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Differential Geometry: The Interface between Pure and Applied Mathematics
Edited by: Mladen Luksic, Clyde Martin, and William Shadwick
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Contemporary Mathematics
1987; 273 pp; softcover
Volume: 68
Reprint/Revision History:
reprinted 1991
ISBN-10: 0-8218-5075-X
ISBN-13: 978-0-8218-5075-6
List Price: US$45
Member Price: US$36
Order Code: CONM/68
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Normally, mathematical research has been divided into "pure" and "applied," and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas.

The papers in this volume represent the proceedings of a conference entitled "Differential Geometry: The Interface Between Pure and Applied Mathematics," which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis, and control theory.

Table of Contents

  • G. S. Ammar -- Geometric aspects of Hessenberg matrices
  • D. E. Betounes -- Differential geometric aspects of continuum mechanics in higher dimensions
  • A. M. Bloch -- Lax-type flows on Grassmann manifolds
  • W. M. Boothby and W. P. Dayawansa -- Some global aspects of the feedback linearization problem
  • R. L. Bryant -- On notions of equivalence of variational problems with one independent variable
  • D. M. DeTurck and G. Kamberov -- A singular problem in elasticity theory
  • L. D. Drager, R. L. Foote, and C. F. Martin -- Controllability of linear systems, differential geometry of curves in Grassmannians, and Riccati equations
  • T. E. Duncan -- Explicit solutions for an estimation problem in manifolds associated with Lie groups
  • R. B. Gardner and W. F. Shadwick -- Overdetermined equivalence problems with an application to feedback equivalence
  • R. Grossman and R. G. Larson -- The symbolic computation of higher-order derivations: symmetries of expressions and actions of group algebras
  • N. Kamran and W. F. Shadwick -- Cartan's method of equivalence and the classification of second-order ordinary differential equations
  • M. Kawski -- A necessary condition for local controllability
  • A. J. Krener -- Normal forms for linear and nonlinear systems
  • B. Mårtensson -- Adaptive stabilization of multivariable linear systems
  • C. Martin and J. Smith -- Approximation, interpolation, and sampling
  • T. A. Posbergh, P. S. Krishnaprasad, and J. E. Marsden -- Stability analysis of a rigid body with a flexible attachment using the energy-Casimir method
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