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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "minutes_928.mws\nThu Sep 2
9 15:35:07 MDT 2005\n" }}{PARA 0 "" 0 "" {TEXT -1 42 "Minutes of our m
eeting, Wednesday, 9/28/05" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "with(plots, display, implicitplot): " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "with(plottools, disk):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "with(DEtools, DEplot):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "#########
#########################################" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "DE1 := D(y)(t) = v(t
):    " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "DE2 := D(v)(t) = \+
2/3*y(t) - 5/3*v(t):" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 54 "#######################################
###############" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "SYS := [DE1, DE2]:  " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "VARS := [y(t), v(t)]:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "TRG \+
:= t=0..10:  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "YRG := y=-
2..2:  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "VRG := v=-2..2: \+
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 59 "PTS := [[1/3,-2/3], [-1/2,-1/6], [1/2,1/2], [0
,2], [0,-2]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "mkIC := u -> [y(0)=op(1,u), \+
v(0)=op(2,u)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "IC := map
(mkIC, PTS):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "P := DEplot(SYS,VARS,TRG,IC,YRG,VRG
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 60 "P := P,implicitplot( 2*y - 5*v = 0, YRG, VRG,
 colour=BLACK):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "P := P, op(  map( t -> disk(
t, 1/20, colour=BLACK), PTS)  ):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "display
([P]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 229 "The plot shows the dir
ection field as we doped out in class on Wednesday, 9/28/05.   The thi
n black line is the v'(t) = 0 line.   The black spots are the initial \+
points of various solutions.  Note the two straight-line solutions." }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "##########################
############################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{MARK "31 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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