Bibliography for the Cauchy-Goursat Theorem

unabridged

 

  1. A correction of an inconsistency in my paper: "Cauchy's theorem on manifolds" [J. Elasticity  56 (1999), no. 2, 129--144; MR 2001a:74002]
    Segev, R.  and G. Rodnay.  
    J. Elasticity  63  (2001),  no. 1, 55--59, MathSciNet.  
  2. Cauchy's theorem on manifolds.
    Segev, R.; Rodnay, G.
    J. Elasticity 56 (1999), no. 2, 129--144 (2000), MathSciNet.  
  3. A proof of Cauchy's theorem.
    Behera, Akrur; Nanda, Sribatsa
    Indian J. Pure Appl. Math. 27 (1996), no. 11, 1107--1110, MathSciNet.  
  4. The development of Cauchy's theorem and its conception. (Chinese)
    Bi, Shu Luo
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban 19 (1993), no. 3, 72--78, MathSciNet.  
  5. Numerical evaluation of analytic functions by Cauchy's theorem.
    Ioakimidis, N. I.; Papadakis, K. E.; Perdios, E. A.
    BIT 31 (1991), no. 2, 276--285, MathSciNet.  
  6. A nonstandard analytic proof of Cauchy-Goursat integral theorem.
    Long, Wen Ting
    J. Harbin Inst. Tech. 1989, no. 4, 100--101, MathSciNet.  
  7. An elementary proof of the generalized Cauchy theorem. (Chinese)
    Du, Chang Guo
    Math. Practice Theory 1989, no. 2, 71--75, MathSciNet.  
  8. An elementary proof of the Cauchy theorem for a simply connected domain. (Czech)  
    Koukol, Jirí
    Casopis Pest. Mat. 112 (1987), no. 3, 257--260, MathSciNet.  
  9. A new proof of Cauchy's theorem. (Romanian)
    Tucsnak, Marius
    Stud. Cerc. Mec. Apl. 43 (1984), no. 3, 279--282, MathSciNet.   
  10. A generalization of the Cauchy theorem. (Romanian)
    Muresan, Tr.
    Bul. Stiint. Inst. Politehn. Cluj-Napoca Ser. Electrotehn.-Energet.-Inform. 25 (1982), 54--58, MathSciNet.  
  11. Cauchy's Theorem  
    Geoffrey C. Berresford  
    American Mathematical Monthly, Vol. 88, No. 10. (Dec., 1981), pp. 741-744, Jstor.   
  12. A note on Cauchy's theorem in classical physics.
    Martins, Luiz C.
    Boll. Un. Mat. Ital. B (5) 18 (1981), no. 3, 1055--1064, MathSciNet.  
  13. Cauchy's theorem on the rigidity of convex polyhedra. (Italian)
    Gario, Paola
    Archimede 33 (1981), no. 1-2, 53--69, MathSciNet.  
  14. An analogue of the Cauchy theorem. (Russian)
    Gurin, A. M.
    Ukrain. Geom. Sb. No. 24 (1981), 32--33, ii., MathSciNet.  
  15. A modification of the Binet-Cauchy theorem. (Russian)
    Pezhkhala, M.
    Zastos. Mat. 17 (1980/81), no. 1, 131--141, MathSciNet.  
  16. On the Use of a Differentiable Homotopy in the Proof of the Cauchy Theorem (in Classroom Notes)  
    R. Vyborny  
    American Mathematical Monthly, Vol. 86, No. 5. (May, 1979), pp. 380-382, Jstor.   
  17. A simple proof of Cauchy theorem.  
    Cerny, Ilja
    Casopis Pest. Mat. 101 (1976), no. 4, 366--369, MathSciNet.  
  18. On Cauchy's theorem in classical physics: some counterexamples.
    Martins, Luiz C.
    Arch. Rational Mech. Anal. 60 (1975/76), no. 4, 325--328, MathSciNet.  
  19. Cauchy's theorem in classical physics.
    Gurtin, Morton E.; Martins, Luiz C.
    Arch. Rational Mech. Anal. 60 (1975/76), no. 4, 305--324, MathSciNet.  
  20. The Gauss-Green and Cauchy Integral Theorems (in Mathematical Notes)  
    W. F. Eberlein  
    American Mathematical Monthly, Vol. 82, No. 6. (Jun. - Jul., 1975), pp. 625-629, Jstor.   
  21. On Cauchy's theorem for real algebraic curves with boundary.  
    Alling, Norman L.
    Pacific J. Math.  57  (1975), no. 2, 315--321, MathSciNet.  
  22. A remark on the converse of Cauchy's theorem.
    Kitamura, Tai-ichi
    Bull. Fac. Sci. Ibaraki Univ. Ser. A No. 4, 17--19. (1972), MathSciNet.  
  23. Yet another constructive variant of the Cauchy theorem. (Russian)
    Zaslavskiui, I. D.; Ceui tin, G. S.
    Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 20 (1971), 36--39, 282--283, MathSciNet.  
  24. The converse of Cauchy's theorem for arbitrary Riemann surfaces.
    Goldstein, Myron
    Proc. Amer. Math. Soc. 25 1970 177--178, MathSciNet.  
  25. Quasi-Cauchy theorems for symmetric and Dini derivatives.
    Lorch, Lee
    Bul. Inst. Politehn. Iasi (N.S.) 14 (18) 1968 fasc. 3--4, 35--37, MathSciNet.  
  26. Cauchy's theorem on a properly bordered domain.
    Chen, Kien-kwong
    Sci. Sinica 13 1964 1747--1754, MathSciNet.  
  27. Complex integration and Cauchy's theorem.
    Watson, G. N.
    Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No. 15 Hafner Publishing Co., New York 1960 vii+79 pp., MathSciNet.  
  28. Cauchy's theorem in Banach spaces.
    Mibu, Yoshimichi
    J. Math. Soc. Japan 11 1959 76--82, MathSciNet.  
  29. A converse of Cauchy's theorem and applications to extremal problems.
    Read, Arthur H.
    Acta Math. 100 1958 1--22, MathSciNet.  
  30. The Cauchy theorem. (Dutch)
    Springer, T. A.
    Simon Stevin 32 1958 68--79, MathSciNet.  
  31. Cauchy's theorem and its converse.
    Ahmad, Mansoor
    Acta Math. 93 (1955), 15--25, MathSciNet.  
  32. A Note on Cauchy's Theorem (in Classroom Notes)  
    Harry Lass  
    American Mathematical Monthly, Vol. 60, No. 2. (Feb., 1953), pp. 110-112, Jstor.  
  33. Cauchy's theorem and formula for quasi-conformal mappings of linear classes. (Russian)
    Sabat, B. V.
    Doklady Akad. Nauk SSSR (N.S.) 69, (1949). 305--308, MathSciNet.  
  34. A generalization of Cauchy's theorem in the calculus of finite differences. (Russian)
    Vitvickiui, N. K.
    Tomsk. Gos. Univ. Ucenye Zapiski 1948, (1948). no. 8, 3--7, MathSciNet.  
  35. A Simplified Approach to Cauchy's Integral Theorem  
    D. V. Widder  
    American Mathematical Monthly, Vol. 53, No. 7. (Aug. - Sep., 1946), pp. 359-363, Jstor.  
  36. An elementary proof of the strong form of the Cauchy theorem.
    Loomis, Lynn H.
    Bull. Amer. Math. Soc. 50, (1944). 831--833, MathSciNet.  
  37. The Cauchy theorem for functions on closed sets.
    Maker, Philip T.
    Bull. Amer. Math. Soc. 48, (1942). 912--916, MathSciNet.  
  38. Cauchy's Paper of 1814 on Definite Integrals  
    H. J. Ettlinger  
    The Annals of Mathematics, 2nd Ser., Vol. 23, No. 3. (Mar., 1922), pp. 255-270, Jstor.  
  39. Ueber den Goursat'schen Beweis des Cauchy'schen Integralsatzes  
    Alfred Pringsheim  
    Transactions of the American Mathematical Society, Vol. 2, No. 4. (Oct., 1901), pp. 413-421, Jstor.  
  40. A Simple Proof of the Fundamental Cauchy-Goursat Theorem  
    Eliakim Hastings Moore  
    Transactions of the American Mathematical Society, Vol. 1, No. 4. (Oct., 1900), pp. 499-506, Jstor.  
  41. Elementary Proof of Cauchy's Theorem  
    Arthur Latham Baker  
    American Journal of Mathematics, Vol. 21, No. 1. (Jan., 1899), p. 24, Jstor.  
  42. Two Proofs of Cauchy's Theorem  
    F. Franklin  
    American Journal of Mathematics, Vol. 9, No. 4. (Jun., 1887), pp. 389-390, Jstor.  

 

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(c) John H. Mathews 2003