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Slope fields
Slope fields are used to visualize the solutions to a differential equation of the
form y’ = f(x,y). Basically, what is presented in the plot are segments tangential
to the solution curves, since y’ = dy/dx, evaluated at any point (x,y), represents
the slope of the tangent line at point (x,y).
For example, to visualize the solution to the differential equation y’ = f(x,y) =
x+y, use the following:
Θ Press „ô, simultaneously if in RPN mode, to access to the PLOT SETUP
window.
Θ Change
TYPE to Slopefield.
Θ Press ˜ and type ‘X+Y’ @@@OK@@@.
Θ Make sure that ‘X’ is selected as the
Indep: and ‘Y’ as the Depnd:
variables.
Θ Press L@@@OK@@@ to return to normal calculator display.
Θ Press „ò, simultaneously if in RPN mode, to access the PLOT
WINDOW screen.
Θ Change the plot window ranges to read:
X-Left:-5, X-Right:5, Y-Near:-5, Y-Far:
5
Θ Press @ERASE @DRAW to draw the slope field plot. Press @EDIT L @LABEL
@MENU to see the plot unencumbered by the menu and with identifying labels.
Θ Press LL@)PICT to leave the EDIT environment.
Θ Press @CANCL to return to the PLOT WINDOW environment. Then, press
$ , or L@@@OK@@@, to return to normal calculator display.
If you could reproduce the slope field plot in paper, you can trace by hand lines
that are tangent to the line segments shown in the plot. This lines constitute lines