1550078481-Ordinary_Differential_Equations__Roberts_

512 Ordinary Differential Equations

on the monitor as shown in Figure A.9. The graphing information box shown
in Figure A.9 also appears.

iii GRAPH l!ll!fD

GRAPH graphs !he equalion y = f[x) inside !he reclangle bounded by the lines x = Xmin, x = Xmax. y = Ymin. and y = Ymax.

Enler !he funclion f[x) = jt2.,.expf·,/2)"sinl5'<)

Enler Xmin = I ·5 and enler Xmax = I

The minimum and maximum values of f[x) on [Xmin. Xmax] are

Ymin = J -7.751371E·01 and Ymax = I 3.793455E +01

Graphing mformalion D

The mirimum and ma<imum values of fix) on lhe inlerval f!<min,Xmax) appear above.

Press lhe GRAPH bullon lo graph U1e function using lhese value_s.

Or change lhe value of Ymin orYrnai< and lhen press GRAPH.

Figure A.9 Entering a Function f(x) and Interval [Xmin, Xmax]

into GRAPH

After reading the comment in the information box, click OK. The GRAPH

button appears. We want to change the values of Ymin and Ymax, according

to the criteria outlined above. Thus, we decided to set Ymin = -10 and

Ymax = 40. So, in the box after "Ymin = " we entered -10 and in the box

after "Ymax = " we entered 40. Then we clicked the GRAPH button which
caused the graph displayed in Figure A.10 to appear on the monitor. The
bounding rectangle is outlined in black. Each subinterval along the top and
bottom of the rectangle represents a change of 1 unit and each subinterval
along the sides of the rectangle represents a change of 5 units. When the
x-axis or y-axis passes through the rectangle, it appears in blue on the mon-
itor. The graph of y = f(x) is approximated in the rectangle by connecting
(xi, f(xi)) to (xH1, f(Xi+i)) by a black line, provided both Xi and Xi+l are
both in the domain off. The domain off within the interval [Xmin, Xmax]
is indicated by a wide green line at the bottom of the rectangle. At the
upper right-hand side of the graph , there is a set of options. The option Same
Function, New Ymin or Ymax is selected. If you click the OK button, the
current graph will disappear and you will be able to change the value ofYmin,
the value of Ymax, or both values. If instead you click on the second option
circle: Same Function, New Xmin, Xmax, Ymin, Ymax and then click the
OK button, you will be able to change the values of any subset of {Xmin,