Hp 50g Graphing Calculator Manual do Utilizador descarregar pdf (Página 416)

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101

Page 12-33

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:

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

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