A Primer Of Infinitesimal Analysis
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Author | : John Lane Bell |
Publisher | : Cambridge University Press |
Total Pages | : 140 |
Release | : 1998-07-28 |
Genre | : Mathematics |
ISBN | : 9780521624015 |
This is the first elementary book to employ the concept of infinitesimals.
Author | : John L. Bell |
Publisher | : Cambridge University Press |
Total Pages | : 7 |
Release | : 2008-04-07 |
Genre | : Mathematics |
ISBN | : 0521887186 |
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author | : Oswald Veblen |
Publisher | : |
Total Pages | : 268 |
Release | : 1907 |
Genre | : Calculus |
ISBN | : |
Author | : Lazare Carnot |
Publisher | : |
Total Pages | : 178 |
Release | : 1832 |
Genre | : Calculus |
ISBN | : |
Author | : Lazare Nicolas Marguerite CARNOT (Count.) |
Publisher | : |
Total Pages | : 158 |
Release | : 1832 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 124 |
Release | : 2008 |
Genre | : Calculus |
ISBN | : 9780511370960 |
Author | : William Benjamin Smith |
Publisher | : |
Total Pages | : 378 |
Release | : 1898 |
Genre | : Calculus |
ISBN | : |
Author | : N J Lennes |
Publisher | : |
Total Pages | : 236 |
Release | : 2020-01-11 |
Genre | : |
ISBN | : 9781659154320 |
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 | : William Benjamin Smith |
Publisher | : |
Total Pages | : 0 |
Release | : 1898 |
Genre | : Calculus |
ISBN | : |
Author | : Oswald Veblen |
Publisher | : |
Total Pages | : 190 |
Release | : 2019-09-07 |
Genre | : |
ISBN | : 9781691656622 |
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 "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 treatmentof the definite integral.