منابع مشابه
Stokes’ Theorem
I. Introduction. Stokes' theorem on a manifold is a central theorem of mathematics. Special cases include the integral theorems of vector analysis and the Cauchy-Goursat theorem. My purpose here is to prove this version of Stokes' Theorem. Let ω be a continuous differential (n − 1)-form on a compact oriented n-manifold M with boundary ∂M. Suppose that ω is differen-tiable on M − ∂M and dω is Le...
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This paper will prove the generalized Stokes Theorem over kdimensional manifolds. We will begin from the definition of a k-dimensional manifold as well as introduce the notion of boundaries of manifolds. Using these, we will construct the necessary machinery, namely tensors, wedge products, differential forms, exterior derivatives, and integrals over manifolds, in order to prove the main result...
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Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney [Geometric integration theory, Princeton Univ. Press, Princeton, NJ, 1957] and by geometric measure theorists because we extend the class of integrable domains. Let oi be an «-form defined on Rm . We s...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1950
ISSN: 2156-2261
DOI: 10.1215/kjm/1250777991