Calculator Program Descriptions

**Creation of These Programs**

The following programs were initially written to supplement the
capabilities of the earlier models of graphing calculators. Many of these
programs are still very useful even with the more advanced calculators.
The syntax and steps used in the programs attempt to mimic the steps often
taken when calculations are done by hand. As a result, some programs may
appear to be longer than necessary for some of the more advanced models.
Because all models are typically represented in any one classroom,
consistency from program to program is important for instructional purposes.

**Entering These Programs**

Many of the calculator models within the TI series can connect to a computer. As a result,
down-loadable versions of the program are also included wherever possible. In any case, each program
is shown line by line (along with instructions and comments)on the web page.

**Evaluate a Function (Intro to Programming)
**

The program itself is rather simple, but has many applications.
Many of the newer models of calculators have built in features to
evaluate a function. For example, some of the TI models conveniently have an
"ask" feature in the table commands. This program also allows you to quickly
evaluate a function by entering a value for x. Because of the nature of the
program, you can enter many x values in a few key strokes. This can be
very helpful when trying to determine an appropriate window when plotting a
graph. You can also use the program to numerically analyze limits or
function behavior. A possible advantage is that you do not need to
change the table format.

Because all programs for a particular model are entered and run the same way, the page also contains instructions if you are new to programming. It can also be a helpful reference for the remaining programs.

**Quadratic Formula**

This program allows you to enter values for a, b, c according
to the quadratic formula to solve equations of the form ax^2+bx+c=0.
Because many courses only consider real solutions, the program response
for complex solutions will appear as "No real solutions". The program
can easily be modified to produce complex solutions if needed.

**Difference Quotient**

This program estimates the value of a derivative at a point by using
.
The limiting process in the definition of the derivative can be
simulated by running the program with various values for * h * and
observing the trend of the approximations as * h * approaches zero.

**Left Right Sums**

This program computes left and right approximations for .
Values for * N * , the number of subdivisions of the interval
[*A*,*B*],
and the values of * A * and * B * are all entered while
running the program. For convenience, the average of the two estimates
is also included. Students who will eventually need other approximation
techniques such as the Midpoint Rule and Simpson's Rule should enter the
Allsums program to save time.

**Allsums**

This program computes five approximations for . The approximations are left, right, trapezoid, midpoint, and Simpson's rules. Values for * N * , the number of subdivisions of the interval [*A*,*B*],
and the values of * A * and * B * are all entered while
running the program.

**Slope Field**

This program plots the slope field for the differential equation in
the form . Because some models
of calculators are case sensitive, it is important to follow the programming
directions carefully.

**Euler (graphical)**

This program plots an approximate solution for the differential equation
using Euler's method. An initial set of coordinates and step size are entered
when running the program.
Solutions can be superimposed on a slope field by running the Slope field
program first. Although previous graphs are not cleared, an appropriate
command can be inserted into the program to clear them. A pause
command is also used in the program to allow the graph to be plotted in
segments. This prevents the student from having to match the step size
with the given window or range.

**Euler (numerical)**

This program gives coordinates for an approximate solution for the
differential
equation
using Euler's method. An initial set of coordinates and step size are entered
when running the program.

**Series**

This program evaluates series of the form
C_{K}X^{K}
or
C_{K}(X-A)^{K}.

An expression such as is entered prior
to running the program.
Values of * N * and * x * are entered when running the program.
This program can be helpful when investigating the behavior of a partial sum or series. The
limiting process can be simulated by running the program with larger and
larger values of * N *.

**Rectangles**

This program is more useful as a learning tool than as a computational
tool. A geometric representation for the approximation to
is emphasized. Using pause commands, the
graph of the function is plotted first. Depending on the choice of rectangle
used (left, right, or anything in between can be selected), the rectangles
are plotted on top of the graph of the function. The last step produces the
value of the approximation. Because this program runs much slower than
the Left Right Sums or Allsums programs, it is not recommended for
routine calculations.

**Newton's Method**

This program generates successive approximations to the solutions
of f(x)=0 according to Newton's Method. The function and its derivative
are entered before running the program. An initial guess of the solution
is entered when running the program.