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Help on differentiation of tensor fields

  1. Jan 12, 2008 #1
    Given a tensor field T(x,y,z), how would I go about differentiating it wrt spacial coordinates?

    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?
     
  2. jcsd
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