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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "1.3 Direction Fields" }}
{PARA 0 "" 0 "" {TEXT -1 60 "  p. 22 #4   First use help, searching fo
r \"direction field\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 345 "w
ith(DEtools):\ndfieldplot([diff(x(t),t)=x(t)*(1-y(t)),diff(y(t),t)=.3*
y(t)*(x(t)-1)], \\\n[x(t),y(t)],t=-2..2,x=-1..2,y=-1..2); #,arrows=LAR
GE,title=`Lotka-Volterra # model`,\\\ncolor=[.3*y(t)*(x(t)-1),x(t)*(1-
y(t)),.1]);\ndfieldplot(diff(y(x),x)=1/2*(-x-(x^2+4*y(x))^(1/2)),y(x),
x=-3..3,y=-3..2,\\\ntitle=`Restricted domain`,color=1/2*(-x-(x^2+4*y))
);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "with(DEtools):\ndfieldplo
t(diff(y(x),x)=1-y(x)^3/8,y(x),x=-3..3,y=-1..4,\\\ntitle=`Problem 4`);
" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "dfieldplot(diff(y(x),x)=x+sin(y(x)),y(x),x=0..3,y=-1.
.4,\\\ntitle=`Problem 6`);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "dfieldplot(diff(x(t),t)=t^3-
x(t)^3,x(t),t=1..3,x=0..2,\\\ntitle=`Problem 8`);" }}{PARA 13 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "eq8:=diff(x
(t),t)=t^3-x(t)^3;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "diff(eq8,t);" }}{PARA 11 "" 1 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "subs(diff(x(t),t)
=t^3-x(t)^3,rhs(\"));" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}{PARA 11 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Lets look at more
 of the help:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "with(DEto
ols):\nDEplot(\{diff(y(x),x)=sin(x)*sin(y(x))\},\\\n\{y(x)\},x=-2..2,[
[y(0)=1],[y(0)=1/2],[y(0)=-1/2],[y(0)=-1]],y=-2..2,stepsize=.05, title
=`Problem 10.c`);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 129 "DEplot(\{diff(y(x),x)=3-y(x)+1/x\},\\\n\{y
(x)\},x=1..10,[[y(1)=1],[y(1)=3],[y(1)=5],[y(1)=7]],y=0..8,stepsize=.0
5, title=`Problem 17`);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 23 "Problems for next week:" }}{PARA 0 "" 0 "
" {TEXT -1 68 "1.4         p. 28  5, 12                              E
uler's method" }}{PARA 0 "" 0 "" {TEXT -1 76 "2.1, 2.2 p. 44  3, 12, 2
3, 27, 29, 32    Falling bodies, separable equations" }}}}{MARK "12 2 \+
0" 38 }{VIEWOPTS 1 1 0 1 1 1803 }