Frank
Please keep in mind the following
NEC is based totally on the extremely thin wire where various
assumption can be made
such as equations being equal to zero in the limit., These same
assumptions can not be held to
when dealing with thick radiators despite the closeness of the
approximations.
Best regards
Art

The reference at http://www.nec2.org/other/nec2prt1.pdf p 21 deals
with the accuracey of NEC 2 in respect to the "Thin wire approximation".
From the NEC-4, theory manual, p 21, para 4: ".... the NEC-4 wire model
employes the extended boundary condition in the thin wire approximation,
so that the current is treated as a tubular distribution on the wire
surface......."

Calculus is based on homogenous materials or planes where you can
refer dy/dx to
some thing aproaching zero. In the case of using this aproach where
the antenna diameter aproaches zero
this is an invalid aproach for accuracy but O.K. for aproximations. So
much for the foibles of theoretical mathematics.

Your comments about calculus are confusing. A derivative
is always non-zero -- unless you are differentiating a constant.
The homogeneity, or otherwise, of a material is irrelevant
to the process of differentiation.

The vanishing thin radiator cannot be applied directly to a non
homogenous material because at the limits of the the diameter
is unable to support the presence of eddy currents(skin depth) . In
other words the assumption of limi tess ness cannot be held if the
presence of skin effect is true.

Most conductors are homogeneous. In fact I cannot think of
a non-homogeneous conductor. Even in plated conductors
the current flows in the plating.

Of course if skin effect is not present then you
have a DC current where only copper losses are present.
As always with mathematics assumptions and preconditions are alway
subject to examination. This in no way takes away from the advantages
oif the NEC programs.
Art

Copper loss still exists for high frequency currents.

73, Frank