Introduction to Infinitesimal Analysis: Functions of One Real Variable by N. J. Lennes

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About this book :-
This text is 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. 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 e’s and d’s. The theory of limits is developed for multiple-valued functions, which gives certain advantages in the treatment of the definite integral.

Book Detail :-
This book has following details information.
Title: Introduction to Infinitesimal Analysis: Functions of One Real Variable by N. J. Lennes by NA
Publisher: John Wiley & Sons
Series: eBooksDirectory
Year: 2007
Pages: 225
Type: PDF
Language: English
ISBN-10 #: B001QAQX0Y, B000UG583I
ISBN-13 #:
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
1. The System of Real Numbers 2. Sets of Points and of Segments 3. Functions in General, Special Classes of Functions 4. Theory of Limits 5. Continuous Functions 6. Infinitesimals and Infinities 7. Derivatives and Differentials 8. Definite Integrals 9. Improper Definite Integrals

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