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Table of contents (9 chapters)
Keywords
About this book
What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.
Reviews
“This instalment … will be welcomed not only by historians but also by teachers anxious to change from the highfalutin talk of Cauchy-style limits all the time when explaining the calculus.” (I.Grattan-Guinness, zbMATH 0949.01030, 2021)
Authors and Affiliations
Bibliographic Information
Book Title: Foundations of Differential Calculus
Authors: Euler
DOI: https://doi.org/10.1007/b97699
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2000
Hardcover ISBN: 978-0-387-98534-3Published: 23 May 2000
Softcover ISBN: 978-1-4757-7426-9Published: 17 March 2013
eBook ISBN: 978-0-387-22645-3Published: 04 May 2006
Edition Number: 1
Number of Pages: XVI, 194
Topics: Real Functions