Keyword | CPC | PCC | Volume | Score | Length of keyword |
---|---|---|---|---|---|

exterior derivative pdf | 0.72 | 0.9 | 375 | 96 | 23 |

exterior | 0.32 | 0.2 | 7267 | 28 | 8 |

derivative | 0.59 | 0.2 | 9402 | 4 | 10 |

0.69 | 0.5 | 476 | 20 | 3 |

Keyword | CPC | PCC | Volume | Score |
---|---|---|---|---|

exterior derivative pdf | 1.51 | 0.3 | 9735 | 24 |

The exterior derivative is defined to be the unique ℝ -linear mapping from k -forms to (k + 1) -forms satisfying the following properties: df is the differential of f , for 0 -forms ( smooth functions) f . d(df ) = 0 for any 0 -form (smooth function) f .

If f is a smooth function (a 0 -form), then the exterior derivative of f is the differential of f . That is, df is the unique 1 -form such that for every smooth vector field X, df (X) = dX f , where dX f is the directional derivative of f in the direction of X .

That is, df is the unique 1 -form such that for every smooth vector field X, df (X) = dX f , where dX f is the directional derivative of f in the direction of X . The exterior product of differential forms (denoted with the same symbol ∧) is defined as their pointwise exterior product .

If a differential k -form is thought of as measuring the flux through an infinitesimal k - parallelotope at each point of the manifold, then its exterior derivative can be thought of as measuring the net flux through the boundary of a (k + 1) -parallelotope at each point.