Introduction to Infinitesimal Analysis Functions of One Real Variable

Veblen, Oswald

ISBN 10: 1673979440 / ISBN 13: 9781673979442

Published by Independently Published, 2019

About this Item

Zustand: Sehr gut | Seiten: 190 | Sprache: Englisch | Produktart: Bücher.

Seller Inventory # 37361931/2

Bibliographic Details

• Title: Introduction to Infinitesimal Analysis Functions of One Real Variable
• Publisher: Independently Published
• Publication Date: 2019
• Language: English
• ISBN 10: 1673979440
• ISBN 13: 9781673979442
• Binding: Soft cover
• Condition: Sehr gut

About this title

Synopsis

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, and in general has largely decreased the number of "’s and _’s. The theory of limits is developed for multiple-valued functions, which gives certain advantages in the treatment of the definite integral.