Re: [Phys-L] notation for partial derivatives

[Diego Saravia <dsa@unsa.edu.ar>]

2014-06-21 12:50 GMT-03:00 John Denker <jsd@av8n.com>:
> On 06/21/2014 07:10 AM, Diego Saravia wrote:
>
> > dE dV componentes of the "diferencial of state vector"
>
> I assume the word "differential" denotes a generic
> /infinitesimal/ change ... which is not the approach
> I would recommend.
>
>   By way of contrast, the expression ΔV denotes a
>   /difference/, a finite difference ... not a
>   differential, not an infinitesimal.  As such, it is
>   not a function of state.  In fact, it is a function
>   of two states, A and B:
>       ΔV = V(A) - V(B)
>
>   If V is a scalar, then ΔV is also a scalar.
>
> Returning from ΔV to dV, the derivative dV is a
> function of state.  It is defined *at* a single
> point in state-space (and its infinitesimal
> neighborhood).  Interestingly, dV is not a scalar.
> It must be considered a vector, for reasons we
> now discuss.

Are you meaning dV? or (dV,dU)

I assume dV is a component, ok could be a one dimmension vector,
but the tangent space in the all mighty S(U,V) could be (dU,dV)

ok, you could be talking of a vector in gradient terms in another
space, for example
in a P,T representation depaV/depaP and depaV/depaT is also, a vector
with components
in dP and dT coordinates.

or perhaps you are asuming diferent kind of multim V_i displacements dV_1 dV_2?