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HP HP-15C Advanced Functions Handbook

HP HP-15C
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10
Section
1:
Using
|
SOLVE
|
Effectively
In
general, every equation
is one of an
infinite family
of
equivalent
equations
with
the
same real roots.
And
some
of
those equations
must
be
easier
to
solve
than
others. While
|
SOLVE
| may
fail
to
find
a
root
for one of
those equations,
it may
succeed with another.
Inaccurate
Equations
[SOLVE|
can't
calculate
an
equation's root incorrectly unless
the
function
is
incorrectly calculated.
The
accuracy
of
your function
subroutine
affects
the
accuracy
of the
root
that
you
find.
You
should
be
aware
of
conditions
that
might cause your
calculated
function value
to
differ
from
the
theoretical value
you
want
it to
have.
[SOLVE|
can't
infer intended values
of
your
function.
Frequently,
you can
minimize calculation error
by
carefully
writing your function subroutine.
Equations
With
Several
Roots
The
task
of
finding
all
roots
of an
equation becomes more
difficult
as the
number
of
roots increases.
And any
roots
that
cluster closely
will
usually
defy
attempts
at
accurate resolution.
You can use
deflation
to
eliminate roots,
as
described
in the
HP-15C
Owner's
Handbook.
An
equation with
a
multiple root
is
characterized
by the
function
and its
first
few
higher-order derivatives being zero
at the
multiple
root.
When
|
SOLVE
|
finds
a
double root,
the
last
half
of
its
digits
may
be
inaccurate.
For a
triple root, two-thirds
of the
root's
digits
tend
to be
obscured.
A
quadruple root tends
to
lose about three-fourths
of
its
digits.
Using
|
SOLVE
|
With
Polynomials
Polynomials
are
among
the
easiest functions
to
evaluate.
That
is
why
they
are
traditionally used
to
approximate functions
that
model
physical processes
or
more complex mathematical
functions.
A
polynomial
of
degree
n can be
represented
as
anxn
+
an
_
ixn
~l
+
...
+
a±x
+
a0
.
This
function equals
zero
at no
more
than
n
real values
of x,
called
zeros
of the
polynomial.
A
limit
to the
number
of
positive
zeros
of
this
function
can be
determined
by
counting
the
number
of
times

Table of Contents

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Preview: Owner's Handbook
Owner's Handbook288 pages

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HP HP-15C Specifications

General IconGeneral
BrandHP
ModelHP-15C
CategoryCalculator
LanguageEnglish

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