Differential Forms

  • Ralph Abraham
  • Jerrold E. Marsden
  • Tudor Ratiu
Part of the Applied Mathematical Sciences book series (AMS, volume 75)

Abstract

Differential k-forms are tensor fields of type (0, k) that are completely antisymmetric. Such tensor fields arise in many applications in physics, engineering, and mathematics. A hint at why this is so is the fact that the classical operations of grad, div, and curl and the theorems of Green, Gauss, and Stokes can all be expressed concisely in terms of differential forms. However, the examples of Hamiltonian mechanics and Maxwell’s equations (see Chapter 8) show that their applicability goes well beyond this.

Keywords

Manifold Assure Meso 

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Ralph Abraham
    • 1
  • Jerrold E. Marsden
    • 2
  • Tudor Ratiu
    • 1
  1. 1.Department of MathematicsUniversity of California—Santa CruzSanta CruzUSA
  2. 2.Control and Dynamical Systems, 107–81California Institute of TechnologyPasadenaUSA

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