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{SECT 0 {PARA 0 "" 0 "" {TEXT 23 22 " mapleL1-2002-text.mws" }{TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 10 
" Math 2250" }}{PARA 0 "" 0 "" {TEXT 23 27 " Maple Project 1, Math 225
0" }}{PARA 0 "" 0 "" {TEXT 23 25 " Due date: March 1, 2002." }}{PARA 
0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 54 " Below appears \+
the computer code in the problem notes," }}{PARA 0 "" 0 "" {TEXT 23 
59 " reproduced here for the purpose of copying with the mouse." }}
{PARA 0 "" 0 "" {TEXT 23 62 " All other text appears in mapleL1-2002.p
df (reference below)." }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 
"" {TEXT 23 63 "References: Edwards-Penney, pages 55--57. File mapleL1
-2002.pdf" }}{PARA 0 "" 0 "" {TEXT 23 54 "            at URL http://ww
w.math.utah.edu/~korevaar/" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 
"" 0 "" {TEXT 23 13 "Notes on 1.1:" }}{PARA 0 "" 0 "" {TEXT 23 28 "# T
est LHS=RHS for u'+ku=kA." }}{PARA 0 "" 0 "" {TEXT 23 50 "M:=50:m:=20:
t:='t':omega:='omega':u0:='u0':k:='k':" }}{PARA 0 "" 0 "" {TEXT 23 52 
"AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):" }}{PARA 0 "" 0 
"" {TEXT 23 17 "uh:=u0*exp(-k*t):" }}{PARA 0 "" 0 "" {TEXT 23 43 "up:=
k*int(exp(k*(x-t))*AA(x,omega),x=0..t):" }}{PARA 0 "" 0 "" {TEXT 23 9 
"u:=uh+up:" }}{PARA 0 "" 0 "" {TEXT 23 19 "LHS:=diff(u,t)+k*u:" }}
{PARA 0 "" 0 "" {TEXT 23 19 "RHS:=k*AA(t,omega):" }}{PARA 0 "" 0 "" 
{TEXT 23 26 "simplify(expand(LHS-RHS));" }}{PARA 0 "" 0 "" {TEXT 23 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" 
{TEXT 23 13 "Notes on 1.2:" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 
"" 0 "" {TEXT 23 33 "M:=50:m:=20:t:='t':omega0:=Pi/12:" }}{PARA 0 "" 
0 "" {TEXT 23 52 "AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
" }}{PARA 0 "" 0 "" {TEXT 23 27 "plot(AA(t,omega0),t=0..24);" }}{PARA 
0 "" 0 "" {TEXT 23 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 23 13 "Notes o
n 1.3:" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 50 
"M:=50:m:=20:t:='t':u0:='u0':k:='k':omega:='omega':" }}{PARA 0 "" 0 "
" {TEXT 23 52 "AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):" }
}{PARA 0 "" 0 "" {TEXT 23 18 "uh:= u0*exp(-k*t):" }}{PARA 0 "" 0 "" 
{TEXT 23 44 "up:= k*int(exp(k*(x-t))*AA(x,omega),x=0..t):" }}{PARA 0 "
" 0 "" {TEXT 23 33 "U:=unapply(uh+up,(t,u0,k,omega)):" }}{PARA 0 "" 0 
"" {TEXT 23 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 23 45 "u1:=U(t,4
0,0.3,Pi/12): u2:=U(t,50,0.3,Pi/12):" }}{PARA 0 "" 0 "" {TEXT 23 22 "p
lot(\{u1,u2\},t=0..72);" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 23 0 "" }
}{PARA 0 "" 0 "" {TEXT 23 13 "Notes on 1.4:" }}{PARA 0 "" 0 "" {TEXT 
23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 29 "t:='t':omega:='omega':k:='k':" 
}}{PARA 0 "" 0 "" {TEXT 23 72 "SS:=35-(15*k/(k^2+omega^2))*(k*cos(omeg
a*(t-3))+omega*sin(omega*(t-3))):" }}{PARA 0 "" 0 "" {TEXT 23 51 "AA:=
(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3))" }{TEXT -1 1 ":" }}
{PARA 0 "" 0 "" {TEXT 23 21 "LHS:=diff(SS,t)+k*SS:" }}{PARA 0 "" 0 "" 
{TEXT 23 19 "RHS:=k*AA(t,omega);" }}{PARA 0 "" 0 "" {TEXT 23 18 "simpl
ify(LHS-RHS);" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 
0 "" {TEXT 23 13 "Notes on 1.5:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 23 52 "AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(om
ega*(t-3)):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 23 46 "plot(\{U(t,
67,0.3,Pi/12),AA(t,Pi/12)\},t=0..48);" }}{PARA 0 "" 0 "" {TEXT 23 0 "
" }}{PARA 0 "" 0 "" {TEXT 23 72 "SS:=35-(15*k/(k^2+omega^2))*(k*cos(om
ega*(t-3))+omega*sin(omega*(t-3))):" }}{PARA 0 "" 0 "" {TEXT 23 51 "AA
:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3))" }{TEXT -1 1 ":" }}
{PARA 0 "" 0 "" {TEXT 23 29 "uss:=unapply(SS,(t,k,omega)):" }}{PARA 0 
"" 0 "" {TEXT 23 45 "plot(\{uss(t,0.3,Pi/12),AA(t,Pi/12)\},t=0..48);" 
}}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 23 13 
"Notes on 1.6:" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" 
{TEXT 23 12 "with(plots):" }}{PARA 0 "" 0 "" {TEXT 23 50 "M:=50:m:=20:
t:='t':u0:='u0':k:='k':omega:='omega':" }}{PARA 0 "" 0 "" {TEXT 23 52 
"AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3));" }}{PARA 0 "" 0 
"" {TEXT 23 18 "Uh:= u0*exp(-k*t):" }}{PARA 0 "" 0 "" {TEXT 23 44 "Up:
= k*int(exp(k*(x-t))*AA(x,omega),x=0..t);" }}{PARA 0 "" 0 "" {TEXT 23 
33 "U:=unapply(Uh+Up,(t,u0,k,omega)):" }}{PARA 0 "" 0 "" {TEXT 23 52 "
implicitplot(U(t,67,k,Pi/12)=31,t=0..72,k=0.2..0.5);" }}{PARA 0 "" 0 "
" {TEXT 23 48 "plot3d(\{U(t,67,k,Pi/12),31\},t=0..72,k=0.2..0.5);" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
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