# general Stokes theorem

Let $M$ be an oriented $r$-dimensional differentiable manifold with
a piecewise differentiable^{} boundary $\partial M$. Further, let $\partial M$ have the
orientation induced by $M$.
If $\omega $ is an $(r-1)$-form on $M$ with compact support, whose components
have continuous^{} first partial derivatives^{} in any coordinate chart, then

$${\int}_{M}d\omega ={\int}_{\partial M}\omega .$$ |

Title | general Stokes theorem |
---|---|

Canonical name | GeneralStokesTheorem |

Date of creation | 2013-03-22 12:44:52 |

Last modified on | 2013-03-22 12:44:52 |

Owner | matte (1858) |

Last modified by | matte (1858) |

Numerical id | 11 |

Author | matte (1858) |

Entry type | Theorem |

Classification | msc 58C35 |

Synonym | Stokes theorem |

Related topic | DifferentialForms |

Related topic | GaussGreenTheorem |

Related topic | ClassicalStokesTheorem |