{VERSION 3 0 "SGI MIPS UNIX" "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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 1 24 0 0 0 0 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 "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 }{PSTYLE "" 0 256 1 {CSTYLE " " -1 -1 "" 1 24 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 "" 0 257 1 {CSTYLE "" -1 -1 "" 1 24 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 256 "" 0 "" {TEXT 266 28 "445/545 Fall 1998 Hando ut #3" }}{PARA 257 "" 0 "" {TEXT -1 14 "Euler's method" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "with(DEtools):\ndp:=dfieldplot( di ff(x(t),t) = cos(x) + x*sin(t), x(t),\n t=-1..5, x=-1..6, \+ \n color=black,arrows=line ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 494 "h:=0.1: \nn:=ceil(4.0/h): \n \+ \nt:=0.0:\nx:=0.0: \ndata[0]:=[t,x]: \n \n for i from 1 to n do \n \n mk := cos(x) + \+ x*sin(t):\n x := x + h*mk:\n t := t + h:\n data[i] := [t,x]: \n \nod: \n[t,x]; \nt: ='t': x:='x': h:='h': \n \ndatalist := [ seq( data[i], i=0..n ) ]: \n \nep:=plot( datalist, 0..4, 0..6, style=POINT):\n \+ \nwith(plots):\ndisplay(dp,ep);" }{TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"#S!\"\"$\"+-mFi>!\"*" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6]dl7$7$$!+\"Hi=5\"!\"*$!+$f]29\"F*7$$!+ \"4x8)*)!#5$!+rS\\#f)F07$7$$!+\")p'e&zF0$!+&Qt08\"F*7$$!+XNMGdF0$!+^hE %p)F07$7$$!+BB;M\\F0$!+48b76F*7$$!+H(eUV#F0$!+9p[u))F07$7$$!+Ru\"R$>F0 $!+_!eM3\"F*7$$\"*heG\"))F0$!+%[>a;*F07$7$$\"+TY,V5F*7$$\" +bh(o;%F0$!+7Q&)p&*F07$7$$\"+fMb5UF0$!+f))>*)**F07$$\"+6RRotF0$!+9,3,5 F*7$7$$\"+^&Q2S(F0$!+[w?H'*F07$$\"+H)*R\\5F*$!+N#zq.\"F*7$7$$\"+W.*41 \"F*$!+zhe3%*F07$$\"+)Gi+O\"F*$!+#QT\"f5F*7$7$$\"+?6Pz8F*$!+i@&fK*F07$ $\"+g/Et;F*$!+%y/u1\"F*7$7$$\"+i4n$p\"F*$!+:o%>P*F07$$\"+m&R0*>F*$!+>` !G1\"F*7$7$$\"+bBt/?F*$!+aTQ_&*F07$$\"+@r06BF*$!+&ehZ/\"F*7$7$$\"+<1:; BF*$!+a3[v)*F07$$\"+2y@JEF*$!+:>X75F*7$7$$\"+J$[Pj#F*$!+M5VI5F*7$$\"+T !*>XHF*$!+d'*o&p*F07$7$$\"+rYJgHF*$!+c70t5F*7$$\"+\\;@]KF*$!+Uu[p#*F07 $7$$\"+PFn\"H$F*$!+r>f06F*7$$\"+KDV]NF*$!+&H!3W*)F07$7$$\"+x&4?i$F*$!+ TEVE6F*7$$\"+RYn^QF*$!+%ftct)F07$7$$\"+I%H&[RF*$!+1?]Q6F*7$$\"+MPtcTF* $!+R*z\\h)F07$7$$\"+YLuqUF*$!+K;tW6F*7$$\"+m()4mWF*$!+zOo_&)F07$7$$\"+ b3'))e%F*$!+s%Ho9\"F*7$$\"+0-czZF*$!+y_qJ&)F07$7$$\"+i3..\\F*$!+9(y`9 \"F*7$$\"+Y\"pp4&F*$!+cG@Y&)F07$7$$!+bUu.6F*$!+'*)fWq(F07$$!+Zubi*)F0$ !+_!>r#\\F07$7$$!+DBzRzF0$!+c;#*RwF07$$!+,#=Wu&F0$!+#Hd;*\\F07$7$$!+)o xb'[F0$!+1(yz`(F07$$!+kL%G]#F0$!+U-g$4&F07$7$$!+V\"=v!=F0$!+.>T#R(F07$ $\"*ll)[vF0$!+Xq;R_F07$7$$\"+3$\\'[7F0$!+*ySZ?(F07$$\"+)e3X,%F0$!+f\"Q oU&F07$7$$\"+w-C@VF0$!+TkU$*pF07$$\"+%42xD(F0$!+2D:QcF07$7$$\"++;#GU(F 0$!+IG;&z'F07$$\"+C:>Z5F*$!+=hTOeF07$7$$\"+-;Fb5F*$!+d%Q7l'F07$$\"+I5y l8F*$!+\"\\S.)fF07$7$$\"+O/>q8F*$!+B=z!f'F07$$\"+W6W#o\"F*$!+DrySgF07$ 7$$\"+O,X'o\"F*$!+A:&\\i'F07$$\"+#Rgx*>F*$!+Eui1gF07$7$$\"+G!)R/?F*$!+ >i`ZnF07$$\"+[9R6BF*$!+HF/%)eF07$7$$\"+M%e\\K#F*$!+(*eQMpF07$$\"+!**4C i#F*$!+^I>(p&F07$7$$\"+)\\O&[EF*$!+dOHYrF07$$\"+u3TIHF*$!+\"H&G&[&F07$ 7$$\"+8%=U(HF*$!+;_QVtF07$$\"+2zIOKF*$!+KP>)G&F07$7$$\"+c'=-I$F*$!+CSa ,vF07$$\"+7m)=a$F*$!+C\\.I^F07$7$$\"+ML$\\i$F*$!+i-J:wF07$$\"+#)3v[QF* $!+'ooi,&F07$7$$\"+\"GZu%RF*$!+')fj*o(F07$$\"+$)e\"y:%F*$!+iH%>%\\F07$ 7$$\"+b3TnUF*$!+3\"H;t(F07$$\"+d7VpWF*$!+S)\\***[F07$7$$\"+\\([Ze%F*$! 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