend The Calculus is not a history book with all the details, but rather an account of some of the most important examples in the evolution of this subject, such as the first methods invented by Newton, to the breaktroughs made by Weirstrass, Cauchy, Cantor, Lebesgue and others.