{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1
{CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0
0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0
0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Dash \+
Item" 0 16 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0
0 -1 3 3 0 0 0 0 0 0 16 3 }{PSTYLE "" 3 256 1 {CSTYLE "" -1 -1 "" 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE
"" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 258 1 {CSTYLE "" -1 -1 "" 1
12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 4 259 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0
1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 260 1 {CSTYLE "" -1
-1 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1
0 }}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 26
"Three Dimensional Graphics" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}
{PARA 258 "" 0 "" {TEXT -1 18 "Jim Herod, Retired" }}{PARA 259 "" 0 "
" {TEXT -1 21 "School of Mathematics" }}{PARA 260 "" 0 "" {TEXT -1 21
"herod@math.gatech.edu" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 ""
0 "" {TEXT -1 496 " Maple can be used to give good intuiti
on for the shape of surfaces, for the calculus on multidimensional fun
ctions, and for the computation of algorithms. If any computer program
is opened for the first time on the occasion that there is a hard pro
blem to be done, the tasks can be formidable. Rather, we begin with so
me simple problems that are introductory in nature. It is the introduc
tion to the use of Maple for drawing surfaces that is of primary impor
tance in this assignment." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 16
"" 0 "" {TEXT -1 85 "We draw the function u(0,x), where u is as given \+
below, on the interval 0 < x < 2 ." }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 49 "u:=(t,x)->exp(-t)*sin(x);\nplot(u(0,x),x=0..2*Pi);" }
}}{PARA 16 "" 0 "" {TEXT -1 62 "We draw an animation for how the graph
changes as t increases." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "
with(plots):\nanimate(u(t,x),x=0..2*Pi,t=0..2);" }}}{PARA 0 "" 0 ""
{TEXT -1 105 "(Suggestion: One way to illustrate an animation on a sta
tic document is to draw a series of \"snapshots.\")" }}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 50 "plot(\{u(0,x),u(2/3,x),u(5/3,x),u(2,x)\},x=
0..2*Pi);" }}}{PARA 16 "" 0 "" {TEXT -1 131 " W provide an alternate w
ay to view a one-dimensional graph changing in time by drawing a surfa
ce, where one axis is the time axis." }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 66 "plot3d(u(t,x),x=0..2*Pi,t=0..2,axes=NORMAL,orientatio
n=[-135,65]);" }}}{PARA 0 "" 0 "" {TEXT -1 147 "Finally, if the surfac
e at been defined in polar coordinates, we could have drawn the surfac
e in that form -- even we could animate such a surface." }}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "u:=(t,r,theta)->t*(1-r^2);" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "animat
e3d([r,theta,u(t,r,theta)],r=0..1,theta=0..2*Pi,t=-1..1,\n coords=c
ylindrical,axes=NORMAL,orientation=[60,80]);" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 ""
0 "" {TEXT -1 103 "Finally, sometimes you want to draw a curve, instea
d of a surface, in three dimensions. We do two here." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "spacecurve([t,t,sin(t
)],t=0..2*Pi,axes=NORMAL,orientation=[-30,50],color=RED);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "spacecurve([cos(t),sin(t),t],t=-Pi.
.Pi,color=ORANGE,orientation=\n[-30,60],axes=normal);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT
-1 24 "Exercise for the student" }}{PARA 0 "" 0 "" {TEXT -1 27 "Draw t
he graph of u(x,y) = " }{XPPEDIT 18 0 "x^2-y^2" "6#,&*$%\"xG\"\"#\"\"
\"*$%\"yGF&!\"\"" }{TEXT -1 38 " over the rectangle [-1, 1] x [-1, 1].
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "1 0" 0 }{VIEWOPTS 1 1 0
1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }