Abstract
Two fundamental topics of differential geometry are presented in this chapter in introductory form: exterior derivative and integration of r-forms. The exterior derivative extends to r-forms the elementary definitions of gradient of a function, curl, and divergence of a vector field as well as the meaning of exact and closed 1-forms. The integration of r-forms allows to extend the definitions of surface and volume integrals as well as the Gauss and Stokes theorems.
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Romano, A., Marasco, A. (2018). Exterior Derivative and Integration. In: Classical Mechanics with Mathematica®. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77595-1_8
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DOI: https://doi.org/10.1007/978-3-319-77595-1_8
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-77594-4
Online ISBN: 978-3-319-77595-1
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