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In this chapter we state and prove Stokes’ Theorem, which is one of the cornerstones of modern differential geometry. In fact, we will prove two versions of Stokes’ Theorem: a local version (Theorem 26.2) using the language of smooth singular cubes from the last chapter, and a global version (Theorem 26.16) which concerns integration over the entire manifold.

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Stokes’ Theorem

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  • 发表日期：

    2026年

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  • Will J. Merry

摘要

In this chapter we state and prove Stokes’ Theorem, which is one of the cornerstones of modern differential geometry. In fact, we will prove two versions of Stokes’ Theorem: a local version (Theorem 26.2) using the language of smooth singular cubes from the last chapter, and a global version (Theorem 26.16) which concerns integration over the entire manifold.