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dn

In mathematics and the physical sciences, dN denotes an infinitesimal change in the quantity N. The symbol d represents the differential, indicating a small, but finite, change used to describe rates, linearizations, and integrals. The precise meaning of dN depends on what N represents and the variables on which N depends.

In one-variable calculus, if N is a function of x, then dN = (dN/dx) dx. This expresses the

As an approximation, dN provides the linearization of N about a point and serves as the basis

In physics and engineering contexts, dN commonly represents the differential change in the number of discrete

In probability and statistics, dN is sometimes treated as a random differential representing the expected infinitesimal

Because dN is context-dependent, its precise meaning hinges on the definitions of N and the variables involved.

differential
of
N
as
the
product
of
the
derivative
and
a
small
change
in
x.
For
multivariable
functions
N
=
N(x1,
x2,
...,
xk),
the
differential
is
dN
=
∑i
(∂N/∂xi)
dxi,
giving
the
first-order
change
in
N
due
to
small
changes
in
all
independent
variables.
for
the
differential
form
in
integration:
the
total
change
in
N
over
a
finite
path
or
interval
satisfies
N(final)
−
N(initial)
=
∫
dN.
objects,
such
as
particles,
photons,
or
events,
counted
in
a
region
of
parameter
space.
For
example,
dN/dE
might
describe
the
energy
spectrum
of
particles,
the
rate
of
events
per
energy
interval,
and
dN
can
be
integrated
over
a
domain
to
obtain
the
total
count
N.
count
in
an
interval,
with
actual
counts
modeled
by
stochastic
processes
such
as
Poisson
processes
where
N
is
a
counting
variable.
It
is
a
differential
and
not
a
standalone
quantity;
it
becomes
meaningful
only
within
equations
describing
rates,
linearizations,
or
integrals.