Manifolds, Vector Fields, and Differential Forms

  • Jerrold E. Marsden
  • Tudor S. Ratiu
Part of the Texts in Applied Mathematics book series (TAM, volume 17)


In preparation for later chapters, it will be necessary for the reader to learn a little bit about manifold theory. We recall a few basic facts here, beginning with the finite-dimensional case. (See Abraham, Marsden, and Ratiu [1988] for a full account.) The reader need not master all of this material now, but it suffices to read through it for general sense and come back to it repeatedly as our development of mechanics proceeds.


Vector Field Tangent Vector Differential Form Exterior Derivative Coordinate Chart 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Jerrold E. Marsden
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.California Institute of TechnologyControl and Dynamical Systems, 107-81PasadenaUSA
  2. 2.Département de mathématiquesEcole polytechnique fédérale de LausanneLausanneSwitzerland

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