한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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19세기 에콜 폴리테크닉의 해석학 교재 : Cauchy, Sturm, Jordan의 Cours d'Analyse

Cours d'Analyse by Cauchy, Sturm and Jordan

  • 투고 : 2016.01.08
  • 심사 : 2016.02.23
  • 발행 : 2016.04.30
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초록

We study the topics of the lectures in Analysis in 19th century at Ecole Polytechnique of France through the lists of the contents of the Cours d'Analyse by Cauchy, Sturm and Jordan, respectively and also we show how they stated the definitions of functions, continuity and limits in their Cours d'Analyse. Through this, we see that in 19th century, in France, analysis included differential and integral calculus, differential equations, variations and applications of these to differential geometry, and it was far from today's mathematical analysis.

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참고문헌

  1. Umberto Bottazzini, The higher calculus: A history of real and complex analysis from Euler to Weierstrass, Springer, New York, 1986.
  2. Robert E. Bradley, C. Edward Sandifer, Cauchy's Cours d'analyse: an annotated translation, Dordrecht[the Netherlands]; London-New York, Springer, 2009.
  3. A L. Cauchy, Cours d'analyse de l'ecole royale polytechnique, 1st partie: analyse algebrique, Paris 1821, In Cauchy [- , series 2, vol.3]
  4. A. L. Cauchy, Resumedes lecons donnees a l'ecole royale polytechnique sur le calcul infinitesimal, vol. 1, Paris, 1823. [In Cauchy [- , series 2, vol. 4]
  5. A. L. Cauchy, Lecons sur le calcul differentiel, Paris, de Bure Freres, 1828, In Cauchy [- , series 2, vol.4]
  6. A. L. Cauchy, Lecons sur les applications du calcul infinitesimal a la geometrie, Paris, 1826-1828, In Cauchy [- , series 2, vol.5]
  7. OEuvres completes d'Augustin Cauchy, publiees sous la direction scientifique de l'Academie des Sciences, Paris: Gauthier-Villars, series 1, 2; 1882.
  8. Ivor Grattan-Guinness, Convolutions in French mathematics, 1800-1840, Birkhauser Verlag, Basel-Boston-Berlin, 1990.
  9. M. C. Jordan, Cours d'analyse de l'ecole polytechnique, Tome Premier, Paris, Gauthier-Villars, Imprimeur-Libraire, 1882.
  10. M. C. Jordan, Cours d'analyse de l'ecole polytechnique, Deuxieme edition, Tome Premier, Paris, Gauthier-villars, Imprimeurs-Libraires, 1893.
  11. M. C. Jordan, Cours d'analyse de l'ecole polytechnique, Deuxieme edition, Tome Deuxieme, Paris, Gauthier-villars, Imprimeusr-Libraires, 1894.
  12. M. Sturm, Cours d'analyse de l'ecole polytechnique, Deuxieme edition, Tome Premier, Paris, Mallet-Bachelier, Imprimeur-Libraire, 1863.
  13. M. Sturm, Cours d'analyse de l'ecole polytechnique, Deuxieme edition, Tome Second, Paris, Gauthier-Villars, Imprimeur-Libraire, 1864.
  14. http://archive.org