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Foundations of Differential Calculus von Euler (englisch) Hardcover-Buch-
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eBay-Artikelnr.:395165323762
Artikelmerkmale
- Artikelzustand
- ISBN-13
- 9780387985343
- Book Title
- Foundations of Differential Calculus
- ISBN
- 9780387985343
- Subject Area
- Mathematics
- Publication Name
- Foundations of Differential Calculus
- Publisher
- Springer New York
- Item Length
- 9.2 in
- Subject
- Calculus, Mathematical Analysis
- Publication Year
- 2000
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 0.2 in
- Item Weight
- 37.7 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xvi, 194 Pages
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
0387985344
ISBN-13
9780387985343
eBay Product ID (ePID)
1661852
Product Key Features
Number of Pages
Xvi, 194 Pages
Publication Name
Foundations of Differential Calculus
Language
English
Publication Year
2000
Subject
Calculus, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.2 in
Item Weight
37.7 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-043386
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)
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.3
Table Of Content
On Finite Differences.- On the Use of Differences in the Theory of Series.- On the Infinite and the Infinitely Small.- On the Nature of Differentials of Each Order.- On the Differentiation of Algebraic Functions of One Variable.- On the Differentiation of Transcendental Functions.- On the Differentiation of Functions of Two or More Variables.- On the Higher Differentiation of Differential Formulas.- On Differential Equations.
Synopsis
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., The positive response to the publication of Blanton's English translations of Euler's Introduction to Analysis of the Infinite confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's Foundations of Differential Calculus as well. The current book constitutes the first 9 out of 27 chapters, with remaining chapters to be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community., The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community., 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.
LC Classification Number
QA331.5
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