Foundations of Differential Calculus

Springer, May 23, 2000 - Mathematics - 194 pages
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.

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Contents

 On Finite Differences 1 On the Use of Differences in the Theory of Series 25 On the Infinite and the Infinitely Small 47 On the Nature of Differentials of Each Order 63 On the Differentiation of Algebraic Functions of One Variable 77 On the Differentiation of Transcendental Functions 99
 On the Differentiation of Functions of Two or More Variables 123 On the Higher Differentiation of Differential Formulas 141 On Differential Equations 167 Index 193 Copyright

Popular passages

Page v - Those quantities that depend on others in this way, namely, those that undergo a change when others change, are called functions of these quantities. This definition applies rather widely and includes all ways in which one quantity can be determined by others.
Page vi - In this way, we are led to a definition of differential calculus: It is a method for determining the ratio of the vanishing increments that any functions take on when the variable, of which they are functions, is given a vanishing increment.
Page vii - To many who have discussed the rules of differential calculus, it has seemed that there is a distinction between absolutely nothing and a special order of quantities infinitely small, which do not quite vanish completely but retain a certain quantity that is indeed less than any assignable quantity.
Page vi - Therefore, differential calculus is concerned not so much with vanishing increments, which indeed are nothing, but with the ratio and mutual proportion. Since these ratios are expressed as finite quantities, we must think of calculus as being concerned with finite quantities.
Page x - I have nothing new to offer, and this is all the less to be required, since in other works I have treated this subject so fully.
Page xi - Here, everything is kept within the bounds of pure analysis, so that in the explanation of the rules of this calculus there is no need for any geometric figures.

References from web pages

JSTOR: "Foundations of Differential Calculus" by Euler
"Foundations of Differential Calculus" by Euler. Translated byjohn D. Blanton. Springer- Verlag, New York, 2000. \$59.95. xiv+ 194 pp., hardcover. ...

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5 The Mathematics and Science of Leonhard Euler (17071783)
5. The Mathematics and Science of Leonhard. Euler (17071783). Rudiger Thiele. Karl-Sudhoff-Institut fur Geschichte der Medizin und der Naturwissenschaften, ...

Zentralblatt MATH Database 1931  2008 0949.01030
Foundations of differential calculus. Transl. from the Latin by John D. Blanton. (English). New York, NY: Springer. xiv, 194 p. DM 119.00;os 869.00; sfr. ...
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... Textbook on the Calculus - Snyder.pdf 11 Mb; Foundations Of Differential Calculus - Euler.pdf 1 Mb; Foundations Of Infinitesimal Calculus 2nd ed. ...
www.torrentz.com/ a6410432d0c88965ca027f6072fb99f5d506e095

Euler L.  Foundations of Differential Calculus :: Электронная ...
Название: Foundations of Differential Calculus Автор: Euler L. Аннотация:. The positive response to the publication of Blanton's English translations of ...
lib.mexmat.ru/ books/ 1800

Foundations Of Differential Calculus - Boek - BESLIST.nl
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A tale of two curricula: Euler's algebra text book
Two exceptions to this are the recent translations by jd Blanton of Introduction to Analysis of the Infinite and Foundations of Differential Calculus, ...
plus.maths.org/ issue45/ features/ sangwin/ index.html

Euler: Foundations Of Differential Calculus | ISBN: 9780387985343 ...
Foundations Of Differential Calculus. Springer, 2000 Hardback, 216 stran Velikost: 921x614 mm ISBN: 9780387985343 (0387985344). Nae cena: 2990.00 Kč ...
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Notes Slide Show Outline 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
Some chapters of Foundations of Differential Calculus ... L. Euler, Foundations of Differential Calculus, translated by J. Blanton, Springer-Verlag, 2000. ...
www.etsu.edu/ math/ gardner/ euler/ Euler-Seminar_files/ outline.htm