Bibliography for the history of the Jacobian

Jordan Bell
September 10, 2014

Dieudonné chapters II and III [7]

Bashmakova and Rudakov [2, p. 82]

Koenigsberger [23, pp. 173, 270, 342, 344, 401]

Hairer [13, p. 66]

References

  • [1] F. F. Abeles (2011) Nineteenth century roots of quasideterminants. Linear Algebra Appl. 435 (5), pp. 1019–1024.
  • [2] I. G. Bashmakova and A. N. Rudakov (2001) Algebra and algebraic number theory. In Mathematics of the 19th century, volume 1, A. N. Kolmogorov and A. P. Yushkevich (Eds.), pp. 35–136. Cited by: Bibliography for the history of the Jacobian.
  • [3] R. A. Brualdi and H. Schneider (1983) Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley. Linear Algebra Appl. 52–53, pp. 769–791.
  • [4] A. Clebsch (Ed.) (1884) C. G. J. Jacobi’s Vorlesungen über Dynamik. second edition, G. Reimer, Berlin.
  • [5] J. L. Coolidge (1963) A history of geometrical methods. Dover Publications.
  • [6] M. J. Crowe (2011) A history of vector analysis: the evolution of the idea of a vectorial system. Dover Publications.
  • [7] J. Dieudonné (Ed.) (1978) Abrégé d’histoire des mathématiques 1700–1900, tome i. Hermann, Paris. Cited by: Bibliography for the history of the Jacobian.
  • [8] J. L. Dorier (1995) A general outline of the genesis of vector space theory. Historia Math. 22 (3), pp. 227–261.
  • [9] J. Elstrodt (2009) Maß- und Integrationstheorie. sixth edition, Springer.
  • [10] D. Fearnley-Sander (1979) Hermann Grassmann and the creation of linear algebra. Amer. Math. Monthly 86 (10), pp. 809–817.
  • [11] A. P. Ferzola (1994) Euler and differentials. College Mathematics Journal 25 (2), pp. 102–111.
  • [12] H. Grassmann (2000) Extension theory. History of Mathematics, Vol. 19, American Mathematical Society. Note: Translated from the German by Lloyd Kannenberg
  • [13] E. Hairer, S. P. Nørsett, and G. Wanner (2008) Solving ordinary differential equations I: nonstiff problems. second edition, Springer. Cited by: Bibliography for the history of the Jacobian.
  • [14] T. Hawkins (1975) Cauchy and the spectral theory of matrices. Historia Math. 2, pp. 1–29.
  • [15] T. Hawkins (2000) Emergence of the theory of Lie groups: an essay in the history of mathematics 1869–1926. Sources and Studies in the History of Mathematics and Physical Sciences, Springer.
  • [16] C. G. J. Jacobi (1841) De determinantibus functionalibus. J. Reine Angew. Math. 22, pp. 319–359. Note: Gesammelte Werke, Band III, pp. 393–438
  • [17] C. G. J. Jacobi (1841) De formatione et proprietatibus determinatium. J. Reine Angew. Math. 22, pp. 285–318. Note: Gesammelte Werke, Band III, pp. 355–392
  • [18] C. G. J. Jacobi (1845) Theoria novi multiplicatoris systemati aequationum differentialium vulgarium applicandi. J. Reine Angew. Math. 29, pp. 333–376. Note: Gesammelte Werke, Band IV, pp. 317–509
  • [19] C. G. J. Jacobi (1896) Ueber die Functionaldeterminanten. Ostwald’s Klassiker der exakten Wissenschaften, Wilhelm Engelmann, Leipzig.
  • [20] V. J. Katz (1982) Change of variables in multiple integrals: Euler to Cartan. Math. Mag. 55 (1), pp. 3–11.
  • [21] E. Knobloch (1994) Determinants. In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, I. Grattan-Guinness (Ed.), Vol. 1, pp. 766–774.
  • [22] E. Knobloch (1994) From Gauss to Weierstrass: determinant theory and its historical evaluations. In The Intersection of History and Mathematics, S. Chikara, S. Mitsuo, and J. W. Dauben (Eds.), Science Networks. Historical Studies, Vol. 15, pp. 51–66.
  • [23] L. Koenigsberger (1904) Carl Gustav Jacobi Jacobi. B. G. Teubner, Leipzig. Cited by: Bibliography for the history of the Jacobian.
  • [24] K. O. May (1965) Derivatives of determinants and other multilinear functions. Math. Mag. 38 (5), pp. 307–308.
  • [25] T. Muir (1960) The theory of determinants in the historical order of development, volume one and volume two. Dover Publications.
  • [26] E. Netto (1898–1904) Rationale Funktionen mehrerer Veränderlichen. In Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Band I, 1. Teil, W. F. Meyer (Ed.), pp. 255–282.
  • [27] V. V. Prasolov (1994) Problems and theorems in linear algebra. Translations of Mathematical Monographs, Vol. 134, American Mathematical Society. Note: Translated from the Russian by D. A. Leites
  • [28] G. B. Price (1947) Some identities in the theory of determinants. Amer. Math. Monthly 54 (2), pp. 75–90.
  • [29] J. G. Ratcliffe (2006) Foundations of hyperbolic manifolds. second edition, Graduate Texts in Mathematics, Vol. 149, Springer.