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{SECT 0 {PARA 215 "" 0 "" {TEXT 216 20 "MAPLE WORKSHEET #2: " }{TEXT 
216 26 "2d Plots and Special Plots" }}{SECT 1 {PARA 216 "" 0 "" {TEXT 
216 22 "Load the plots package" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 12 "with(plots):" }}}}{SECT 1 {PARA 217 "" 0 "" {TEXT 216 50 "Tangen
t line to the graph of a function at a point" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 15 "f := x->sin(x):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "plot1:=plot(f(x), x=-Pi..Pi,\n" }{MPLTEXT 1 0 39 "num
points=200, color=red, thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "x0 := Pi/3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 12 "y0 := f(x0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "g := \+
D(f):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "m := g(x0):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot2 := plot(m*(x-x0)+y0, x
=-Pi..Pi,\n" }{MPLTEXT 1 0 25 "color=blue, thickness=2):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "display(\{plot1, plot2\},\n" }
{MPLTEXT 1 0 21 "scaling=constrained,\n" }{MPLTEXT 1 0 50 "titlefont=[
COURIER,BOLD,24], title=`Tangent line`," }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "t" }{MPLTEXT 1 0 33 "ickmarks=[spacing(Pi),[-1,0,1]]);
" }}}}{SECT 1 {PARA 218 "" 0 "" {TEXT 216 22 "Coloring and tickmarks" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "colorarray:=[yellow,cyan]:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "filledsine:=n->plot(sin
(x),x=n*Pi..(n+1)*Pi,\n" }{MPLTEXT 1 0 43 "color=colorarray[modp(n,2)+
1],filled=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display
(filledsine(0),\n" }{MPLTEXT 1 0 20 "scaling=constrained," }{MPLTEXT 
1 0 32 "tickmarks=[spacing(Pi),[-1,0,1]]" }{MPLTEXT 1 0 2 ");" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 
5 "seq(\n" }{MPLTEXT 1 0 21 "filledsine(n),n=0..3\n" }{MPLTEXT 1 0 3 "
),\n" }{MPLTEXT 1 0 46 "plot(sin(x),x=0..4*Pi,color=navy,thickness=3)
\n" }{MPLTEXT 1 0 2 "\}," }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 33 "tickm
arks=[spacing(Pi),[-1,0,1]]," }{MPLTEXT 1 0 21 "scaling=constrained);"
 }}}}{SECT 1 {PARA 219 "" 0 "" {TEXT 216 21 "Taylor approximations" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "series(sin(x),x=0,17):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "convert(series(sin(x),x=0,17
),polynom):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "taysin := (n
)-> series(sin(x),x=0,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "taypolsin := (n)-> convert(taysin(n+1), polynom):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "taypolsin(20):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 51 "plot(\{sin(x),taypolsin(3)\}, x=-Pi..Pi,thic
kness=3,\n" }{MPLTEXT 1 0 33 "tickmarks=[spacing(Pi),[-1,0,1]]," }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 72 "titlefont=[HELVETICA,BOLD,24],ti
tle=`Third Order Taylor Approximation`);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "plot(\{sin(x),taypolsin(5)\}, x=-Pi..Pi,thickness=3,
\n" }{MPLTEXT 1 0 32 "tickmarks=[spacing(Pi),[-1,0,1]]" }{MPLTEXT 1 0 
2 ",\n" }{MPLTEXT 1 0 72 "titlefont=[HELVETICA,BOLD,24],title=`Fifth O
rder Taylor Approximation`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 57 "plot(\{sin(x), seq(taypolsin(2*n+1), n=0..4)\}, x=-10..10,\n" }
{MPLTEXT 1 0 52 "numpoints=200, view=[-10..10,-10..10], thickness=3,\n
" }{MPLTEXT 1 0 32 "tickmarks=[spacing(Pi),[-1,0,1]]" }{MPLTEXT 1 0 
22 ",scaling=constrained,\n" }{MPLTEXT 1 0 79 "titlefont=[HELVETICA,BO
LD,24],title=`Taylor approximations up to Ninth Order`);" }}}}{SECT 0 
{PARA 220 "" 0 "" {TEXT 216 10 "Polarplots" }}{SECT 0 {PARA 221 "" 0 "
" {TEXT 216 20 "Ordinary polarplots:" }}{SECT 1 {PARA 0 "" 0 "" {TEXT 
216 15 "Setting options" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "s
etoptions(scaling=constrained,tickmarks=[0,0],axes=none);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "-I+setoptionsG6\"6%/I(scalingGF$I,constrainedGF$/
I*tickmarksGF$7$\"\"!F,/I%axesGF$I%noneGF$" }}}}{SECT 1 {PARA 0 "" 0 "
" {TEXT 216 10 "Polarplots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "polarplot(sin(t), t=0..2*Pi,\n" }{MPLTEXT 1 0 24 "thickness=3, col
or=red,\n" }{MPLTEXT 1 0 51 "titlefont=[HELVETICA,BOLD,24],title=`Pola
rplot I`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "polarplot(sin
(2*t), t=0..2*Pi,\n" }{MPLTEXT 1 0 24 "thickness=3, color=red,\n" }
{MPLTEXT 1 0 52 "titlefont=[HELVETICA,BOLD,24],title=`Polarplot II`);"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "polarplot(sin(16*t), t=0
..2*Pi,\n" }{MPLTEXT 1 0 24 "thickness=3, color=red,\n" }{MPLTEXT 1 0 
53 "titlefont=[HELVETICA,BOLD,24],title=`Polarplot III`);" }}}}{SECT 1
 {PARA 0 "" 0 "" {TEXT 216 16 "Coloring problem" }}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 31 "polarplot(sin(2*t), t=0..2*Pi,\n" }{MPLTEXT 1 
0 36 "thickness=3, color=red,filled=true);" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot3d([r*cos(t),r*sin(t),0]
,t=0..2*Pi,r=0..2*sin(2*t),\n" }{MPLTEXT 1 0 32 "grid=[80,10],style=pa
tchnogrid,\n" }{MPLTEXT 1 0 29 "color=red,orientation=[0,0]);" }}}}
{SECT 1 {PARA 0 "" 0 "" {TEXT 216 15 "Array of colors" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "col:=[\n" }{MPLTEXT 1 0 44 "red,blue,coral
,cyan,violet,gold,green,gray,\n" }{MPLTEXT 1 0 66 "grey,khaki,magenta,
maroon,orange,pink,plum,aquamarine,sienna,tan,\n" }{MPLTEXT 1 0 46 "tu
rquoise,brown,wheat,white,yellow,black,navy\n" }{MPLTEXT 1 0 2 "]:" }}
}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 16 "A flower routine" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "flower:=(p,r,c)->plot([r*sin(4*p*t)
*cos(t),r*sin(4*p*t)*sin(t),t=0..2*Pi],\n" }{MPLTEXT 1 0 37 "thickness
=2, color=col[modp(c,5)+1]):" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 8 
"A flower" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }
{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 18 "flower(2,n/10,n),\n" }
{MPLTEXT 1 0 8 "n=1..7)\n" }{MPLTEXT 1 0 3 "\});" }{TEXT 218 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 
5 "seq(\n" }{MPLTEXT 1 0 19 "flower(1,1-1/n,n),\n" }{MPLTEXT 1 0 8 "n=
2..8)\n" }{MPLTEXT 1 0 3 "\});" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 
29 "Loading the plottools package" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 16 "with(plottools):" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 11 "F
lower tile" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "flowertile:=di
splay(\{\n" }{MPLTEXT 1 0 31 "seq(flower(1,1-1/n,n),n=2..7),\n" }
{MPLTEXT 1 0 43 "polygonplot([[1,1],[-1,1],[-1,-1],[1,-1]],\n" }
{MPLTEXT 1 0 13 "thickness=3)\n" }{MPLTEXT 1 0 4 "\}):\n" }{MPLTEXT 1 
0 20 "display(flowertile);" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 12 "
Tile display" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "flowertiles:
=display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 5 "seq(\n" }
{MPLTEXT 1 0 31 "translate(flowertile,2*n,2*m),\n" }{MPLTEXT 1 0 9 "n=
0..5),\n" }{MPLTEXT 1 0 8 "m=0..5)\n" }{MPLTEXT 1 0 14 "\},axes=none):
\n" }{MPLTEXT 1 0 21 "display(flowertiles);" }}}}{SECT 1 {PARA 0 "" 0 
"" {TEXT 216 28 "Transformation for 3D layers" }}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 32 "f:=n->transform((x,y)->[x,y,n]):" }}}}{SECT 1 
{PARA 0 "" 0 "" {TEXT 216 17 "Layers of flowers" }}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }
{MPLTEXT 1 0 23 "f(n)(flower(n+1,1,n)),\n" }{MPLTEXT 1 0 8 "n=1..4)\n"
 }{MPLTEXT 1 0 23 "\},orientation=[26,65]);" }}}}{SECT 1 {PARA 0 "" 0 
"" {TEXT 216 9 "Rotation:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 
"display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 8 "rotate(\n" }
{MPLTEXT 1 0 32 "translate(flower(n+1,1,n),2,0),\n" }{MPLTEXT 1 0 9 "n
*2*Pi/5\n" }{MPLTEXT 1 0 3 "),\n" }{MPLTEXT 1 0 8 "n=0..4)\n" }
{MPLTEXT 1 0 13 "\},axes=none);" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 
216 22 "Flowers on a cylinder:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "g:=h->transform((x,y)->\n" }{MPLTEXT 1 0 33 "[cos(2*Pi*x/h),sin(
2*Pi*x/h),y]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "newflower
tile:= display(\{\n" }{MPLTEXT 1 0 39 "seq(flower(1, 1-1/n, n), n = 2 \+
.. 7)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" 
}{MPLTEXT 1 0 15 "g(6)(display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }
{MPLTEXT 1 0 39 "seq(translate(newflowertile,2*n,2*m), \n" }{MPLTEXT 
1 0 17 "n =0..5),m=0..2)\n" }{MPLTEXT 1 0 6 "\})), \n" }{MPLTEXT 1 0 
45 "plot3d([cos(u),sin(u),v],u=0..2*Pi,v=-1..5, \n" }{MPLTEXT 1 0 45 "
color=blue,style=patchnogrid,glossiness=0.5)\n" }{MPLTEXT 1 0 3 "\});"
 }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 216 24 "Stereographic Projection" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "stereo:=transform((x,y)->\n
" }{MPLTEXT 1 0 59 "[2*x/(x^2+y^2+1),2*y/(x^2+y^2+1),(x^2+y^2-1)/(x^2+
y^2+1)]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "cusp:=transfor
m((x,y)->\n" }{MPLTEXT 1 0 36 "[x,y,0.3*arctan(25*sqrt(x^2+y^2))]):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "bulb:=transform((x,y)->\n"
 }{MPLTEXT 1 0 32 "[x,y,1-.5/(1+(5*x)^2+(5*y)^2)]):" }}}}{SECT 1 
{PARA 0 "" 0 "" {TEXT 216 10 "3D flowers" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 
26 "stereo(flower(2,n/10,n)),\n" }{MPLTEXT 1 0 8 "n=1..5)\n" }{MPLTEXT
 1 0 3 "\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{
\n" }{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 24 "cusp(flower(2,n/10,n)),
\n" }{MPLTEXT 1 0 8 "n=1..5)\n" }{MPLTEXT 1 0 23 "\},scaling=constrain
ed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }
{MPLTEXT 1 0 5 "seq(\n" }{MPLTEXT 1 0 24 "bulb(flower(2,n/10,n)),\n" }
{MPLTEXT 1 0 8 "n=1..5)\n" }{MPLTEXT 1 0 3 "\});" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 5 "seq(\n" }
{MPLTEXT 1 0 26 "stereo(flower(2,n/10,n)),\n" }{MPLTEXT 1 0 9 "n=1..5)
,\n" }{MPLTEXT 1 0 64 "polygonplot3d([[0,0,-1],[0,0,-3]],thickness=5,c
olor=aquamarine)\n" }{MPLTEXT 1 0 3 "\});" }}}{PARA 0 "" 0 "" {TEXT 
216 42 "Flowertile pasted on the faces of a cube: " }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 33 "cube1:=transform((x,y)->[x,y,1]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "cube2:=transform((x,y)->[x,y
,-1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "cube3:=transform(
(x,y)->[x,1,y]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "cube4:=
transform((x,y)->[x,-1,y]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "cube5:=transform((x,y)->[1,x,y]):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "cube6:=transform((x,y)->[-1,x,y]):" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 37 "cube1(flow
ertile),cube2(flowertile),\n" }{MPLTEXT 1 0 37 "cube3(flowertile),cube
4(flowertile),\n" }{MPLTEXT 1 0 38 "cube5(flowertile),cube6(flowertile
)\},\n" }{MPLTEXT 1 0 21 "scaling=constrained);" }}}}{SECT 1 {PARA 0 "
" 0 "" {XPPEDIT 216 0 "Typesetting:-mrow(Typesetting:-mi(\"Genuine\", \+
bold = \"true\", italic = \"false\", mathvariant = \"bold\", fontweigh
t = \"bold\"), Typesetting:-mo(\" \", bold = \"true\", mathvariant = \+
\"bold\", fontweight = \"bold\", fence = \"false\", separator = \"fals
e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\",
 movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rs
pace = \"0.0em\"), Typesetting:-mn(\"3\", bold = \"true\", mathvariant
 = \"bold\", fontweight = \"bold\"), Typesetting:-mi(\"d\", bold = \"t
rue\", italic = \"false\", mathvariant = \"bold\", fontweight = \"bold
\"), Typesetting:-mo(\" \", bold = \"true\", mathvariant = \"bold\", f
ontweight = \"bold\", fence = \"false\", separator = \"false\", stretc
hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim
its = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.
0em\"), Typesetting:-mi(\"flowers\", bold = \"true\", italic = \"false
\", mathvariant = \"bold\", fontweight = \"bold\"));" "-I%mrowG6#/I+mo
dulenameG6\"I,TypesettingGI(_syslibGF'6(-I#miGF$6'Q(GenuineF'/%%boldGQ
%trueF'/%'italicGQ&falseF'/%,mathvariantGQ%boldF'/%+fontweightGF7-I#mo
GF$6/Q\"~F'F/F5F8/%&fenceGF4/%*separatorGF4/%)stretchyGF4/%*symmetricG
F4/%(largeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'rs
paceGFN-I#mnGF$6&Q\"3F'F/F5F8-F,6'Q\"dF'F/F2F5F8F:-F,6'Q(flowersF'F/F2
F5F8" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "spaceflower:=\n" }
{MPLTEXT 1 0 56 "plot3d([r*cos(t),r*sin(t),0],t=0..2*Pi,r=0..2*sin(4*t
),\n" }{MPLTEXT 1 0 33 "grid=[120,15],style=patchnogrid,\n" }{MPLTEXT 
1 0 19 "orientation=[0,0]):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 21 "display(spaceflower);" }}}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 17 "with(plottools):\n" }{MPLTEXT 1 0 33 "spacestereo
:=transform((x,y,z)->\n" }{MPLTEXT 1 0 1 "[" }{MPLTEXT 1 0 55 "2*x/(x^
2+y^2+1),2*y/(x^2+y^2+1),(x^2+y^2-1)/(x^2+y^2+1)" }{MPLTEXT 1 0 3 "]):
" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "disp
lay([\n" }{MPLTEXT 1 0 26 "spacestereo(spaceflower),\n" }{MPLTEXT 1 0 
49 "line([0,0,-3],[0,0,-1],color=green,thickness=4),\n" }{MPLTEXT 1 0 
11 "translate(\n" }{MPLTEXT 1 0 32 "scale(spaceflower,1/2,1/2,1/2),\n"
 }{MPLTEXT 1 0 8 "0,0,-2)\n" }{MPLTEXT 1 0 24 "],orientation=[-32,70],
\n" }{MPLTEXT 1 0 39 "lightmodel=light3,scaling=constrained);" }}}}}
{SECT 1 {PARA 222 "" 0 "" {TEXT 216 18 "The golden spiral:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g := (1+sqrt(5))/2:\n" }{MPLTEXT 1 
0 17 "mu := g^(2/Pi): \n" }{MPLTEXT 1 0 41 "spiral := polarplot(mu^t, \+
t=-6*Pi..2*Pi,\n" }{MPLTEXT 1 0 41 "numpoints=200, thickness=3, color=
blue):\n" }{MPLTEXT 1 0 16 "display(spiral,\n" }{MPLTEXT 1 0 38 "tickm
arks=[0,0], scaling=constrained,\n" }{MPLTEXT 1 0 53 "titlefont=[HELVE
TICA,BOLD,24],title=`Golden Spiral`);" }}}}{SECT 1 {PARA 223 "" 0 "" 
{TEXT 216 21 "The golden rectangle:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "goldrec := polygonplot(\n" }{MPLTEXT 1 0 50 "[ [mu^(2
*Pi), mu^(Pi/2)], [-mu^(Pi), mu^(Pi/2)], \n" }{MPLTEXT 1 0 55 "[-mu^(P
i), -mu^(3*Pi/2)], [mu^(2*Pi), -mu^(3*Pi/2)] ],\n" }{MPLTEXT 1 0 37 "s
tyle=line, thickness=3, color=red): " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "display(\{ spiral,goldrec \},\n" }{MPLTEXT 1 0 39 "sc
aling=constrained, tickmarks=[0,0], \n" }{MPLTEXT 1 0 75 "titlefont=[H
ELVETICA,BOLD,24],title=`Golden Spiral in a Golden Rectangle`);" }}}}}
{SECT 1 {PARA 224 "" 0 "" {TEXT 216 12 "Implicitplot" }}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 14 "implicitplot(\n" }{MPLTEXT 1 0 1 "[" }
{MPLTEXT 1 0 50 "seq(x^2 - y^2 = k,k=1..6)], x=-Pi..Pi, y=-Pi..Pi,\n" 
}{MPLTEXT 1 0 28 "color=[seq(col[i],i=1..6)],\n" }{MPLTEXT 1 0 28 "gri
d=[100,20], thickness=2,\n" }{MPLTEXT 1 0 54 "titlefont=[HELVETICA,BOL
D,24],title=`Implicit Plots`);" }}}}{SECT 1 {PARA 225 "" 0 "" {TEXT 
216 20 "The numpoints option" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "plot(sin(1/x), x=-1..1,\n" }{MPLTEXT 1 0 40 "numpoints=1000, thick
ness=2, color=red,\n" }{MPLTEXT 1 0 28 "title=`Rapid Oscillations`);" 
}}}}{SECT 1 {PARA 226 "" 0 "" {TEXT 216 33 "Examples from the student \+
package" }}{SECT 0 {PARA 227 "" 0 "" {TEXT 216 25 "Load the student pa
ckage:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}
}}{SECT 0 {PARA 228 "" 0 "" {TEXT 216 46 "Draw tangent lines to the gr
aph of a function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a := k
->showtangent(cos(x), x=1/k, thickness=1):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 53 "display(\{seq(a(k), k=1..5)\}, view=[-3.3..3.3,-3..
3],\n" }{MPLTEXT 1 0 20 "scaling=constrained," }{MPLTEXT 1 0 32 "tickm
arks=[spacing(Pi),[-1,0,1]]" }{MPLTEXT 1 0 2 ");" }}}}{SECT 0 {PARA 
229 "" 0 "" {TEXT 216 13 "Riemann sums:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "ri1 := rightbox(x^2, x=0..2, 10,\n" }{MPLTEXT 1 0 39 
"color=red, thickness=3, numpoints=100):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "ri2 := leftbox(x^2, x=0..2,10, \n" }{MPLTEXT 1 0 42 "
color=yellow, thickness=3, numpoints=100):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "display(\{ ri1, ri2 \},\n" }{MPLTEXT 1 0 18 "tickma
rks=[10,0],\n" }{MPLTEXT 1 0 60 "titlefont=[TIMES,ROMAN,32], title=`Th
e Riemann integral I`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "
ri3 := rightbox(x^2, x=0..2,50,\n" }{MPLTEXT 1 0 39 "color=red, thickn
ess=3, numpoints=100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "r
i4 := leftbox(x^2, x=0..2,50,\n" }{MPLTEXT 1 0 42 "color=yellow, thick
ness=3, numpoints=100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "
display(\{ ri3, ri4 \},\n" }{MPLTEXT 1 0 18 "tickmarks=[10,0],\n" }
{MPLTEXT 1 0 61 "titlefont=[TIMES,ROMAN,32], title=`The Riemann integr
al II`);" }}}}}{SECT 1 {PARA 230 "" 0 "" {TEXT 216 12 "Densityplots" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot3d(sin(x*y), x=-Pi..Pi,
 y=-Pi..Pi,\n" }{MPLTEXT 1 0 70 "scaling=constrained, grid=[100,100], \+
style=patchnogrid, shading=zhue);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "plot3d(sin(x*y), x=-Pi..Pi, y=-Pi..Pi,\n" }{MPLTEXT 
1 0 88 "scaling=constrained, grid=[100,100], style=patchnogrid, shadin
g=zhue,orientation=[0,0]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "densityplot(sin(x*y), x=-Pi..Pi, y=-Pi..Pi,\n" }
{MPLTEXT 1 0 28 "axes=boxed, grid=[100,100],\n" }{MPLTEXT 1 0 36 "styl
e=patchnogrid,color=aquamarine);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 47 "densityplot(x*exp(-x^2-y^2), x=-2..2, y=-2..2,\n" }{MPLTEXT 
1 0 44 "grid=[49,49], axes=none, style=patchnogrid);" }}}}{SECT 1 
{PARA 231 "" 0 "" {TEXT 216 10 "Fieldplots" }}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 57 "fieldplot( [x/(x^2+y^2+4)^(1/2), -y/(x^2+y^2+4)^(1/2
)], \n" }{MPLTEXT 1 0 18 "x=-2..2, y=-2..2,\n" }{MPLTEXT 1 0 48 "arrow
s=SLIM,grid=[15,15],fieldstrength=maximal,\n" }{MPLTEXT 1 0 35 "thickn
ess=2, color=x*y, axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "fieldplot([1/x, 1/y], x=-10..10, y=-10..10,\n" }{MPLTEXT 1 0 61 
"arrows=LINE, grid=[10,10],thickness=3, axes=none, color = x);" }}}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2
 33 1 1 }