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

exterior derivative of a 2 form | 1.57 | 0.8 | 377 | 70 | 31 |

exterior | 0.31 | 0.5 | 4717 | 4 | 8 |

derivative | 0.81 | 0.8 | 2773 | 46 | 10 |

of | 0.78 | 0.5 | 766 | 51 | 2 |

a | 1.47 | 0.6 | 4697 | 33 | 1 |

2 | 0.69 | 0.1 | 5673 | 26 | 1 |

form | 1.7 | 0.3 | 9870 | 99 | 4 |

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

exterior derivative of a 2-form | 0.89 | 0.8 | 5473 | 86 |

exterior derivative of integral | 0.16 | 1 | 2187 | 12 |

derivative of 2 x 2 | 1.97 | 0.3 | 8780 | 72 |

derivative of a x 2 | 1.82 | 0.9 | 2270 | 71 |

derivative of ex 2 | 0.82 | 1 | 8855 | 81 |

derivative of x 2 e x | 0.74 | 0.4 | 4338 | 10 |

derivative of 2e 3x | 1.2 | 0.5 | 7417 | 39 |

derivative of 2 x 3 | 1.55 | 0.9 | 5864 | 59 |

derivative of 2e x | 1.02 | 0.6 | 7704 | 74 |

derivative of 2 over x | 0.57 | 0.8 | 3505 | 13 |

derivative of e 2 x | 0.89 | 0.5 | 3255 | 68 |

derivative of x 2 | 0.7 | 0.6 | 685 | 53 |

derivative of x 2 x | 1.42 | 0.9 | 6306 | 80 |

f 2 x derivative | 0.54 | 0.8 | 8761 | 54 |

derivatives of x 2 | 1.13 | 0.8 | 5344 | 35 |

e x 2 derivative | 1.32 | 1 | 5698 | 20 |

derivative e 3x 2 | 1.87 | 1 | 1078 | 20 |

derivative e 2x 2 | 0.7 | 0.7 | 2648 | 36 |

derivative of x 2e x | 1.97 | 0.1 | 8904 | 42 |

the derivative of 2 x | 1.52 | 0.2 | 5279 | 51 |

derivative of 2e 2x | 0.98 | 1 | 82 | 12 |

derivative e x 2 | 0.78 | 0.9 | 9210 | 26 |

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 .

Thinking of a function as a zero-form, the exterior derivative extends linearly to all differential k -forms using the formula when is a -form and where is the wedge product . The exterior derivative of a -form is a -form. For example, for a differential k -form where is the permutation tensor . It is always the case that .

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 .