The basic types of derivatives operating on a Vector Field are the Curl , Divergence , and Gradient .

Vector derivative identities involving the Curl include

(1) | |

(2) | |

(3) | |

(4) | |

(5) |

(6) | |

(7) | |

(8) |

Vector derivative identities involving the Divergence include

(9) | |

(10) | |

(11) | |

(12) | |

(13) | |

(14) |

(15) | |

(16) | |

(17) | |

(18) | |

(19) | |

(20) |

(21) | |

(22) | |

(23) |

Vector derivative identities involving the Gradient include

(24) | |

(25) | |

(26) | |

(27) | |

(28) | |

(29) | |

(30) | |

(31) |

Vector second derivative identities include

(32) | |

(33) |

(34) | |

(35) | |

(36) | |

(37) | |

(38) | |

(39) | |

(40) | |

(41) |

Combination identities include

(42) | |

(43) | |

(44) | |

(45) | |

(46) |

**References**

Gradshteyn, I. S. and Ryzhik, I. M. ``Vector Field Theorem.'' Ch. 10 in
*Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA: Academic Press, pp. 1081-1092, 1980.

Morse, P. M. and Feshbach, H. ``Table of Useful Vector and Dyadic Equations.'' *Methods of Theoretical Physics, Part I.*
New York: McGraw-Hill, pp. 50-54 and 114-115, 1953.

© 1996-9

1999-05-26