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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 115 " Plotting with 2 and 3-dimensional functions\n   \+
                                   \n\n\nWe need to use   with(plots)
\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 150 "The first function we look at is  sin(x)cos(y).\nWe plot the c
urve and look at its contours.\nWe then repeat this process with sever
al other functions.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=sin(x)*
cos(y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&-%$sinG6#%\"xG\"\"
\"-%$cosG6#%\"yGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot3
d(f,x=0..2*Pi,y=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
35 "contourplot(f,x=0..2*Pi,y=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Second functi
on:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "g:=(x^2+3*y^2)*exp(-x^2-y^
2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG*&,&*$)%\"xG\"\"#\"\"\"\"
\"\"*$)%\"yGF*F+\"\"$F,-%$expG6#,&F'!\"\"F-F5F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 26 "plot3d(g,x=-3..3,y=-3..3);" }}{PARA 13 "" 1 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "contourpl
ot(g,x=-3..3,y=-3..3);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 16 "Third function:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h:=x*y;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG*&%\"xG\"\"\"%\"yGF'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot3d(h,x=-2..2,y=-2..2);" 
}}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "contourplot(h,x=-2..2,y=-2..2);" }}{PARA 13 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 17 "Fourth function:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "l:=x/(x^2+y^2+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG*&%
\"xG\"\"\",(*$)F&\"\"#F'\"\"\"*$)%\"yGF+F'F,F,F,!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot3d(l,x=-4..4,y=-4..4);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "contourplot(l,x=-4..4,y=-4..4);" }}{PARA 13 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 108 "We now look at a function of three variables,\nand \+
we plot two of its contours.\nThe contours are ellipsoids.\n" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "q:=x^2+4*y^2+z^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"qG,(*$)%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF)F*\"\"%*$)%
\"zGF)F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 146 "The function implicitplot3d will plot th
e points that\ngive the function q a specified value;\nie, implicitplo
t can be used to plot a contour of q.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 54 "implicitplot3d(q=1,x=-1..1,y=-1..1,z=-1..1,color=red);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 57 "implicitplot3d(q=4,x=-2..2,y=-2..2,z=-2..2,color=yellow);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 152 "We are going to plot th
e two contours on the same graph.\nThe second contour totally surround
s the first one,\nso we plot just half of the second contour." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "one
:=implicitplot3d(q=1,x=-1..1,y=-1..1,z=-1..1,color=red):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "two:=implicitplot3d(q=4,x=-2..2,y=0
..2,z=-2..2,color=yellow):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "display3d(\{one,two\});" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
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