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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 34 "Visualizing Differential
 Equations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 42 "The cell below defines a Maple procedure  " }{TEXT 256 10 "slop
efield" }{TEXT -1 77 "  that can be used to draw slope fields like the
 ones in the browser window. " }{TEXT 257 16 " Evaluate it now" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 955 "with(plottools):\nwith(plots):\n\nslopefield :=
 \n    proc(fcn, xlow, xhigh, ylow, yhigh)\n    local slopes, hx, hy, \+
dx, dy, kx, ky, x, y, i, j, m, pit;\n\n    hx := (xhigh - xlow)/30:\n \+
   hy := (yhigh - ylow)/30:\n    dx := (xhigh - xlow)/8:\n    dy := (y
high - ylow)/8:\n\n    slopes := \{\}:\n    \n    for i from 0 to 8 do
\n        x := evalf(xlow + i * dx):\n        for j from 0 to 8 do\n  \+
         y := evalf(ylow + j * dy):\n\n           m := traperror(fcn(x
, y)):\n\n           if type(m, numeric) then\n              if abs(m \+
* hx) <= hy then \n                 kx := hx:\n                 if abs
(m) > 0.001 then ky := hy/abs(m) else ky := 0 fi:\n              fi:\n
              slopes := slopes union\n                   \{line([x - k
x, y - m * kx], [x + kx, y + m * kx])\}:\n           fi:\n         od:
\n    od:\n\n    pit := display(slopes, axes = NONE, \n               \+
            color = BLACK, \n                           scaling = CONS
TRAINED):\n\n    display([pit]);\n\nend:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "The following cell illust
rates how  " }{TEXT 258 10 "slopefield" }{TEXT -1 12 "  is used.  " }
{TEXT 259 15 "Evaluate it now" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "f := (t, y)
 -> y/t:\n  slopefield(f, -3, 3, -3, 3);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 130 "This  procedure takes five arguments.\n\n\0111.  The name of t
he function appearing on the right hand side of the differential equat
ion" }}{PARA 257 "" 0 "" {TEXT -1 3 "\n\nd" }{TEXT 261 14 "y/dt = f(t,
 y)" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 45 "\nThis function m
ust be defined in a line like" }}{PARA 258 "" 0 "" {TEXT -1 2 "\n\n" }
{TEXT 260 29 "MyFcn := (t, y) -> t * sin(y)" }}{PARA 0 "" 0 "" {TEXT 
-1 375 "\n\nwith the independent variable first and the dependent vari
able second.  It must be a function \011of two variable even if only o
ne is used.\n\n\0112.\011The lower limit for the range of the t-axis v
ariable.\n\n\0113.\011The upper limit for the range of the t-axis vari
able.\n\n\0114.\011The lower limit for the range of the y-axis variabl
e.\n\n\0115.\011The upper limit for the range of the y-axis variable.
\n" }}}}{MARK "0 0 0" 34 }{VIEWOPTS 1 1 0 1 1 1803 }