TI-89 GRAPHING CALCULATOR
SLOPE FIELDS AND INTEGRAL SOLUTION CURVES
APPROXIMATED VIA EULER’S METHOD
Use the following procedure in order to draw the slope field for a given differential
equation on the TI-89 Graphing Calculator:
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Click on MODE and use the up and down arrow keys to move the cursor to the
type of equation (function is the default setting).
Use the right arrow key to display the other selections.
Move the cursor so that DIFFERENTIAL is highlighted and then press ENTER
twice.
In the Y = screen, enter the expression for the differential equation in Y1. Use “t”
instead” of x in the expression and use “Y1” instead of just Y. Hit ENTER.
When you hit the GRAPH key, the slope field (sometimes called the direction
field) should be displayed. Change the window as necessary for appropriate
viewing/interpretation. ZOOM Decimal might be a good starting place.
Use the following procedure in order to draw the integral solution curve for the
differential equation as approximated via Euler’s Method:
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Change the solution method for the graph by selecting the Diamond key followed
by the Graph Format key (labeled as F in yellow above the evaluation bar key ½ ).
Move the cursor to Solution Method and then use the right arrow in order to select
option 2 for Euler. Hit ENTER to save your selection. (Note that RK is another
iterative method called the Runge-Kutta method).
If you wish to graph a specific solution based on an initial condition, go back to
the Y = screen and enter an initial condition value on the line marked Yi1. Note
that you can change the initial x value as well on the line labeled as t0.
If you want to use a specific value for dx in your calculations, change the t-step
setting in the Window menu to the desired value.
When you hit enter, the solution curve as approximated by Euler’s method will be
superimposed on the slope field. Keep in mind that the calculator will graph
solution curves as functions so that it will draw, for example, a semicircle rather
than a complete circle given a single initial condition.
If you want to draw additional solution curves on the same graph, select the F8
menu (2nd F3), where you can input additional initial condition values.
If you use the trace option, you will be able to view the coordinates that would be
generated with each iterative calculation of Euler’s Method.