{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 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 {PARA 0 "" 0 "" {TEXT 23 10 "1.1 notes:" }}{PARA 0 "" 0 "" 
{TEXT 23 28 "# Test LHS=RHS for u'+ku=kA." }}{PARA 0 "" 0 "" {TEXT 23 
0 "" }}{PARA 0 "" 0 "" {TEXT 23 41 "t:='t': u0:='u0': omega:='omega': \+
k:='k':" }}{PARA 0 "" 0 "" {TEXT 23 45 "myANS:=your hand-derived formu
la for u=uh+up:" }}{PARA 0 "" 0 "" {TEXT 23 27 "LHS:=diff(myANS,t)+k*m
yANS:" }}{PARA 0 "" 0 "" {TEXT 23 32 "RHS:=k*(35-15*cos(omega*(t-3))):
" }}{PARA 0 "" 0 "" {TEXT 23 26 "simplify(expand(LHS-RHS));" }}{PARA 
0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 10 "1.2 notes:" }}
{PARA 0 "" 0 "" {TEXT 23 42 "The answer check uses similar code to 1.1
." }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 10 "1.3 \+
notes:" }}{PARA 0 "" 0 "" {TEXT 23 29 "Modify this plotting example:" 
}}{PARA 0 "" 0 "" {TEXT 23 26 "a:=0: b:=24: omega:=Pi/12:" }}{PARA 0 "
" 0 "" {TEXT 23 24 "f:=t->sin(omega*(t-3))):" }}{PARA 0 "" 0 "" {TEXT 
23 18 "plot(f(t),t=a..b);" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "
" 0 "" {TEXT 23 10 "1.4 notes:" }}{PARA 0 "" 0 "" {TEXT 23 38 "t:='t':
u0:='u0':k:='k':omega:='omega':" }}{PARA 0 "" 0 "" {TEXT 23 52 "U:=(t,
u0,k,omega)-> your answer of u=uh+up from 1.1:" }}{PARA 0 "" 0 "" 
{TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 9 "# Example" }}{PARA 0 "" 0 
"" {TEXT 23 67 "U:=(t,u0,k,omega)->u0*exp(-k*t)*cos(omega*t): # Not th
e 1.1 answer!" }}{PARA 0 "" 0 "" {TEXT 23 45 "u1:=U(t,40,0.3,Pi/12): u
2:=U(t,50,0.3,Pi/12):" }}{PARA 0 "" 0 "" {TEXT 23 22 "plot(\{u1,u2\},t
=0..72);" }}{PARA 0 "" 0 "" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 
0 "" }}{PARA 0 "" 0 "" {TEXT 23 10 "1.5 notes:" }}{PARA 0 "" 0 "" 
{TEXT 23 29 "# define AA, U and uss, then:" }}{PARA 0 "" 0 "" {TEXT 
23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 46 "plot(\{U(t,69,0.3,Pi/12),AA(t,P
i/12)\},t=0..48);" }}{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 "" }}{PARA 
0 "" 0 "" {TEXT 23 10 "1.6 notes:" }}{PARA 0 "" 0 "" {TEXT 23 56 "# Le
t U:=(t,u0,k,omega)-> your answer of uh+up from 1.1:" }}{PARA 0 "" 0 "
" {TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT 23 12 "with(plots):" }}{PARA 
0 "" 0 "" {TEXT 23 38 "t:='t':u0:='u0':k:='k':omega:='omega':" }}
{PARA 0 "" 0 "" {TEXT 23 52 "implicitplot(U(t,69,k,Pi/12)=30,t=0..72,k
=0.2..0.5);" }}{PARA 0 "" 0 "" {TEXT 23 48 "plot3d(\{U(t,69,k,Pi/12),3
0\},t=0..72,k=0.2..0.5);" }}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }