{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 
{CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 
2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times
" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 
2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" 
-1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 
1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" 
{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}
{SECT 0 {PARA 5 "" 0 "" {TEXT -1 17 "Isotimic surfaces" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 218 "plot1 := implicitplot3d(x+2*y-3*z=
1,x=-2..2,y=-2..2,z=-2..2):\nplot2 := implicitplot3d(x+2*y-3*z=2,x=-2.
.2,y=-2..2,z=-2..2):\nplot3 := implicitplot3d(x+2*y-3*z=3,x=-2..2,y=-2
..2,z=-2..2):\ndisplay3d(\{plot1,plot2,plot3\});\n" }{TEXT -1 122 "The
se isotimic surfaces are planes x+2y-3z = const, with constants 1, 2 a
nd 3; that is, planes with normal vector i+2j-3k." }}{PARA 13 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "plot1:=imp
licitplot3d(x^2+y^2+z^2=1,x=-3..3,y=0..3,z=-3..3):\nplot2:=implicitplo
t3d(x^2+y^2+z^2=4,x=-3..3,y=0..3,z=-3..3):\nplot3:=implicitplot3d(x^2+
y^2+z^2=9,x=-3..3,y=0..3,z=-3..3):\ndisplay3d(\{plot1,plot2,plot3\},ax
es=FRAME);\n" }{TEXT -1 47 "Isotimic spheres: level sets of x^2 + y^2 \+
+ z^2" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 289 "plot1:=implicitplot3d(x^2+y^2=1,x=-3..3,y=0..3,z=-3.
.3,\n    scaling=CONSTRAINED):\nplot2:=implicitplot3d(x^2+y^2=4,x=-3..
3,y=0..3,z=-3..3,\n    scaling=CONSTRAINED):\nplot3:=implicitplot3d(x^
2+y^2=9,x=-3..3,y=0..3,z=-3..3,\n    scaling=CONSTRAINED):\ndisplay3d(
\{plot1,plot2,plot3\},axes=FRAME);\n" }{TEXT -1 43 "Isotimic cylinders
: level sets of x^2 + y^2" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 297 "plot1:=implicitplot3d(x^2/4+y^2/9+
z^2=1,x=-2..2,y=0..3,z=-1..1,scaling=CONSTRAINED):\nplot2:=implicitplo
t3d(x^2/4+y^2/9+z^2=4,x=-3..3,y=0..6,z=-2..2,scaling=CONSTRAINED):\npl
ot3:=implicitplot3d(x^2/4+y^2/9+z^2=9,x=-6..6,y=0..9,z=-3..3,scaling=C
ONSTRAINED):\ndisplay3d(\{plot1,plot2,plot3\},axes=FRAME);" }}{PARA 
13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 351 
"plot1:=implicitplot3d(sqrt(x^2+y^2)-z=0,x=-2..2,y=-2..2,\nz=-2..4,sca
ling=CONSTRAINED,grid=[20,20,20]):\nplot2:=implicitplot3d(sqrt(x^2+y^2
)-z=1,x=-2..2,y=-2..2,\nz=-2..4,scaling=CONSTRAINED,grid=[20,20,20]):
\nplot3:=implicitplot3d(sqrt(x^2+y^2)-z=2,x=-2..2,y=-2..2,\nz=-2..4,sc
aling=CONSTRAINED,grid=[20,20,20]):\ndisplay3d(\{plot1,plot2,plot3\},a
xes=FRAME);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 43 "contourplot(sqrt(x^2+y^2),x=-2..2,y=-2..2);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 45 "contourplot3d(sqrt(x^2+y^2),x=-2..2,y=-2..2);" }}{PARA 13 "" 1 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "implicitp
lot3d( x^3 + y^3 + z^3 + 1 = (x + y + z + 1)^3,x=-2..2,y=-2..2,z=-2..2
,grid=[13,13,13]);\n" }{TEXT -1 27 "Maple example implicit plot" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 92 "implicitplot3d(\{x^2 - y^2 + z^2 = 1,y = exp(-x*z)\},x=-Pi..Pi,y
=-Pi..Pi,z=-1..1,axes=FRAME);\n" }{TEXT -1 38 "Maple example: multiple
 implicit plots" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 92 "implicitplot3d( (x-1)^2 + (y+1)^2 + z^2 = 4,x
=-1..3,y=-3..1,z=-2..2,color=blue,axes=FRAME);\n" }{TEXT -1 56 "Colour
 implicit plots with solid colours (Maple example)" }}{PARA 13 "" 1 "
" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 256 50 "Thanks to John Hebron for providing his \+
Maple code" }{TEXT -1 1 "." }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 13 "Vector fields" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}
{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "fieldplot( [x
/(x^2+y^2+4)^(1/2),-y/(x^2+y^2+4)^(1/2)],x=-2..2,y=-2..2);" }}{PARA 
13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "
fieldplot([y,-sin(x)-y/10],x=-10..10,y=-10..10,arrows=SLIM, color=x);
" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "fieldplot3d([2*x,2*y,1],x=-1..1,y=-1..1,z=-1..1,\ngri
d=[5,5,5]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 84 "gradplot3d(x+2*y-3*z,x=-2..2,y=-2..2,z=-2..2,arr
ows=SLIM,\ngrid=[5,5,5],axes=FRAME);\n" }{TEXT -1 41 "Gradient vector \+
field for isotimic planes" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "gradplot3d(x^2+y^2+z^2,x=-3..3,y=-3
..3,z=-3..3,arrows=SLIM,\ngrid=[5,5,5],axes=FRAME);\n" }{TEXT -1 42 "G
radient vector field for isotimic spheres" }}{PARA 13 "" 1 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "gradplot3d(x^2+y
^2,x=-3..3,y=-3..3,z=-3..3,arrows=SLIM,\ngrid=[5,5,5],axes=FRAME,scali
ng=CONSTRAINED);\n" }{TEXT -1 44 "Gradient vector field for isotimic c
ylinders" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 76 "gradplot3d(sqrt(x^2+y^2)-z,x=-2..2,y=-2..2,z=-2..4,
arrows=SLIM,axes=FRAME);\n" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 190 "DEplot([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=LARGE,\ntit
le=`Lotka-Volterra model`,color=[.3*y(t)*(x(t)-1),x(t)*(1-y(t)),.1]);
\n" }{TEXT -1 259 "DEplot plots the direction field for a system of di
fferential equations, which are defined by a vector field; this is equ
ivalent to plotting a vector field.  The Lotka-Volterra model is a sim
plified model for predator-prey interactions in population dynamics." 
}}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 13 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }