Given a tensor field T(x,y,z), how would I go about differentiating it wrt spacial coordinates?(adsbygoogle = window.adsbygoogle || []).push({});

I would presume that it would work like this:

[tex]

\begin{equation}

\frac{\partial T}{\partial x} = \lim_{h\to 0}\frac{T(x+h,y,z)-T(x,y,z)}{h}

\end{equation}

[/tex]

However, this does not seem to take into account that tensor quantities themselves can act as functions of the spacial coordinates. My understanding is that a tensor field can, in some instances, act like a field that returns functions (or maps). If T returns tensors that are dependent on x, y, or z, wouldn't this have to be taken into account? Or is that another type of differentiation?

**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!

# Help on differentiation of tensor fields

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Help differentiation tensor | Date |
---|---|

Where can I get help with David Bachman's A Geometric Approach to Differential Forms? | Aug 31, 2015 |

Help me check a fact about Berry phase | May 22, 2015 |

Question about geometric algebra -- Can any one help? | Feb 25, 2015 |

Need some help understanding boundary operator on simplicies | Feb 2, 2015 |

Transitional Lines Help | Oct 8, 2014 |

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