{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 37 "The forward Euler Method for solving " }
{XPPEDIT 18 0 "diff(y,t) = f(t,y);" "6#/-%%diffG6$%\"yG%\"tG-%\"fG6$F(
F'" }{TEXT -1 23 " with an initial value " }{XPPEDIT 18 0 "y(t0) = y0;
" "6#/-%\"yG6#%#t0G%#y0G" }{TEXT -1 33 ".  We assume a fixed spacing (
by " }{XPPEDIT 18 0 "h;" "6#%\"hG" }{TEXT -1 12 ") mesh with " }
{XPPEDIT 18 0 "n+1;" "6#,&%\"nG\"\"\"\"\"\"F%" }{TEXT -1 10 " points.
\n\n" }{MPLTEXT 1 0 208 "EulerMethod := proc( f, t0, y0, h, n ) local \+
a, i, t, y;\n  t := evalf(t0);\n  y := evalf(y0);\n  a := [[t,y]];\n  \+
for i from 1 to n do\n    y := y + h * f(t,y);\n    t := t + h;\n    a
 := [op(a),[t,y]];\n  od;\nend;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>
%,EulerMethodGR6'%\"fG%#t0G%#y0G%\"hG%\"nG6&%\"aG%\"iG%\"tG%\"yG6\"F1C
&>8&-%&evalfG6#9%>8'-F66#9&>8$7#7$F4F:?(8%\"\"\"FD9(%%trueGC%>F:,&F:FD
*&9'FD-9$6$F4F:FDFD>F4,&F4FDFKFD>F?7$-%#opG6#F?FAF1F1F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f := (t,y)->t/y;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fGR6$%\"tG%\"yG6\"6$%)operatorG%&arrowGF)*&9$\"\"
\"9%!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "em := Eu
lerMethod( f,0,1,0.1,10 );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#emG7-
7$\"\"!$\"\"\"F'7$$F)!\"\"F(7$$\"\"#F,$\"++++55!\"*7$$\"\"$F,$\"+!)>!)
H5F27$$\"\"%F,$\"+%zL*e5F27$$\"\"&F,$\"+Qwq'4\"F27$$\"\"'F,$\"+S')HU6F
27$$\"\"(F,$\"+4V#[>\"F27$$\"\")F,$\"+G.T`7F27$$\"\"*F,$\"+%>OsJ\"F27$
$\"#5F,$\"+q5c&Q\"F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "plot
(em);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURV
ESG6$7-7$\"\"!$\"\"\"F(7$$\"1+++++++5!#;F)7$$\"1+++++++?F.$\"1++++++55
!#:7$$\"1+++++++IF.$\"1+++!)>!)H5F47$$\"1+++++++SF.$\"1+++%zL*e5F47$$
\"1+++++++]F.$\"1+++Qwq'4\"F47$$\"1+++++++gF.$\"1+++S')HU6F47$$\"1++++
+++qF.$\"1+++4V#[>\"F47$$\"1+++++++!)F.$\"1+++G.T`7F47$$\"1+++++++!*F.
$\"1+++%>OsJ\"F47$F)$\"1+++q5c&Q\"F4-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%
+AXESLABELSG6$%!GF_o-%%VIEWG6$%(DEFAULTGFco" 1 2 0 1 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "4 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }