Grad Operator

(A.119) |

which is usually called the

(A.120) |

For two scalar fields and ,

(A.121) |

can be written more succinctly as

(A.122) |

Suppose that we rotate the coordinate axes through an angle about . By analogy with Equations (A.17)-(A.19), the old coordinates ( , , ) are related to the new ones ( , , ) via

(A.123) | ||

(A.124) | ||

(A.125) |

Now,

(A.126) |

giving

(A.127) |

and

(A.128) |

It can be seen, from Equations (A.20)-(A.22), that the differential operator transforms in an analogous manner to a vector. This is another proof that is a good vector.