Abstract
The integral of an n-form on an n-manifold is defined by piecing together integrals over sets in ℝn using a partition of unity subordinate to an atlas. The change-of-variables theorem guarantees that the integral is well defined, independent of the choice of atlas and partition of unity. Two basic theorems of integral calculus, the change-of-variables theorem and Stokes’ theorem, are discussed in detail along with some applications.
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© 1988 Springer Science+Business Media New York
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Abraham, R., Marsden, J.E., Ratiu, T. (1988). Integration on Manifolds. 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_7
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DOI: https://doi.org/10.1007/978-1-4612-1029-0_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6990-8
Online ISBN: 978-1-4612-1029-0
eBook Packages: Springer Book Archive