வகையீடு (கணிதம்) (Tamil Wikipedia)

Analysis of information sources in references of the Wikipedia article "வகையீடு (கணிதம்)" in Tamil language version.

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Courant 1937i, II, §9: "Here we remark merely in passing that it is possible to use this approximate representation of the increment Δy by the linear expression hƒ(x) to construct a logically satisfactory definition of a "differential", as was done by Cauchy in particular." Courant, Richard (1937i), Differential and integral calculus. Vol. I, Wiley Classics Library, New York: யோன் வில்லி அன் சன்ஸ் (published 1988), பன்னாட்டுத் தரப்புத்தக எண் 978-0-471-60842-4, MR 1009558.
See, for instance, the influential treatises of Courant 1937i, Kline 1977, Goursat 1904, and Hardy 1905. Tertiary sources for this definition include also Tolstov 2001 and Ito 1993, §106. Courant, Richard (1937i), Differential and integral calculus. Vol. I, Wiley Classics Library, New York: யோன் வில்லி அன் சன்ஸ் (published 1988), பன்னாட்டுத் தரப்புத்தக எண் 978-0-471-60842-4, MR 1009558. Kline, Morris (1977), "Chapter 13: Differentials and the law of the mean", Calculus: An intuitive and physical approach, John Wiley and Sons. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155. Tolstov, G.P. (2001), "Differential", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer, பன்னாட்டுத் தரப்புத்தக எண் 978-1556080104. Ito, Kiyosi (1993), Encyclopedic Dictionary of Mathematics (2nd ed.), MIT Press, பன்னாட்டுத் தரப்புத்தக எண் 978-0-262-59020-4.
Cauchy 1823. See also, for instance, Goursat 1904, I, §14. Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.
Goursat 1904, I, §17 Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.
Goursat 1904, I, §§14,16 Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.

archive.org

See, for instance, the influential treatises of Courant 1937i, Kline 1977, Goursat 1904, and Hardy 1905. Tertiary sources for this definition include also Tolstov 2001 and Ito 1993, §106. Courant, Richard (1937i), Differential and integral calculus. Vol. I, Wiley Classics Library, New York: யோன் வில்லி அன் சன்ஸ் (published 1988), பன்னாட்டுத் தரப்புத்தக எண் 978-0-471-60842-4, MR 1009558. Kline, Morris (1977), "Chapter 13: Differentials and the law of the mean", Calculus: An intuitive and physical approach, John Wiley and Sons. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155. Tolstov, G.P. (2001), "Differential", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer, பன்னாட்டுத் தரப்புத்தக எண் 978-1556080104. Ito, Kiyosi (1993), Encyclopedic Dictionary of Mathematics (2nd ed.), MIT Press, பன்னாட்டுத் தரப்புத்தக எண் 978-0-262-59020-4.
Cauchy 1823. See also, for instance, Goursat 1904, I, §14. Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.
Goursat 1904, I, §17 Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.
Goursat 1904, I, §§14,16 Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.

encyclopediaofmath.org

See, for instance, the influential treatises of Courant 1937i, Kline 1977, Goursat 1904, and Hardy 1905. Tertiary sources for this definition include also Tolstov 2001 and Ito 1993, §106. Courant, Richard (1937i), Differential and integral calculus. Vol. I, Wiley Classics Library, New York: யோன் வில்லி அன் சன்ஸ் (published 1988), பன்னாட்டுத் தரப்புத்தக எண் 978-0-471-60842-4, MR 1009558. Kline, Morris (1977), "Chapter 13: Differentials and the law of the mean", Calculus: An intuitive and physical approach, John Wiley and Sons. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155. Tolstov, G.P. (2001), "Differential", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer, பன்னாட்டுத் தரப்புத்தக எண் 978-1556080104. Ito, Kiyosi (1993), Encyclopedic Dictionary of Mathematics (2nd ed.), MIT Press, பன்னாட்டுத் தரப்புத்தக எண் 978-0-262-59020-4.

ujf-grenoble.fr

math-doc.ujf-grenoble.fr

Cauchy explicitly denied the possibility of actual infinitesimal and infinite quantities (Boyer 1959, pp. 273–275), and took the radically different point of view that "a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge to zero" (Cauchy 1823, ப. 12; translation from Boyer 1959, ப. 273). Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27.
Cauchy 1823. See also, for instance, Goursat 1904, I, §14. Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.

webcitation.org

Cauchy explicitly denied the possibility of actual infinitesimal and infinite quantities (Boyer 1959, pp. 273–275), and took the radically different point of view that "a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge to zero" (Cauchy 1823, ப. 12; translation from Boyer 1959, ப. 273). Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27.
Cauchy 1823. See also, for instance, Goursat 1904, I, §14. Cauchy, Augustin-Louis (1823), Résumé des Leçons données à l'Ecole royale polytechnique sur les applications du calcul infinitésimal, archived from the original on 2009-05-04, பார்க்கப்பட்ட நாள் 2012-10-27. Goursat, Édouard (1904), A course in mathematical analysis: Vol 1: Derivatives and differentials, definite integrals, expansion in series, applications to geometry, E. R. Hedrick, New York: Dover Publications (published 1959), MR 0106155.