{VERSION 5 0 "IBM INTEL NT" "5.0" }
{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 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title
" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }
3 1 0 0 12 12 1 0 1 0 2 2 19 1 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 21 "Acceleration and etc." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(plots): with(linalg):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Example 6 from page 730" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "r:=t->[t^2,t^2,t^3];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dr:=t->diff(r(t),t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "v:=t->dr(t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "v(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "speed:=t->sqrt(innerprod(v(t),v(t)));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "speed(t);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 31 "diffspeed:=t->diff(speed(t),t);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "diffspeed(t);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "T:=t->dr(t)/sqrt(innerprod(dr(t),dr(t)));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "T(t);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "dT:=t->diff(T(t),t);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "dT(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "N:=t->dT(t)/sqrt(innerprod(dT(t),dT(t)));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "N(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
66 "kappa1:=sqrt(innerprod(dT(t),dT(t)))/sqrt(innerprod(dr(t),dr(t)));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "acceleration1:=t->diffs
peed(t)*T(t)+kappa1(t)*(speed(t)^2)*N(t);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "acceleration1(t);" }}}{EXCHG }{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 31 "acceleration2:=t->diff(v(t),t);" }{TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "acceleration2(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "evalm(subs(t=4,acceleration1
(t)));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "su
bs(t=4,acceleration2(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Exer
cise: page 734, number 32." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "r:=t->[t,(cos(t))^2,(sin(t))^2];" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "dr:=t->diff(r(t),t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "v:=t->dr(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 5 "v(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "speed:=t->sqr
t(innerprod(v(t),v(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "
speed(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "diffspeed:=t->
diff(speed(t),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diffsp
eed(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "T:=t->dr(t)/sqrt
(innerprod(dr(t),dr(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 
"T(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dT:=t->diff(T(t),
t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "dT(t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "N:=t->dT(t)/sqrt(innerprod(dT(t),dT
(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "N(t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "kappa1:=sqrt(innerprod(dT(t),dT(t))
)/sqrt(innerprod(dr(t),dr(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 64 "acceleration1:=t->diffspeed(t)*T(t)+kappa1(t)*(speed(t)^2)*N(t
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "acceleration1(t);" }}
}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "acceleration2:=t->d
iff(v(t),t);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "acceleration2(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ev
alm(subs(t=4,acceleration1(t)));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "subs(t=4,acceleration2(t));" }}}{EXCHG }
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "50" 0 }
{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }