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Euler's definition of the derivative
Author(s):
Harold
M.
Edwards
Journal:
Bull. Amer. Math. Soc.
44
(2007),
575-580.
MSC (2000):
Primary 01A50;
Secondary 01-01, 03-03
Posted:
June 8, 2007
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Abstract:
Euler's method of defining the derivative of a function is not a failed effort to describe a limit. Rather, it calls for rewriting the difference quotient in a way that remains meaningful when the denominator is zero.
References:
-
- 1.
- Carl B. Boyer, A History of Mathematics, Wylie, New York, 1968. MR 0234791 (38:3105)
- 2.
- William Dunham, The Calculus Gallery, Princeton Univ., Princeton and Oxford, 2005. MR 2112402 (2005k:01003)
- 3.
- Leonhard Euler, Institutiones Calculi Differentialis, St. Petersburg, 1755. Foundations of Differential Calculus, John D. Blanton, trans., Springer, New York, 2000. MR 1753095 (2002d:01025)
- 4.
- Leonhard Euler, Introductio in Analysin Infinitorum, Lausanne, Bousquet, 1748. Introduction to the Analysis of the Infinite, John D. Blanton, trans., Springer, New York, 1988. MR 961255 (89g:01067)
- 5.
- Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford, New York, 1972. MR 0472307 (57:12010)
- 6.
- Dirk J. Struik, A Concise History of Mathematics, Dover, New York, 1948. MR 919604 (88i:01004)
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Additional Information:
Harold
M.
Edwards
Affiliation:
Department of Mathematics, New York University, 251 Mercer Street, New York, New York 10012
DOI:
10.1090/S0273-0979-07-01174-3
PII:
S 0273-0979(07)01174-3
Keywords:
Elliptic curves,
elliptic functions,
Riemann surfaces of genus one
Received by editor(s):
January 26, 2007
Posted:
June 8, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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