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.
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© 1988 Springer Science+Business Media New York
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Abraham, R., Marsden, J.E., Ratiu, T. (1988). Differential Forms. In: Manifolds, Tensor Analysis, and Applications. Applied Mathematical Sciences, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1029-0_6
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DOI: https://doi.org/10.1007/978-1-4612-1029-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6990-8
Online ISBN: 978-1-4612-1029-0
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