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Differential geometry as a tool for applied mathematicians

Invited Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 810)

Keywords

  • Vector Field
  • Base Space
  • Exterior Derivative
  • Integral Manifold
  • Coordinate Component

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References

  1. J. A. Schouten, Ricci-Calculus (Springer-Verlag, Berlin, 1954)

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  2. É. Cartan, Les Systèmes différentiels extérieurs et leurs applications Géométriques (Hermann, Paris, 1945)

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  3. W. Slebodzinski, Exterior Forms and their Applications (Polish Scientific Publishers, Warsaw, 1970)

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  4. Y. Choquet-Bruhat, Géométrie différentielle et systèmes extérieurs (Dunod, Paris, 1968)

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  5. F. B. Estabrook "Some Old and New Techniques for the Practical Use of Differential Forms" in R. Miura, Ed., Bäcklund Transformation, the Inverse Scattering Method, Solitons and their Application, Lecture Notes in Mathematics No. 515 (Springer-Verlag, Berlin, New York, 1976)

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  6. B. K. Harrison and F. B. Estabrook, "Geometric Approach to Invariance Groups and Solution of Partial Differential Systems," J. Math. Phys. 12, 653–666 (1971)

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  7. F. B. Estabrook and H. D. Wahlquist, "The Geometric Approach to Sets of Ordinary Differential Equations and Hamiltonian Mechanics, SIAM Review 17, 201–220 (1975).

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  8. R. Hermann, Differential Geometry and the Calculus of Variations, 2nd Edition, Vol. XVII, Interdisciplinary Mathematics (Math Sci Press, Brookline, MA, 1977)

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  9. H. D. Wahlquist and F. B. Estabrook, "Prolongation Structures of Nonlinear Evolution Equations" J. Math. Phys. 16, 1–7 (1975)

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  10. F. B. Estabrook and H. D. Wahlquist, "Prolongation Structures of Nonlinear Evolution Equations. II", J. Math. Phys. 17, 1293–7 (1976)

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  11. F. B. Estabrook, H. D. Wahlquist and R. Hermann, "Differential-Geometric Prolongations and Bäcklund Transformations," in R. Hermann, Ed., The Ames Research Center (NASA) 1976 Conference on the Geometric Theory of Non-Linear Waves. Lie Groups: History Frontiers and Applications, Vol. VI, (Math Sci Press, Brookline, MA, 1977).

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  13. F. B. Estabrook and H. D. Wahlquist, "Prolongation Structures, Connection Theory and Bäcklund Transformation" in F. Calogero, Ed., Nonlinear Evolution Equations Solvable by the Spectral Transform, Research Notes in Mathematics No. 26 (Pittman, London, San Francisco, Melbourne, 1978)

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© 1980 Springer-Verlag

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Estabrook, F.B. (1980). Differential geometry as a tool for applied mathematicians. In: Martini, R. (eds) Geometrical Approaches to Differential Equations. Lecture Notes in Mathematics, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089971

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  • DOI: https://doi.org/10.1007/BFb0089971

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10018-8

  • Online ISBN: 978-3-540-38166-2

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