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 $f^\prime(A)\approx{f(A+H)-f(A)\over H}$. 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 $\int\limits_a^bf(x)dx$. 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 $\int\limits_a^bf(x)dx$. 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 ${\hbox{dy}\over \hbox{dx}}=\hbox{f(x,y)}$. 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  ${\hbox{dy}\over \hbox{dx}}=\hbox{f(x,y)}$ 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 ${\hbox{dy}\over \hbox{dx}}=\hbox{f(x,y\ )}$ 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  $\sum\limits_{K=0}^N$CKXK or  $\sum\limits_{K=0}^N$CK(X-A)K.
An expression such as $\hbox{$X^{\hbox{K}}$}\over \hbox{K!}$ 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 $\int\limits_a^bf(x)dx$ 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.