It is possible to use Symbolic Vector to perform the typical vector operations we use in Physics (for example, electromagnetism)? I mean, for example, applying vector identities to vector fields, like
rot ( rot (A)) = grad( div(A)) - laplacian(A)
o, more interesting for me, to obtain dispersion relations from differential equations. I have seen the documentation for symbolic vectors and tensors, but I assume that there should be more detailed information somewhere. There is already a thread on a closely related subject
but I am not able to obtain a practical conclusion.
Is there an example or tutorial of these type of calculations with Mathematica?
You are right, of course. I manage with those vectors operations you refer to, by setting a coordinate system. But I am asking for these type of calculations:
That should be Ok. The only issue that I have ever encountered is that you need to use variables in the matrix so WMA knows the dimensionality of your problem. For example, I would be careful using a single variable for a matrix because some operations assume the variables as scalars (or more accurately, they can handle either scalar or matrix arguments so a single variable is assumed to be scalar). So set k={{a,b},{c,d}} or k=Array[a,{2,2}]
Your equations can then be expressed using MatrixExp[], Div, Cross, Grad, etc
