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.
KeywordsVector Field Vector Bundle Differential Form Volume Form Dual Basis
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