Re: SOLVER( and-then-what-?-please-tell-me
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Re: SOLVER( and-then-what-?-please-tell-me
JTK writes:
> How do I use the solver?? I have a TI83
> I though about 2X=4 (X equals 2,yes i know that. But just as an example..)
> So i write
> Solver(2X=4 [ENTER]
> But get an error report.
There are two facilities on the TI-83 for coming up with numerical solutions to
equations. Both of them require that you work with an expression equated to
zero -- an easy algebraic step. In the present case we might be looking to
solve the simple equation 2X - 4 = 0.
On the TI-83 _home screen_ you can use the SOLVE( command to solve for the
value of a single undetermined variable. If the expression you have entered
involves several variables (the example in the manual uses an expression in P
and Q) then the calculator will use already-assigned values for all variables
except for the one you are targeting.
The SOLVE( command is only available from the catalog (but as the manual points
out you could write a program to "cover" the need to retrieve this command).
The user must then enter the expression that should be equated to zero (but not
the "=0" itself), the variable whose value is to be determined, and an initial
"guess" at what the value should be. In simple cases (like the present) you
can put in any number as an initial guess, In more complex cases, where there
may be two or more different possible solutions or where the numerical methods
the calculator uses for solution do not deal well with approximations that are
too far off the mark, the result you get (or the speed with which you get it)
may well be affected by the initial guess you input. It is also possible to
input an additional argument, a list that sets an _interval_ in which the
solution must be contained, which can be of further help to the calculator in
tough cases.
This is good for a "one-off" solution. When you need to investigate
relationships between multiple variables, it is probably easier to work in the
environment of the TI-83's solver (accessed from the MATH menu), which uses
the same built-in routines but which presents a different interface to the
user. The explanation in the manual is none too clear -- the word "equation"
is repeatedly used where "expression" is meant. But once you get the hang of
the process it is simplicity itself to use. A relationship between several
variables in the form of 0 = f(A,B,C,...) is stored as _eqn_. This may
involve "expression variables" such as Y1, Y2, etc. into which have been stored
"chunks" of a larger expression. A spot is given below to assign a value to
each variable that occurs in the entered expression (or in any of its chunks).
Put a given value into each variable (an initial guess at a value into the
target variable). If you like, you can set a search interval at the bottom of
the screen.
While you are sitting on the location for the to-be-determined value, you press
ALPHA [SOLVE], and the calculator does its thing. Neat. Change a value
somewhere and do it again. And so forth...
Two things should be noted about using this tool. First, whether you use
SOLVE( or whether you work in the solver, you may be putting in too much effort
to solve simple equations. An easy algebraic process may lead you to develop
an _expression_ for the result, which would be a faster and more powerful (from
the point of view of the user) solution. This is why it will always be
desirable to learn basic algebraic skills. The solver is at its best with
problems that do not yield to simple algebra (higher-degree polynomial
equations or equations involving transcendental functions). This is also the
right tool to use to explore relationships among several interdependent
variables. For example, you can learn a lot about the geometry of triangles
by fooling around with the law of cosines in the solver.
The second point is that the solver does _not_ itself use algebraic processes
of solution to achieve its results. In the case of 2x - 4 = 0 , for example,
the calculator doesn't "add 4 and divide by 2", but instead uses an iterative
(repeating) process of approximation and refinement. There's a lot of good
mathematics involved in learning how to set up and control such a process, and
getting to know the kind of things that can "go bad" when you try to solve
using these methods. This topic has traditionally reserved for study in the
arcane topic of Numerical Methods. It would seem appropriate that this
subject matter begin moving down in the curriculum (as other topics have over
the centuries) and be more widely studied with the aid of these powerful
analytical tools we have in our hands nowadays. On the other hand, reading the
newspapers these days, it seems that (at least in some states) students instead
are going to be encouraged to "just say no" to all of these deeper ideas.
Interesting times we live in.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<