{VERSION 4 0 "SUN SPARC SOLARIS" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "#sfb mar 20, 2003 " 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "#q7 #2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
155 "zbar:=Int(Int(Int((rho*cos(phi))*k*rho^2*sin(phi),rho=0..R),phi=0
..Pi/2),theta=0..2*Pi)/Int(Int(Int(k*rho^2*sin(phi),rho=0..R),phi=0..P
i/2),theta=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "in
t(int(int((rho*cos(phi))*k*rho^2*sin(phi),rho=0..R),phi=0..Pi/2),theta
=0..2*Pi)/int(int(int(k*rho^2*sin(phi),rho=0..R),phi=0..Pi/2),theta=0.
.2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "coordplot3d(spherical,[0..1
,0..Pi,0..Pi/2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "#now c
ylindrical" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "zbar:=Int(Int
(Int(z*k*r,z=0..sqrt(R^2-r^2)),r=0..R),theta=0..2*Pi)/mass;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "zbar:=int(int(int(z*k*r,z=0.
.sqrt(R^2-r^2)),r=0..R),theta=0..2*Pi)/(2*k*Pi*R^3/3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "# Look at the region[0123] again?" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "#How to plot parametric
 surfaces in maple" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#Torus
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "plot3d([(2+cos(s))*cos(
t),(2+cos(s))*sin(t),sin(s)],s=0..2*Pi,t=0..2*Pi,axes=boxed,title=\"To
rus\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "#The funky homew
ork problem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot3d([s+t,
s-t,s^2+t^2],s=-1..1,t=-1..1,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "# another view of our circular paraboloid" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot3d([r*cos(theta),r*sin(t
heta),r^2],r=0..1,theta=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "# compare with standard plot3d" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 43 "plot3d(x^2+y^2,x=-1..1,y=-1..1,axes=boxed);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "#Mobius strip -- how would
 you show it has only one side" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 94 "plot3d([(2+s*cos(t/2))*cos(t),(2+s*cos(t/2))*sin(t),s*sin(t/2)
],t=0..2*Pi,s=-1..1,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "#line integrals" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 9 "F:=[0,y];" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "r:=[cos(t),sin(t)];#0..Pi" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "A:=fieldplot([0,y],x=-2..2,y=-2..2,arrows=thick,gri
d=[6,6]):A;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "B:=plot([cos
(t),sin(t),t=0..Pi],thickness=3,color=green):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "display(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "g:=dot
prod(eval(F,\{x=cos(t),y=sin(t)\}),diff(r,t),orthogonal);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "lineint:=int(g,t=0..Pi);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "C:=plot3d([cos(t),sin(t),s*g
],t=0..Pi,s=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(
plottools);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "T:=transform
((x,y)->[x,y,0]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "displa
y(C,T(A),T(B));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "#Note th
is is cheating, it uses the fact that [cos(t),sin(t)] has a constant v
elocity." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "F:=[-y,x];r:=[c
os(t),sin(t)];ranget:=t=0..2*Pi;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "A:=fieldplot(F,x=-2..2,y=-2..2,arrows=thick,grid=[6,6
]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "B:=plot([r[1],r[2],r
anget],thickness=3,color=green):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "g:=dotprod(eval(F,\{x=r[1],y=r[2]\}),diff(r,t),orthog
onal);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "lineint:=int(g,ra
nget);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "C:=plot3d([r[1],r
[2],s*g],ranget,s=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"display(C,T(A),T(B));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}}{MARK "50" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }