{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 494 "  # The following p
rocedure uses Euler's method to compute\n  # approximate solutions to \+
Initial Value Problems of the form\n  #      d(y(x),x)=f(x,y)  y(xo)=y
o\n  # Meaning of the variables:\n  # f function in two varaibles\n  #
 xo initial x-value\n  # yo initial y-value ( y(xo)=yo )\n  # x1 last \+
x-value, \n  # h stepsize (the smaller the more precise)\n  # !!!!!   \+
NOTE: Use Shift-Return to start new line , this way all !!!! \n  # !!!
!!   commands will be executed at the same time              !!!!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 695 "  Euler:=proc(f,xo,yo,x1,h)
        # means Euler is a procedure using f,xo,yo,x1,h as entries \n \+
 local x,y,hh,p,e,yk;             # local variables, will not leave th
e procedure\n  global output,y1;                # the output will be t
he list y(xo),y(xo+h),y(xo+2h),....\n  y:=yo;                         \+
  # initialization \n  hh:=h;\n  e:=NULL;\n  for x from xo by hh to x1
 do     # Start of loop in which  y(xo),y(xo+h),y(xo+2h),....\n       \+
p:=[x,y];                   # will be computed iteratively\n       e:=
e,p;\n       yk:=y;\n       y:=evalhf(y+hh*f(x,y));     # using linear
 approximation to comput next y-value\n  od;                          \+
    # end of loop\n  output:=[e];\n  y1:=yk;\n  end:" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 " # Lets use that procedure" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 " g:=(x,y)->x+cos(y);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 " Euler(g,0,1,3,.1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "y1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "outpu
t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "display([plot(output,0..3,0.
.5)]);" }}}}{MARK "6 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }