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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "restart; with(plots)
: #animation tools" }}}{SECT 1 {PARA 18 "" 0 "" {TEXT -1 12 "Shell Met
hod" }}{PARA 19 "" 0 "" {TEXT -1 22 "Coreen Mett, Fall 1998" }}{PARA 
0 "" 0 "" {TEXT -1 101 "Given a simple region in the first quadrant, r
evolve the region about the y-axis and generate shells." }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 36 "User defines function(s) and domain:" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "First function:" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->sin(x); " }}}}{SECT 1 {PARA 4 "" 0 
"" {TEXT -1 27 "Second function (optional):" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "g:=x->x/4;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 7 
"Domain:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=1; " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "b:=fsolve(f(x)=g(x),x=1..3);
" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 "Plot:" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 47 "p:=plot(\{f(x),g(x)\},x=a..b): plots[display](
p);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "Construct edges (if nece
ssary):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "A:=[a,g(a)]; B:=[
a,f(a)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "C:=[b,g(b)]; D_
:=[b,f(b)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "left_line:=p
lot([A,B]): right_line:=plot([D_,C]):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "plots[display](p,left_line,right_line,view=[0..b+1,0.
.1.5]);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Revolve about y-axi
s:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "N:=5; #number of frame
s desired in animation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f
or k from 1 to N do " }}{PARA 0 "" 0 "" {TEXT -1 8 "        " }
{MPLTEXT 1 0 17 "alpha:=2*Pi*k/N: " }}{PARA 0 "" 0 "" {TEXT -1 8 "    \+
    " }{MPLTEXT 1 0 73 "r_f:=plot3d([y*sin(-t),y*cos(t),f(y)], t=0..al
pha, y=a..b, axes=normal): " }}{PARA 0 "" 0 "" {TEXT -1 9 "         " 
}{MPLTEXT 1 0 73 "r_g:=plot3d([y*sin(-t),y*cos(t),g(y)], t=0..alpha, y
=a..b, axes=normal): " }}{PARA 0 "" 0 "" {TEXT -1 9 "         " }
{MPLTEXT 1 0 94 "inner_core:= plot3d([a*sin(-t),a*cos(t),s*f(a)+(1-s)*
g(a)], t=0..alpha, s=0..1, axes=normal): " }}{PARA 0 "" 0 "" {TEXT -1 
10 "          " }{MPLTEXT 1 0 42 "p[k]:=plots[display](r_f,r_g,inner_c
ore): " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 3 "od:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "plots[display](p[j]$j=1..N,i
nsequence=true,orientation=[20,70]);" }}}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 14 "Create shells:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
5 "N:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plots[display](
p[1],color=blue); chunk:=%:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "for k from 1 to N do " }}{PARA 0 "" 0 "" {TEXT -1 9 "         " }
{MPLTEXT 1 0 17 "delta:= (b-a)/N: " }}{PARA 0 "" 0 "" {TEXT -1 9 "    \+
     " }{MPLTEXT 1 0 22 "left:= a+(k-1)*delta: " }}{PARA 0 "" 0 "" 
{TEXT -1 10 "          " }{MPLTEXT 1 0 19 "right:= left+delta:" }}
{PARA 0 "" 0 "" {TEXT -1 10 "          " }{MPLTEXT 1 0 21 "mid := left
+delta/2: " }}{PARA 0 "" 0 "" {TEXT -1 10 "          " }{MPLTEXT 1 0 
16 "radius:=f(mid): " }}{PARA 0 "" 0 "" {TEXT -1 10 "          " }
{MPLTEXT 1 0 108 "outer_rim:= plot3d([right*sin(-t), right*cos(t), s*f
(mid)+(1-s)*g(mid)],  t=0..alpha, s=0..1, axes=normal): " }}{PARA 0 "
" 0 "" {TEXT -1 10 "          " }{MPLTEXT 1 0 105 "inner_rim:= plot3d(
[left*sin(-t), left*cos(t), s*f(mid)+(1-s)*g(mid)],  t=0..alpha, s=0..
1, axes=normal):" }}{PARA 0 "" 0 "" {TEXT -1 10 "          " }
{MPLTEXT 1 0 179 "top_face:= plot3d([r*sin(-t),r*cos(t),f(mid)], t=0..
alpha, r=left..right, axes=normal): bottom_face:= plot3d([r*sin(-t),r*
cos(t),g(mid)], t=0..alpha, r=left..right, axes=normal): " }}{PARA 0 "
" 0 "" {TEXT -1 11 "           " }{MPLTEXT 1 0 78 "shell[k]:= plots[di
splay](chunk,inner_rim, outer_rim, top_face, bottom_face): " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 86 "plots[display](shell[j]$j=1..N,style=patchnogrid
,orientation=[10,80],insequence=true);" }}}}}{MARK "0 0 0" 0 }
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