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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Robert Bryant, Phillip Griffiths and Daniel Grossman
Title: Exterior differential systems and Euler-Lagrange partial differential equations
Additional book information: University of Chicago Press, 2003, 216 pp., ISBN 0-226-07793-4, $45.00$, cloth; ISBN 0-226-07794-2, $17.00$, paper

References [Enhancements On Off] (What's this?)

1.
Anderson, I.M., The Variational Bicomplex, Technical Report, Utah State University, 1989.
  • J. M. Ball and V. J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rational Mech. Anal. 90 (1985), no. 4, 325–388. MR 801585, DOI 10.1007/BF00276295
  • R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior differential systems, Mathematical Sciences Research Institute Publications, vol. 18, Springer-Verlag, New York, 1991. MR 1083148, DOI 10.1007/978-1-4613-9714-4
    • 4.
    Carathéodory, C., Über die Variationsrechnung bei mehrfachen Integralen, Acta Sci. Mat. (Szeged), 4 (1929) 193-216.
  • Élie Cartan, Œuvres complètes. Partie I, 2nd ed., Éditions du Centre National de la Recherche Scientifique (CNRS), Paris, 1984 (French). Groups de Lie. [Lie groups]. MR 753096
  • Mark J. Gotay, An exterior differential systems approach to the Cartan form, Symplectic geometry and mathematical physics (Aix-en-Provence, 1990) Progr. Math., vol. 99, Birkhäuser Boston, Boston, MA, 1991, pp. 160–188. MR 1156539
  • Phillip A. Griffiths, Exterior differential systems and the calculus of variations, Progress in Mathematics, vol. 25, Birkhäuser, Boston, Mass., 1983. MR 684663
  • Ernst Hairer, Christian Lubich, and Gerhard Wanner, Geometric numerical integration, Springer Series in Computational Mathematics, vol. 31, Springer-Verlag, Berlin, 2002. Structure-preserving algorithms for ordinary differential equations. MR 1904823, DOI 10.1007/978-3-662-05018-7
  • Martin Juráš and Ian M. Anderson, Generalized Laplace invariants and the method of Darboux, Duke Math. J. 89 (1997), no. 2, 351–375. MR 1460626, DOI 10.1215/S0012-7094-97-08916-X
  • H. A. Kastrup, Canonical theories of Lagrangian dynamical systems in physics, Phys. Rep. 101 (1983), no. 1-2, 167. MR 733784, DOI 10.1016/0370-1573(83)90037-6
    • 11.
    Kosmann-Schwarzbach, Y., Les Théorèmes de Noether, Éditions de École Polytechnique, Palaiseau, France, 2004.
  • Emmy Noether, Invariant variation problems, Transport Theory Statist. Phys. 1 (1971), no. 3, 186–207. MR 406752, DOI 10.1080/00411457108231446
  • Peter J. Olver, Applications of Lie groups to differential equations, 2nd ed., Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993. MR 1240056, DOI 10.1007/978-1-4612-4350-2
  • Peter J. Olver, Equivalence and the Cartan form, Acta Appl. Math. 31 (1993), no. 2, 99–136. MR 1223167, DOI 10.1007/BF00990539
  • Peter J. Olver, Moving frames—in geometry, algebra, computer vision, and numerical analysis, Foundations of computational mathematics (Oxford, 1999) London Math. Soc. Lecture Note Ser., vol. 284, Cambridge Univ. Press, Cambridge, 2001, pp. 267–297. MR 1839146
  • Wolfgang Reichel, Uniqueness theorems for variational problems by the method of transformation groups, Lecture Notes in Mathematics, vol. 1841, Springer-Verlag, Berlin, 2004. MR 2068382, DOI 10.1007/b96984
  • Toru Tsujishita, On variation bicomplexes associated to differential equations, Osaka Math. J. 19 (1982), no. 2, 311–363. MR 667492
  • A. M. Vinogradov, The ${\cal C}$-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory, J. Math. Anal. Appl. 100 (1984), no. 1, 1–40. MR 739951, DOI 10.1016/0022-247X(84)90071-4
  • Hermann Weyl, Geodesic fields in the calculus of variation for multiple integrals, Ann. of Math. (2) 36 (1935), no. 3, 607–629. MR 1503239, DOI 10.2307/1968645
    • Review Information:

    Reviewer: Peter J. Olver
    Affiliation: University of Minnesota
    Journal: Bull. Amer. Math. Soc. 42 (2005), 407-412
    Published electronically: April 1, 2005
    Review copyright: © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.