Analysis of Ideas Changing in the History of Mathematical Analysis

Authors

  • Ming-Xing Hu  Department of Mathematics, Huaibei Normal University, Huaibei, Anhui, PRC, China
  • De-Peng Kong  Department of Mathematics, Huaibei Normal University, Huaibei, Anhui, PRC, China

DOI:

https://doi.org/10.32628/IJSRST218477

Keywords:

Analysis, Mathematical History, Asymptotic Analysis, Representation

Abstract

Analysis is a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. In the history of mathematics, analysis is the first subject became epidemic, the development of analysis originated from the British mathematician and physicist, the Sir Isaac Newton, and the German mathematician, Gottfried Wilhelm Leibniz, who developed the theory of Calculus, with hundred-years developing, the modern analysis is now very ample and has widely applications, it has grown into an enormous and central field of mathematical research, with applications throughout the sciences and in areas such as finance, economics, and sociology. In this paper, we investigated in some detail with the changing of the ideas in mathematical analysis. By numerating historical facts and the mathematical ideas, we concluded the result that the ideas changing is because of the changing of the studying objects, the conclusion are studied detailly in the paper.

References

  1. I. Newton, “Philosophiae Naturalis Principia Mathematica,” Cambridge University Press, 1687, 1st ed. Cambridge, U.K
  2. E. I. Gordon, A. G. Kusraev, Kutateladze S.S. (2002) Excursus into the History of Calculus. In: Infini-tesimal Analysis. Mathematics and Its Applications, vol 544. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0063-4_1
  3. A. Stubhaug. (2000) Into Mathematical History. In: Niels Henrik Abel and his Times. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04076-8_22
  4. M. Otte. (2007) Mathematical history, philosophy and education. Educ Stud Math 66, 243–255. https://doi.org/10.1007/s10649-007-9079-z
  5. J. B. J. Fourier. (1822) Théorie Analytique de la Chaleur, Didot, Paris, 499-508.
  6. G. H. Hardy. (1908) Mendelian Proportions in a Mixed Population. Science, 28(706), 49-50.
  7. G. H. Hardy, A Course of Pure Mathematics, Cambridge University Press, 2010, 10th ed. Cambridge, U.K
  8. D. Huybrechts, Complex Geometry, Springer-Verlag, 2005, 1st ed.
  9. J. B. J. Fourier. (1808) Mémoire sur la propagation de la Chaleur dans les corps solides, Nouveau Bulle-tin des Sciences par la Société Philomathique, tome 1, no. 6, pp. 112-116
  10. E.M. Stein, R. Shakarich, Fourier Analysis: An Introduction, Princeton University Press, 2014, 2nd ed. New Jersy, U.S.A
  11. E. M. Stein, R. Shakarich, Real Analysis, Princeton University Press, 2014, 2nd ed. New Jersy, U.S.A
  12. E. M. Stein, R. Shakarich, Functional Analysis, Princeton University Press, 2014, 2nd ed. New Jersy, U.S.A
  13. J. J Kulikowski, P. O. Bishop. (1981) Fourier analysis and spatial representation in the visual cortex. Experientia 37, 160–163. https://doi.org/10.1007/BF01963207
  14. E. Hewitt, K. A. Ross, Abstract Harmonic Analysis, Springer-Verlag, 1979, 1st ed.
  15. E. Landau. (1926) Die Bedeutungslosigkeit der Pfeiffer'schen Methode für die analytische Zahlentheo-rie. Monatsh. f. Mathematik und Physik 34, 1–36. https://doi.org/10.1007/BF01694887
  16. H. Lebesgue. (1902) Intégrale, Longueur, Aire. Annali di Matematica, Serie III 7, 231–359. https://doi.org/10.1007/BF02420592
  17. I. M. James, History of Topology, North-Holland, 1999, 1st ed.
  18. J. Peiffer, (1983) Joseph Liouville (1809-1882): ses contributions à la théorie des fonctions d'une variable complexe, Rev. Hist. Sci. 36, 209-248.
  19. J. F. Pommaret. (1991) Intrinsic differential algebra. In: Jacob G., Lamnabhi-Lagarrigue F. (eds) Alge-braic Computing in Control. Lecture Notes in Control and Information Sciences, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006943
  20. Homan, Andrew J, "Applications of microlocal analysis to some hyperbolic inverse problems" (2015). Open Access Dissertations. 473. https://docs.lib.purdue.edu/open_access_dissertations/47
  21. Floer, A. (1988). Morse theory for Lagrangian intersections. Journal of Differential Geometry, 28(3), 513-547, DOI: 10.4310/jdg/1214442477

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Published

2021-08-30

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Section

Research Articles

How to Cite

[1]
Ming-Xing Hu, De-Peng Kong "Analysis of Ideas Changing in the History of Mathematical Analysis " International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 8, Issue 4, pp.505-510, July-August-2021. Available at doi : https://doi.org/10.32628/IJSRST218477