hey all!(adsbygoogle = window.adsbygoogle || []).push({});

i was hoping someone could either state an article or share some knowledge with a way (if any) to derive the vector calculus "del" relationships. i.e. $$ \nabla \cdot ( \rho \vec{V}) = \rho (\nabla \cdot \vec{V}) + \vec{V} \cdot (\nabla\rho)$$

now i do understand this to be like the product rule but is there any way to derive this in a similar fashion to other vector calculus identities, perhaps using the Kronecker delta or the permutation epsilon?

as an example, i can derive almost any trig identity using $$e^{i \theta}=\cos \theta+i \sin \theta$$ by making changes to [itex]\theta[/itex], perhaps letting [itex]\theta = \alpha + \beta[/itex] and then equating real and imaginary parts and doing a little bit of algebra.

is there anything like this for vector identities (perhaps not a base equation, but a method?)

thanks for your help!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector calc identities

Loading...

Similar Threads - Vector calc identities | Date |
---|---|

Math methods in physics book - vector calc proof | Jan 14, 2013 |

Vector Calc: Can you verify my answer? | Jun 7, 2009 |

Rigorous book for multivariable + vector calc? | Jan 26, 2009 |

Extrema with Lagrange in Vector Calc. | Sep 29, 2008 |

Vector calc proof question | Sep 22, 2008 |

**Physics Forums - The Fusion of Science and Community**