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}{SCP_R 1 0 99{COM_R 2 0{TEXT 1 47 "MAPLE WORKSHEET #2: 2d Plots \+
and Special Plots."}}{SEP_R 3 0}{INP_R 4 0 "> "{TEXT 0 12 "with(p
lots):"}}{SEP_R 5 0}{INP_R 6 0 "> "{TEXT 0 17 "f := x->cos(x^2);"
}}{OUT_R 7 0 6{DAG :3n3\`f`@8,2n3\`x`,1,3n5\`operator`n4\`arrow`p
7(3n3\`cos`,2*3a2x0001j2x0002p7p7}}{SEP_R 8 0}{INP_R 9 0 "> "
{TEXT 0 66 "pl1:=plot(f(x), x=-Pi..Pi,\012numpoints=200, color=re
d, thickness=3):"}}{SEP_R 10 0}{INP_R 11 0 "> "{TEXT 0 14 "x0 := \+
Pi^2/22:"}}{SEP_R 12 0}{INP_R 13 0 "> "{TEXT 0 12 "y0 := f(x0);"}
}{OUT_R 14 0 13{DAG :3n3\`y0`(3n3\`cos`,2+3*3n3\`Pi`j2x0004/3j2x0
001j2x0484}}{SEP_R 15 0}{INP_R 16 0 "> "{TEXT 0 10 "g := D(f);"}}
{OUT_R 17 0 16{DAG :3n3\`g`@8,2n3\`x`,1,3n5\`operator`n4\`arrow`p
7+3*5(3n3\`sin`,2*3a2x0001j2x0002j2x0001p18p1Ci2x0002p7p7}}{SEP_R
 18 0}{INP_R 19 0 "> "{TEXT 0 11 "m := g(x0);"}}{OUT_R 20 0 19
{DAG :3n3\`m`+3*5(3n3\`sin`,2+3*3n3\`Pi`j2x0004/3j2x0001j2x0484p1
0pBj2x0002/3i2x0001j2x0011}}{SEP_R 21 0}{INP_R 22 0 "> "{TEXT 0 
63 "pl2 := plot(m*(x-x0)+y0, x=-Pi..Pi,\012color=yellow, thicknes
s=2):"}}{SEP_R 23 0}{INP_R 24 0 "> "{TEXT 0 109 "display(\{pl1, p
l2\},\012scaling=constrained, tickmarks=[7,0],\012titlefont=[COUR
IER,BOLD,18], title=`Tangent line`);"}}{SEP_R 25 0}{INP_R 26 0 ">
 "{TEXT 0 40 "taysin := (n)-> series( sin(x), x=0, n):"}}{SEP_R 
27 0}{INP_R 28 0 "> "{TEXT 0 49 "taypolsin := (n)-> convert(taysi
n(n+1), polynom):"}}{SEP_R 29 0}{INP_R 30 0 "> "{TEXT 0 14 "taypo
lsin(20);"}}{OUT_R 31 0 30{DAG +15n3\`x`j2x0001*3p1j2x0003/3i2x00
01j2x0006*3p1j2x0005/3p3j2x0120*3p1j2x0007/3pAj2x5040*3p1j2x0009/
3p3j3x00362880*3p1j2x0011/3pAj3x39916800*3p1j2x0013/3p3j4x0062270
20800*3p1j2x0015/3pAj5x0001307674368000*3p1j2x0017/3p3j5x03556874
28096000*3p1j2x0019/3pAj6x00121645100408832000}}{SEP_R 32 0}
{INP_R 33 0 "> "{TEXT 0 108 "plot(\{sin(x),taypolsin(3)\}, x=-Pi.
.Pi,thickness=3,tickmarks=[7,0],title=`Third Order Taylor Approxi
mation`);"}}{SEP_R 34 0}{INP_R 35 0 "> "{TEXT 0 108 "plot(\{sin(x
),taypolsin(5)\}, x=-Pi..Pi,thickness=3,tickmarks=[7,0],title=`Fi
fth Order Taylor Approximation`);"}}{SEP_R 36 0}{INP_R 37 0 "> "
{TEXT 0 173 "plot(\{sin(x), seq(taypolsin(2*n+1), n=0..4)\}, x=-1
0..10,\012numpoints=200, view=[-10..10,-3..3], thickness=3, tickm
arks=[7,0],\012title=`Taylor approximations up to Ninth Order`);"
}}{SEP_R 38 0}{COM_R 39 0{TEXT 1 11 "Polarplots:"}}{SEP_R 40 0}
{INP_R 41 0 "> "{TEXT 0 94 "polarplot(sin(4*t), t=0..2*Pi,\012thi
ckness=3, color=yellow, tickmarks=[0,0],\012title=`Polarplot`);"}
}{SEP_R 42 0}{INP_R 43 0 "> "{TEXT 0 91 "polarplot(sin(16*t), t=0
..2*Pi,\012thickness=3, color=red, ickmarks=[0,0],\012title=`Pola
rplot`);"}}{SEP_R 44 0}{INP_R 45 0 "> "{TEXT 0 196 "g := (1+sqrt(
5))/2:\012mu := g^(2/Pi): \012spiral := polarplot(mu^t, t=-6*Pi..
2*Pi,\012numpoints=200, thickness=3, color=cyan):\012display(spir
al,\012tickmarks=[0,0], scaling=constrained,\012title=`Golden Spi
ral`);"}}{SEP_R 46 0}{INP_R 47 0 "> "{TEXT 0 166 "goldrec := poly
gonplot(\012[ [mu^(2*Pi), mu^(Pi/2)], [-mu^(Pi), mu^(Pi/2)], \012
[-mu^(Pi), -mu^(3*Pi/2)], [mu^(2*Pi), -mu^(3*Pi/2)] ],\012style=l
ine, thickness=3, color=red): "}}{SEP_R 48 0}{INP_R 49 0 "> "
{TEXT 0 112 "display(\{ spiral,goldrec \},\012scaling=constrained
, tickmarks=[0,0], \012title=`Golden Spiral in a Golden Rectangle
`);"}}{SEP_R 50 0}{COM_R 51 0{TEXT 1 13 "Implicitplot:"}}{SEP_R 
52 0}{INP_R 53 0 "> "{TEXT 0 134 "implicitplot(\012\{ x^2 - y^2 =
 1, seq(y = cos(k*x),k=1..5) \}, x=-Pi..Pi, y=-Pi..Pi,\012grid=[1
00,20], thickness=3,\012title=`Combining Plots`);"}}{SEP_R 54 0}
{COM_R 55 0{TEXT 1 45 "Plotting solutions of differential equatio
ns:"}}{SEP_R 56 0}{INP_R 57 0 "> "{TEXT 0 74 " p := dsolve(\{ dif
f(y(x), x) = sin(x*y(x)), y(0)=2 \}, y(x), type=numeric):"}}
{SEP_R 58 0}{INP_R 59 0 "> "{TEXT 0 113 "odeplot(p, [x,y(x)], 0..
6, labels=[x,y],\012thickness=3, color=red,\012title=`Solution of
 y'(x)=sin(xy(x)) at y(0)=2`);"}}{SEP_R 60 0}{COM_R 61 0{TEXT 1 
10 "Numpoints:"}}{SEP_R 62 0}{INP_R 63 0 "> "{TEXT 0 92 "plot(sin
(1/x), x=-1..1,\012numpoints=1000, thickness=2, color=red,\012tit
le=`Rapid Oscillations`);"}}{SEP_R 64 0}{COM_R 65 0{TEXT 1 34 "Ex
amples from the student package:"}}{SEP_R 66 0}{INP_R 67 0 "> "
{TEXT 0 14 "with(student):"}}{SEP_R 68 0}{INP_R 69 0 "> "{TEXT 0 
43 "a := k->showtangent(x^2, x=k, thickness=2):"}}{SEP_R 70 0}
{INP_R 71 0 "> "{TEXT 0 41 "display(\{seq(a(k), k=-8..8)\}, axes=
none);"}}{SEP_R 72 0}{INP_R 73 0 "> "{TEXT 0 72 "ri1 := rightbox(
x^2, x=0..2, 10,\012color=red, thickness=3, numpoints=100):"}}
{SEP_R 74 0}{INP_R 75 0 "> "{TEXT 0 74 "ri2 := leftbox(x^2, x=0..
2,10, \012color=yellow, thickness=3, numpoints=100):"}}{SEP_R 76 
0}{INP_R 77 0 "> "{TEXT 0 100 "display(\{ ri1, ri2 \},\012tickmar
ks=[10,0],\012titlefont=[TIMES,ROMAN,32], title=`The Riemann inte
gral I`);"}}{SEP_R 78 0}{INP_R 79 0 "> "{TEXT 0 71 "ri3 := rightb
ox(x^2, x=0..2,50,\012color=red, thickness=3, numpoints=100):"}}
{SEP_R 80 0}{INP_R 81 0 "> "{TEXT 0 73 "ri4 := leftbox(x^2, x=0..
2,50,\012color=yellow, thickness=3, numpoints=100):"}}{SEP_R 82 0
}{INP_R 83 0 "> "{TEXT 0 101 "display(\{ ri3, ri4 \},\012tickmark
s=[10,0],\012titlefont=[TIMES,ROMAN,32], title=`The Riemann integ
ral II`);"}}{SEP_R 84 0}{INP_R 85 0 "> "{TEXT 0 84 "plot(\012\{ s
eq([n*cos(t), (1/n)*sin(t), t=0..2*Pi],n=1..20) \},\012thickness=
3, axes=none);"}}{SEP_R 86 0}{COM_R 87 0{TEXT 1 13 "Densityplots:
"}}{SEP_R 88 0}{INP_R 89 0 "> "{TEXT 0 107 "plot3d(sin(x*y), x=-P
i..Pi, y=-Pi..Pi,\012scaling=constrained, grid=[60,60], style=pat
chnogrid, shading=zhue);"}}{SEP_R 90 0}{INP_R 91 0 "> "{TEXT 0 70
 "densityplot(sin(x*y), x=-Pi..Pi, y=-Pi..Pi,\012axes=boxed, grid
=[60,60]);"}}{SEP_R 92 0}{INP_R 93 0 "> "{TEXT 0 91 "densityplot(
x*exp(-x^2-y^2), x=-2..2, y=-2..2,\012grid=[49,49], axes=none, st
yle=patchnogrid);"}}{SEP_R 94 0}{COM_R 95 0{TEXT 1 11 "Fieldplots
:"}}{SEP_R 96 0}{INP_R 97 0 "> "{TEXT 0 109 "fieldplot( [x/(x^2+y
^2+4)^(1/2), -y/(x^2+y^2+4)^(1/2)], x=-2..2, y=-2..2,\012thicknes
s=3, color=x*y, axes=none);"}}{SEP_R 98 0}{INP_R 99 0 "> "{TEXT 0
 99 "fieldplot([y, -sin(x)-y/10], x=-10..10, y=-10..10,\012arrows
=LINE, thickness=3, axes=none, color = x);"}}{SEP_R 100 0}}{END}