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Volumn 48, Issue 2-3, 2001, Pages 137-174

History of the infinitely small and the infinitely large in calculus

Author keywords

Calculus; Didactic observations; Differential; History; Infinitely large; Infinitely small; Infinitesimal; Limit; Nonstandard analysis

Indexed keywords


EID: 21244482649     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1016090528065     Document Type: Review
Times cited : (24)

References (62)
  • 4
    • 33748872412 scopus 로고
    • Infinitesimals
    • Bell, J.L.: 1988, 'Infinitesimals', Synthese 75, 285-315.
    • (1988) Synthese , vol.75 , pp. 285-315
    • Bell, J.L.1
  • 5
    • 0005289866 scopus 로고
    • Differentials, higher-order differentials and the derivative in the Leibnizian calculus
    • Bos, H.J.M.: 1974, 'Differentials, higher-order differentials and the derivative in the Leibnizian calculus', Archive for History of the Exact Sciences 14, 1-90.
    • (1974) Archive for History of the Exact Sciences , vol.14 , pp. 1-90
    • Bos, H.J.M.1
  • 8
    • 52549111431 scopus 로고
    • Cavalieri, limits and discarded infinitesimals
    • Boyer, C.B.: 1941, 'Cavalieri, limits and discarded infinitesimals', Scripta Mathematica 8, 79-91.
    • (1941) Scripta Mathematica , vol.8 , pp. 79-91
    • Boyer, C.B.1
  • 10
    • 52549089528 scopus 로고
    • Indivisibles and 'ghosts of departed quantities' in the history of mathematics
    • Cajori, F.: 1925, 'Indivisibles and 'ghosts of departed quantities' in the history of mathematics', Scientia 37, 301-306.
    • (1925) Scientia , vol.37 , pp. 301-306
    • Cajori, F.1
  • 11
    • 52549122368 scopus 로고
    • Grafting of the theory of limits on the calculus of Leibniz
    • Cajori, F.: 1923, 'Grafting of the theory of limits on the calculus of Leibniz', American Mathematical Monthly 30, 223-234.
    • (1923) American Mathematical Monthly , vol.30 , pp. 223-234
    • Cajori, F.1
  • 12
    • 52549121550 scopus 로고
    • Discussion of fluxions: From Berkeley to Woodhouse
    • Cajori, F.: 1917, 'Discussion of fluxions: from Berkeley to Woodhouse', American Mathematical Monthly 24, 145-154.
    • (1917) American Mathematical Monthly , vol.24 , pp. 145-154
    • Cajori, F.1
  • 14
    • 33847373787 scopus 로고
    • Abraham Robinson and nonstandard analysis: History, philosophy, and foundations of mathematics
    • W. Aspray and P Kitcher (eds.), University of Minnesota Press, Minneapolis
    • Dauben, J.W.: 1988, 'Abraham Robinson and nonstandard analysis: history, philosophy, and foundations of mathematics', in W. Aspray and P Kitcher (eds.), History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis, pp. 177-200.
    • (1988) History and Philosophy of Modern Mathematics , pp. 177-200
    • Dauben, J.W.1
  • 15
  • 17
    • 84904688919 scopus 로고
    • Dudley, U. (ed.): Mathematical Association of America, Washington, DC
    • Dudley, U. (ed.):1993, Readings for Calculus, Mathematical Association of America, Washington, DC.
    • (1993) Readings for Calculus
  • 20
    • 3042731434 scopus 로고
    • 2 vols., Mathematical Association of America, Washington, DC
    • Eves, H.: 1983, Great Moments in Mathematics, 2 vols., Mathematical Association of America, Washington, DC.
    • (1983) Great Moments in Mathematics
    • Eves, H.1
  • 21
    • 52549084677 scopus 로고
    • The use of history in teaching mathematics
    • Fauvel, J. (ed.)
    • Fauvel, J. (ed.): 1991, The use of history in teaching mathematics, Special Issue of For the Learning of Mathematics 11(2).
    • (1991) For the Learning of Mathematics , vol.11 , Issue.2 SPEC. ISSUE
  • 23
    • 0742319083 scopus 로고    scopus 로고
    • Fauvel, J. and van Maanen J. (eds.): Kluwer Academic Publishers, Dordrecht
    • Fauvel, J. and van Maanen J. (eds.): 2000, History in Mathematics Education: The ICMI Study, Kluwer Academic Publishers, Dordrecht.
    • (2000) History in Mathematics Education: The ICMI Study
  • 24
    • 34249969590 scopus 로고
    • The calculus as algebraic analysis: Some observations on mathematical analysis in the 18 century
    • Fraser, C: 1989, 'The calculus as algebraic analysis: some observations on mathematical analysis in the 18 century', Archive for History of the Exact Sciences 39, 317-335.
    • (1989) Archive for History of the Exact Sciences , vol.39 , pp. 317-335
    • Fraser, C.1
  • 25
    • 0002186150 scopus 로고
    • Who gave you the epsilon? Cauchy and the origins of rigorous calculus
    • Grabiner, J.W.: 1983a, 'Who gave you the epsilon? Cauchy and the origins of rigorous calculus', American Mathematical Monthly 90, 185-194.
    • (1983) American Mathematical Monthly , vol.90 , pp. 185-194
    • Grabiner, J.W.1
  • 26
    • 52549120066 scopus 로고
    • The changing concept of change: The derivative from Fermat to Weierstrass
    • Grabiner, J.W.: 1983b, 'The changing concept of change: the derivative from Fermat to Weierstrass', Mathematics Magazine 56, 195-206.
    • (1983) Mathematics Magazine , vol.56 , pp. 195-206
    • Grabiner, J.W.1
  • 31
    • 52549121825 scopus 로고
    • Infinitesimals from Leibniz to Robinson: Time to bring them back to school
    • Harnik, V.: 1986, 'Infinitesimals from Leibniz to Robinson: time to bring them back to school', Mathematical Intelligencer 8(2), 41-47, 63.
    • (1986) Mathematical Intelligencer , vol.8 , Issue.2 , pp. 41-47
    • Harnik, V.1
  • 32
  • 38
    • 33746550806 scopus 로고
    • Fluxions, limits, and infinite littlenesse: A study of Newton's presentation of the calculus
    • Kitcher, P.: 1973, 'Fluxions, limits, and infinite littlenesse: a study of Newton's presentation of the calculus', Isis 64, 33-49.
    • (1973) Isis , vol.64 , pp. 33-49
    • Kitcher, P.1
  • 39
    • 0040796947 scopus 로고
    • Euler and infinite series
    • Kline, M.: 1983, 'Euler and infinite series', Mathematics Magazine 56, 307-314.
    • (1983) Mathematics Magazine , vol.56 , pp. 307-314
    • Kline, M.1
  • 41
    • 52549116101 scopus 로고
    • Cauchy and the continuum: The significance of non-standard analysis for the history and philosophy of mathematics
    • Lakatos, I.: 1978, 'Cauchy and the continuum: the significance of non-standard analysis for the history and philosophy of mathematics', Mathematical Intelligencer 1, 151-161.
    • (1978) Mathematical Intelligencer , vol.1 , pp. 151-161
    • Lakatos, I.1
  • 42
    • 0039721083 scopus 로고
    • Fourier series: The genesis and evolution of a theory
    • Langer, R.E.: 1947, 'Fourier series: the genesis and evolution of a theory', American Mathematical Monthly 54(S), 1-86.
    • (1947) American Mathematical Monthly , vol.54 , Issue.S , pp. 1-86
    • Langer, R.E.1
  • 44
    • 0039969739 scopus 로고    scopus 로고
    • 'On the historical development of infinitesimal mathematics', I, II
    • Laugwitz, D.: 1997, 'On the historical development of infinitesimal mathematics', I, II, American Mathematical Monthly 104, 447-455, 660-669.
    • (1997) American Mathematical Monthly , vol.104 , pp. 447-455
    • Laugwitz, D.1
  • 45
    • 52549105683 scopus 로고
    • Use of the history of mathematics in the teaching of the subject
    • MacKinnon, N. (ed.)
    • MacKinnon, N. (ed.): 1992, Use of the history of mathematics in the teaching of the subject, Special Issue of Mathematical Gazette 76(475).
    • (1992) Mathematical Gazette , vol.76 , Issue.475 SPEC. ISSUE
  • 46
    • 52549088197 scopus 로고
    • History in the mathematics curriculum
    • May. K. O.: 1974, 'History in the mathematics curriculum', American Mathematical Monthly 81, 899-901.
    • (1974) American Mathematical Monthly , vol.81 , pp. 899-901
    • May, K.O.1
  • 48
    • 52549095198 scopus 로고
    • Why the history and philosophy of mathematics should not be rated X
    • Pimm, D.: 1982, 'Why the history and philosophy of mathematics should not be rated X', For the Learning of Mathematics 3, 12-15.
    • (1982) For the Learning of Mathematics , vol.3 , pp. 12-15
    • Pimm, D.1
  • 51
    • 0345079765 scopus 로고
    • The discovery of the series formula for π by Leibniz, Gregory, and Nilakantha
    • Roy, R.: 1990, 'The discovery of the series formula for π by Leibniz, Gregory, and Nilakantha', Mathematics Magazine 63, 291-306.
    • (1990) Mathematics Magazine , vol.63 , pp. 291-306
    • Roy, R.1
  • 55
    • 52549105939 scopus 로고
    • New models of the real-number line
    • Steen, L.A.: 1971, 'New models of the real-number line', Scientific American 225, 92-99.
    • (1971) Scientific American , vol.225 , pp. 92-99
    • Steen, L.A.1
  • 58
    • 33750542425 scopus 로고
    • Swetz, F. et al. (eds.): Mathematical Association of America, Washington, DC
    • Swetz, F. et al. (eds.): 1995, Learn from the Masters!, Mathematical Association of America, Washington, DC.
    • (1995) Learn from the Masters!
  • 60
    • 3042817704 scopus 로고
    • (translated from the Russian by A. Shenitzer), Birkhäuser, Boston
    • Vilenkin, N.Y.; 1995, In Search of Infinity (translated from the Russian by A. Shenitzer), Birkhäuser, Boston.
    • (1995) In Search of Infinity
    • Vilenkin, N.Y.1
  • 61
    • 52549119496 scopus 로고
    • History in the mathematics curriculum: Its status, quality and function
    • Wilder, R.L.: 1972, 'History in the mathematics curriculum: its status, quality and function', American Mathematical Monthly 79, 479-495.
    • (1972) American Mathematical Monthly , vol.79 , pp. 479-495
    • Wilder, R.L.1
  • 62
    • 27844434563 scopus 로고
    • Mathematical Association of America, Washington, DC
    • Young, R.M.: 1992, Excursions in Calculus, Mathematical Association of America, Washington, DC.
    • (1992) Excursions in Calculus
    • Young, R.M.1


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