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{SECT 0 {PARA 208 "" 0 "" {TEXT 200 0 "" }{TEXT 200 0 "" }{TEXT 200 9 
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{EXCHG {PARA 0 "" 0 "" {TEXT 200 11 "Start with:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{PARA 0 "" 0 "" {TEXT 200 0 
"" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 216 12 "Level curves" }}{PARA 0 "" 
0 "" {TEXT 200 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 200 307 "There are \+
two related commands with virtually the same syntax: \"contourplot\" a
nd \"contourplot3d\". The difference is that \"contourplot\" creates a
 2D graph, typically looking down from the top (or z-axis), while \"co
ntourplot3d\" creates a 3D graph with level curves raised to the appro
priate levels.   " }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" 
{TEXT 200 25 "The syntax is as follows:" }}{PARA 0 "" 0 "" {TEXT 200 
0 "" }}{PARA 212 "" 0 "" {TEXT 210 13 "contourplot( " }{TEXT 211 10 "e
xpression" }{TEXT 212 36 ", var1 = a..b, var2 = c..d, options)" }}
{PARA 213 "" 0 "" {TEXT 200 0 "" }}{PARA 214 "" 0 "" {TEXT 200 3 "and"
 }}{PARA 215 "" 0 "" {TEXT 200 0 "" }}{PARA 216 "" 0 "" {TEXT 213 15 "
contourplot3d( " }{TEXT 214 10 "expression" }{TEXT 215 36 ", var1 = a.
.b, var2 = c..d, options)" }}{PARA 217 "" 0 "" {TEXT 200 0 "" }}{PARA 
0 "" 0 "" {TEXT 200 22 "Here are the examples:" }}{PARA 0 "" 0 "" 
{TEXT 200 0 "" }}{PARA 218 "" 0 "" {TEXT 200 15 "\"contourplot\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "contourplot(y^2-x,x=-2..2,y=
-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 127 "This fascinating pic
ture does not appear to tell much about the graph of the function. Try
 increasing the number of \"levels\":" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "contourplot(y^2-x,x=-2..2,y=-2..2,contours=20);" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 149 "By the time
 you are taking your first midterm, you will be able to describe the s
hape of the graph given the function and a plot like that (or else)." 
}}{PARA 0 "" 0 "" {TEXT 200 59 "For now, let us use the 3D version of \+
the command as help. " }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}}{EXCHG 
{PARA 219 "" 0 "" {TEXT 200 17 "\"contourplot3d\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 61 "contourplot3d(y^2-x,x=-2..2,y=-2..2,axes=nor
mal,contours=20);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 360 "Rotate the
 3D graph so that the readings of theta and phi in the menu bar are -9
0 for theta and 0 for phi. (If you are impatient, just type in the val
ues for theta and phi.) You should see approximately the same picture \+
as with the 2D plot. Notice that the 2D plot is color-coded. The level
 curves on a lower \"level\" are red, on the higher \"level\" yellow. \+
" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 49 "How
 would you describe the shape of the 3D graph?" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 90 "Here a
re some options that might come handy when doing homework or preparing
 for the exam:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "contourpl
ot(y^2-x,x=-5..5,y=-5..5,contours=[-2,-1,0,1,2,3]);" }{MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 80 "contourplot(y^2-x,x=-2..2,y=-2..2,contours=20,f
illed=true,coloring=[green,red]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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