Bibliography for the Fundamental Theorem of Calculus

unabridged

 

  1. The fundamental theorem of calculus in two dimensions   
    Eisenberg, Bennett; Sullivan, Rosemary
    Amer. Math. Monthly  109  (2002),  no. 9, 806--817, Jstor.  
  2. A proof of the fundamental theorem of calculus using Hausdorff measures.
    Volintiru, Constantin
    Real Anal. Exchange 26 (2000/01), no. 1, 381--389, MathSciNet.  
  3. A fundamental theorem of calculus for the Kurzweil-Henstock integral in B Rm.
    Cabral, Emmanuel; Lee, Peng-Yee
    Real Anal. Exchange 26 (2000/01), no. 2, 867--876, MathSciNet.  
  4. The geometric ratio of the fundamental theorem of calculus. (Spanish)
    Córdoba, Antonio
    Gac. R. Soc. Mat. Esp. 3 (2000), no. 3, 435--446, MathSciNet.  
  5. The fundamental theorem of calculus for Lebesgue integral.
    Bárcenas, Diómedes
    Divulg. Mat. 8 (2000), no. 1, 75--85, MathSciNet.  
  6. The fundamental theorem of calculus for multidimensional Banach space-valued Henstock vector integrals.
    Federson, Márcia
    Real Anal. Exchange 25 (1999/00), no. 1, 469--480, MathSciNet.  
  7. A Kinematic Approach to the Fundamental Theorem of Calculus  
    Barbanel, Julius  
    The UMAP journal, UMAP, 1999, vol. 20, no. 2, pp. 101--115, COMAP.  
  8. "Sim X" and the Fundamental Theorem of Calculus  
    Sprows, David J.  
    Mathematics and computer education, 1999, vol. 33, no. 3, pp. 257, Ingenta.  
  9. Fundamental theorem of calculus for locally bounded spaces.
    Bayoumi, Aboubakr
    J. Nat. Geom. 15 (1999), no. 1-2, 101--106, MathSciNet.  
  10. The Fundamental Theorem of Calculus for Gauge Integrals  
    Jack Lamoreaux and Gerald Armstrong  
    Mathematics Magazine: Volume 71, Number 3, Pages: 208-212, 1998.
  11. An Example Demonstarting the Fundamental Theorem of Calculus  
    Bob Palais  
    College Math Journal: Volume 29, Number 4, Pages: 311-313, 1998.
  12. The fundamental theorem of geometric calculus via a generalized Riemann integral.
    Macdonald, Alan
    Adv. Appl. Clifford Algebras 8 (1998), no. 1, 5--16, MathSciNet.  
  13. From Tanaka's formula to Itô's formula: the fundamental theorem of stochastic calculus.
    Rajeev, B.
    Proc. Indian Acad. Sci. Math. Sci. 107 (1997), no. 3, 319--327, MathSciNet.  
  14. The Point-Slope Formula Leads to the Fundamental Theorem of Calculus (in Classroom Capsules)  
    Anthony J. Macula  
    The College Mathematics Journal, Vol. 26, No. 2. (Mar., 1995), pp. 135-139, Jstor.  
  15. Newton, Leibniz and the "fundamental theorem of integral calculus". Geometric and algorithmic aspects. (Italian)
    Giacardi, Livia
    Geometry, fluxions and differentials (Italian), 289--328, Ist. Ital. Studi Filos. Semin. Sci. (N.S.), 8, Città Sole, Naples, 1995, MathSciNet.  
  16. A counterexample to the "fundamental theorem of stochastic calculus of variations".
    Kazimierczyk, P.
    Arch. Mech. (Arch. Mech. Stos.) 46 (1994), no. 5, 789--795 (1995), MathSciNet.  
  17. Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus  
    Thompson, Patrick W.  
    Educational studies in mathematics, 1994, vol. 26, no. 2/3, pp. 229, Ingenta.  
  18. Stochastic integration via white noise and the fundamental theorem of calculus.
    Redfern, M.
    Stochastic analysis on infinite-dimensional spaces (Baton Rouge, LA, 1994), 255--263, Pitman Res. Notes Math. Ser., 310, Longman Sci. Tech., Harlow, 1994, MathSciNet.  
  19. What is the fundamental theorem of integral calculus?  
    Toumasis, C.  
    International journal of mathematical education in science and technology, 1993, vol. 24, no. 5, pp. 685, Ingenta.  
  20. Why there is no "fundamental theorem of calculus" for the Riemann integral  
    Berberian, S. K.
    Exposition. Math. 11 (1993), no. 3, 271--279, MathSciNet.  
  21. A note on the fundamental theorem of calculus for manifolds. (Chinese)
    Wen, Tao
    Acta Sci. Natur. Univ. Norm. Hunan. 16 (1993), no. 4, 317--321, MathSciNet.  
  22. The fundamental theorem of calculus in an abstract setting.
    Száz, Árpád
    Tatra Mt. Math. Publ. 2 (1993), 167--174, MathSciNet.  
  23. Even more on the fundamental theorem of calculus.
    Swartz, Charles
    Proyecciones 12 (1993), no. 2, 129--135, MathSciNet.  
  24. A generalization of the fundamental theorem of calculus and differentiability of convex functions. (Chinese)
    Nan, Chao Xun
    Anhui Shida Xuebao Ziran Kexue Ban 16 (1993), no. 2, 5--7, MathSciNet.  
  25. How Should We Introduce Integration?  
    David M. Bressoud  
    College Math Journal: Volume 23, Number 4, Pages: 296-298, 1992.
  26. A simple proof of the fundamental theorem of Kirby calculus on links.
    Lu, Ning
    Trans. Amer. Math. Soc. 331 (1992), no. 1, 143--156, MathSciNet.  
  27. Uniform Probability Density Functions and the Fundamental Theorem of Calculus  
    Dobbs, David E.  
    Mathematics and computer education, 1992, vol. 26, no. 2, pp. 166, Ingenta.  
  28. The Fundamental Theorem of Calculus is Forever Fundamental  
    Schechter, Murray
    Mathematics and computer education, 1992, vol. 26, no. 1, pp. 40, Ingenta.  
  29. Visualizing differentials in integration to picture the fundamental theorem of calculus  
    Tall, David  
    MT, 1991, no. 137, pp. 29, Ingenta.  
  30. A Fundamental Theorem of Calculus that Applies to All Riemann Integrable Functions  
    Michael W. Botsko  
    Mathematics Magazine: Volume 64, Number 5, Pages: 347-348, 1991.
  31. Is There Calcus Without The Fundamental Theorem?  
    Johnson, Marvin L.  
    Mathematics and computer education, 1991, vol. 25, no. 2, pp. 165, Ingenta.  
  32. Discovering the Fundamental Theorem of Calculus Using Computer Algebra Systems  
    Gordon, Sheldon P.  
    Mathematics and computer education, 1991, vol. 25, no. 1, pp. 6, Ingenta.  
  33. Lebesgue's "fundamental theorem of calculus" revisited.
    Berberian, S. K.
    Paul Halmos, 265--285, Springer, New York, 1991, MathSciNet.  
  34. Fundamental theorem of Yeh-Wiener calculus.
    Chang, Joo Sup; Park, Chull; Skoug, David
    Stochastic Anal. Appl. 9 (1991), no. 3, 245--262, MathSciNet.  
  35. Sur l'histoire du théorème fondamental de l'algèbre: théorie des équations et calcul intégral. (French) [On the history of the fundamental theorem of algebra: the theory of equations and integral calculus]  
    Gilain, Christian
    Arch. Hist. Exact Sci.  42  (1991),  no. 2, 91--136, MathSciNet.  
  36. Fundamental theorems of calculus for packing measures on the real line.
    Haase, H.
    Math. Nachr. 148 (1990), 293--302, MathSciNet.  
  37. Fundamental theorem of Wiener calculus.
    Park, Chull; Skoug, David; Smolowitz, Lawrence
    Internat. J. Math. Math. Sci. 13 (1990), no. 3, 443--452, MathSciNet.  
  38. Presenting The Fundamental Theorem Of Calculus  
    Dobbs, David E.  
    Mathematics and computer education, 1989, vol. 23, no. 3, pp. 183, Ingenta.  
  39. Using Computer Algebra Systems To Teach The Fundamental Theorem Of Calculus  
    Mathews, John H.  
    Mathematics and computer education, 1989, vol. 23, no. 3, pp. 199-204, Ingenta.  
  40. A fundamental theorem of dyadic calculus for the unit square.
    Schipp, Ferenc; Wade, William R.
    Appl. Anal. 34 (1989), no. 3-4, 203--218, MathSciNet.  
  41. More on the Fundamental Theorem of Calculus (in The Teaching of Mathematics)  
    Charles Swartz, Brian S. Thomson  
    American Mathematical Monthly, Vol. 95, No. 7. (Aug. - Sep., 1988), pp. 644-648, Jstor.  
  42. Fundamental theorems of calculus for Hausdorff measures on the real line.
    Withers, W. D.
    J. Math. Anal. Appl. 129 (1988), no. 2, 581--595, MathSciNet.  
  43. A Riemann type integration and the fundamental theorem of calculus.
    Pfeffer, Washek F.
    Rend. Circ. Mat. Palermo (2) 36 (1987), no. 3, 482--506 (1988), MathSciNet.  
  44. The multidimensional fundamental theorem of calculus.
    Pfeffer, Washek F.
    J. Austral. Math. Soc. Ser. A 43 (1987), no. 2, 143--170, MathSciNet.  
  45. The fundamental theorem of linearised Regge calculus.
    Barrett, J. W.
    Phys. Lett. B 190 (1987), no. 1-2, 135--136, MathSciNet.  
  46. Stronger Versions of the Fundamental Theorem of Calculus (in The Teaching of Mathematics)  
    Michael W. Botsko, Richard A. Gosser  
    American Mathematical Monthly, Vol. 93, No. 4. (Apr., 1986), pp. 294-296, Jstor.  
  47. The kinematical aspect of the fundamental theorem of calculus  
    Betounes, David E.
    Amer. J. Phys. 51 (1983), no. 6, 554--560, MathSciNet.  
  48. An elementary version of the fundamental theorem of integral calculus. (Slovenian)
    Volcic, Aljosa
    Obzornik Mat. Fiz. 29 (1982), no. 4, 97--100, MathSciNet.  
  49. An Advanced Calculus Proof of the Fundamental Theorem of Algebra (in Classroom Notes)  
    Frank Forelli  
    The American Mathematical Monthly, Vol. 88, No. 5. (May, 1981), pp. 347-348, Jstor.  
  50. A note on the fundamental theorem of calculus.
    Yosida, Kôsaku
    Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), no. 5, 241, MathSciNet.  
  51. On generalisation of fundamental theorem of integral calculus for Banach-space-valued functions for application in multivariate-analysis.
    Ghosh, S.
    Bull. Calcutta Math. Soc. 72 (1980), no. 5, 287--297, MathSciNet.  
  52. Multiplication and the fundamental theorem of calculus---a survey.
    Fleissner, Richard J.
    Real Anal. Exchange 2 (1976/77), no. 1, 7--34, MathSciNet.  
  53. A remark on the fundamental theorem of integral calculus. (Bulgarian)
    Prodanov, Ivan
    Fiz.-Mat. Spis. B'lgar. Akad. Nauk. 18(51) (1975), no. 2, 123--125, MathSciNet.  
  54. A generalization of the fundamental theorem of the calculus. Collection of articles dedicated to Professor Tsing Houa Teng on the occasion of his 70th birthday.
    Chu, M. L.; Pu, H. W.
    Tamkang J. Math. 4 (1973), no. 2, 131--137, MathSciNet.  
  55. Some corrections to my paper: "A stochastic calculus and its application to some fundamental theorems of natural selection".
    Mode, Charles J.
    J. Appl. Probability 4 1967 609--611, MathSciNet.  
  56. A stochastic calculus and its application to some fundamental theorems of natural selection.
    Mode, Charles J.
    J. Appl. Probability 3 1966 327--352, MathSciNet.  
  57. Spoof of the Fundamental Theorem of Calculus (in Classroom Notes)  
    R. L. Eisenman  
    American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), p. 371, Jstor.  
  58. The fundamental theorems of the differential calculus.
    Young, W. H.
    Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No. 11 Hafner Publishing Co., New York 1960 ix+72 pp., MathSciNet.  
  59. On a fundamental theorem of the calculus of variations.
    Serrin, James
    Acta Math. 102 1959 1--22, MathSciNet.  
  60. On the fundamental theorems of the differential and integral calculus in linear spaces. (Russian)
    Gavurin, M. K.
    Vestnik Leningrad. Univ. 13 1958 no. 7, 38--48, MathSciNet.  
  61. On the fundamental theorems of the calculus.
    Gál, István S.
    Trans. Amer. Math. Soc. 86 1957 309--320, MathSciNet.  
  62. A Fundamental Theorem of Calculus (in Classroom Notes)  
    M. K. Fort, Jr.  
    American Mathematical Monthly, Vol. 63, No. 5. (May, 1956), pp. 334-335, Jstor.  
  63. On the Applications of the Fundamental Theorem of Integral Calculus (in Classroom Notes)  
    Paul Schillo  
    American Mathematical Monthly, Vol. 63, No. 5. (May, 1956), pp. 340-341, Jstor.  
  64. The Fundamental Theorem of the Calculus (in Classroom Notes)  
    Louis Brand  
    American Mathematical Monthly, Vol. 62, No. 6. (Jun. - Jul., 1955), pp. 440-441, Jstor.  
  65. The Fundamental Theorem of the Differential Calculus (in Classroom Notes)  
    W. R. Ransom  
    American Mathematical Monthly, Vol. 62, No. 5. (May, 1955), pp. 361-363, Jstor.  
  66. A Natural Approach to the Fundamental Theorem of the Integral Calculus (in Classroom Notes)  
    J. P. Hoyt  
    American Mathematical Monthly, Vol. 61, No. 6. (Jun. - Jul., 1954), pp. 413-415, Jstor.  
  67. A Fundamental Theorem of the Calculus (in Classroom Notes)  
    Israel Halperin  
    American Mathematical Monthly, Vol. 61, No. 2. (Feb., 1954), pp. 122-123, Jstor.  

 

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(c) John H. Mathews 2003