{VERSION 5 0 "IBM INTEL NT" "5.0" }
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{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "Cour
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0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times
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{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 
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1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "T
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1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 
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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 17 "Plotting Surfaces" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 50 "P
lotting the graph of a function of two variables." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 84 "Let's plot the graph of f
(x,y) = x^2-y^2.  To do this, we'll use the plot3d command." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 199 "In its most ba
sic form, the plot3d command takes three arguments.  The first is the \+
expression that defines the function to be plotted, and the next two a
re the ranges of the independent variables.  " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot3d(x^2-
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1.000000 72.000000 55.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 218 "Note: To see a different view, use the mouse to click an
d drag in the plot.  To change some of the plot options, right-click o
n the plot, and select an option.  For example, try using the mouse to
 add axes to the plot." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 74 "Here is the same command, with some options added di
rectly to the command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "plot3d(x^2-y^2,x=-1..1,y=-1..1,axes
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 185 "With the \"style=patchcontour\" o
ption, the lines drawn in the surface are contours lines instead of th
e xy grid.  If you look at the plot \"from above'', you will see the c
ontour diagram." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 147 "Here is another surface.  Experiment with some of the pl
ot options in the following command.  For example, what does the conto
ur diagram look like?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
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1.000000 59.000000 74.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 10 "Exercise: " }{TEXT -1 
196 "Before going on, try plotting some different functions.  For exam
ple, try some of the functions from Problem 12.2/16 (the matching prob
lem), or try plotting your \"monkey saddle\" (Problem 12.3/32)." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 18 "" 0 "" 
{TEXT -1 27 "Surfaces Defined Implicitly" }{TEXT 257 0 "" }}{PARA 19 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 233 "A surface can be \+
defined implicitly, rather than as the graph of a function of two vari
ables.  That is, instead of defining the surface as z=f(x,y), it may b
e defined as a level set g(x,y,z) = C.  There is a command in Maple, c
alled " }{TEXT 258 15 "implicitplot3d " }{TEXT -1 103 "that can be use
d to plot such surfaces.  To use it, we must first load a library of f
unctions with the " }{TEXT 259 13 "with(plots): " }{TEXT -1 8 "command
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 
7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefin
ed\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Let's first plot somethin
g simple:  the sphere x^2+y^2+z^2=1." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 109 "implicitplot3d(x^2+y^2+z^2=1,x=-2..2,y=-2..2,z=-2..2
,grid=[20,20,20],style=patchcontour,scaling=constrained);" }}{PARA 13 
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