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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Fancy1.mws" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "parametric plot" }}
{PARA 0 "" 0 "" {TEXT -1 9 "animation" }}{PARA 0 "" 0 "" {TEXT -1 41 "
plot multiple functions on the same graph" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "plotting multiple parametric plots
 using a loop" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 25 "3-D plot (simple example)" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 3 "sum" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart; with(plots): " }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "basic par
ametric plot: x=cos(t), y=sin(t), for t from 0..2 Pi" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot([cos(t),sin(
t),t=0..2*Pi]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Exercise : make a plot of an ellip
se with a 2:1 x:y ratio." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Here is a template for animating a
 simple function of x and t :" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 67 "animate(t*cos(x),x=-3..3,t=0..1,frames=20,num
points=50,color=blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Note that you have to click on \+
the graph, then use the player controls to run the animation." }}
{PARA 0 "" 0 "" {TEXT -1 81 "Turning on 'balloon help' under Help will
 make understanding the controls easier!" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 "Exercise: Using this basic plan, c
reate an animation of a wave traveling " }}{PARA 0 "" 0 "" {TEXT -1 
34 "in the +x direction y=A cos(kx-wt)" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Here is a way to make \+
multiple plots on the same graph. " }}{PARA 0 "" 0 "" {TEXT -1 45 "The
 first two lines 'save up' one plot each. " }}{PARA 0 "" 0 "" {TEXT 
-1 71 "Notice the colons at the end of the line to suppress output on \+
h and j." }}{PARA 0 "" 0 "" {TEXT -1 36 "Then the 'display' plots them
 both. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 36 "     h:=plot(x^2,x=0..6,color=blue):" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 38 "     j:=plot(15-3*x,x=0..6,color=red):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "     display(\{h,j\},title=`two fun
ctions on the same graph`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "The same idea can be appli
ed to animations." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "c:=animate(cos(5*x-3*t),x=-3..3,t=0
..2,frames=20,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "d:=an
imate(cos(5*x+3*t),x=-3..3,t=0..2,frames=20,color=red):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{c,d\});" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "The idea of 'sa
ving up' and displaying can be automated in a loop. " }}{PARA 0 "" 0 "
" {TEXT -1 74 "Here are several offset circles, each a parametric plot
, all done at once." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "     N:=20;radius:=20;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "     for k from 1 to N do" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 61 "     circ.k:=[k/5+radius*cos(t),2*k+radiu
s*sin(t),t=-Pi..Pi]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "     od:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "     plot(\{circ.(1..N)\},c
olor=black,title=`wind speed increases with height`);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Here is a
n example of a plot3D command. It plots functions of x and y" }}{PARA 
0 "" 0 "" {TEXT -1 69 "plot3d(100*sin(x*y)^2,x=-1..1,y=-Pi..Pi,view=-2
00..200,grid=[40,40]);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 83 "The sum command is a very convenient one in certain \+
situations. Here is an example." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "
k:='k'; # free up k" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "    \+
 y:=sum(k^3,k=1..m);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "   \+
  simplify(y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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