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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "I'll try to bring all unre
turned old quizzes and exams to class Wed." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "We will use the Maple m
anual more now than before, particularly Chapter 7." }}{PARA 0 "" 0 "
" {TEXT -1 33 "Exercises:  p. 750  7, 11, 15, 17" }}{PARA 0 "" 0 "" 
{TEXT -1 25 "p. 762  1, 11, 15, 17, 19" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[0, 1],[-2,-2]]);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(A);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(A);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 28 "Example 9 in the Maple book." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 47 "de1:=diff(x(t),t)=-y(t)+(1-x(t)^2-y(t)^2)*x(t);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "de2:=diff(y(t),t)=x(t)+(1-
x(t)^2-y(t)^2)*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ini
ts:=\{[0,.5,0], [0,1.5,0], [0,2,0], [2,0,0]\};" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "show:=x=-2..2,y=-2..2;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 75 "DEplot([de1,de2],[x(t),y(t)],t=0..9,show,inits
, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "1
2.3, 17." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "de1:=diff(x(t),
t)=y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "de2:=diff(y(t),
t)=-x(t)+epsilon*(1-x(t)^2)*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "inits:=
\{[0,1,0],[0,.5,0], [0,1.5,0], [0,2,0], [2,0,0]\};" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 35 "show:=x=-2..2,y=-2..2; epsilon:=.3;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "DEplot([de1,de2],[x(t),y(t)]
,t=0..6,show,inits, stepsize=0.1, arrows=thin);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 9 "12.3, 11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
64 "d1:=diff(x(t),t)=x(t)+y(t); d2:=diff(y(t),t)=5*y(t)-x(t)*y(t)+6;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(\{a+b=0,5*b-a*b+6=0
\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "inits:=\{[x
(0)=3.5,y(0)=-3], [x(0)=2.5,y(0)=-2], [x(0)=1.5,y(0)=-2], [x(0)=2.5,y(
0)=-3]\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "DEplot([d1,d2]
,[x(t),y(t)],t=0..6,x=1..4,y=-4..-1,inits, stepsize=0.1, arrows=thin);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "12.3, 1." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 81 "d1:=diff(x(t),t)=3*x(t)+2*y(t)-y(t)^2; d2:=di
ff(y(t),t)=-2*x(t)-2*y(t)+x(t)*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "solve(\{3*a+2*b-b^2=0, -2*a-2*b+a*b=0\},\{a,b\}); eva
lf(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "inits:=\{[x(0)=.
1,y(0)=0], [x(0)=.2,y(0)=-.2], [x(0)=.3,y(0)=-.4], [x(0)=.4,y(0)=-.5]
\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "DEplot([d1,d2],[x(t)
,y(t)],t=0..6,x=-1..1,y=-1..1,inits, stepsize=0.1, arrows=thin);" }}
{PARA 0 "" 0 "" {TEXT -1 19 "Solutions to exam3." }}{PARA 0 "" 0 "" 
{TEXT -1 115 "1.  Electrical circuit.  i(t) is current through the 10 \+
ohm res, i1 through the inductor, i2 through the 5 ohm res." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "sys:=\{i(t)=i1(t)+i2(t), i1
(0)=0, i2(0)=0, i(0)=0, q(0)=0, 10*i(t)+20*diff(i1(t),t)=10, -20*diff(
i1(t),t)+5*i2(t)+30*q(t)=0, i2(t)=diff(q(t),t)\};" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 50 "sol1:=dsolve(sys,\{i(t),i1(t),i2(t),q(t)\},l
aplace);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "30*rhs(sol1[2])
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "1. mechanical" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "restart; ms:=\{diff(x(t),t,t)=-x(t
)+diff(y(t)-x(t),t), x(0)=-2, D(x)(0)=0, diff(y(t),t,t)=-y(t)+diff(x(t
)-y(t),t), y(0)=0, D(y)(0)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 23 "dsolve(ms,\{x(t),y(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "with(inttrans): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
2 "2," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "invlaplace(exp(-3*
s)/s^2,s,t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "3." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "alias(Y(s)=laplace(y(t),t,s));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "laplace(y(t)+int(y(v)*cos(2*
(t-v)), v=0..t)=t,t,s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "
solve(\",Y(s));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "invlapla
ce(\",s,t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "4." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "dsolve(\{diff(w(t),t,t)+9*w(t)=Dira
c(t-Pi), w(0)=1, D(w)(0)=0\}, w(t), laplace);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "plot(rhs(\"),t=0..10);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 2 "5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "sys5:=
\{diff(x(t),t)=-y(t)+Dirac(t), x(0)=0, diff(y(t),t)=x(t)+sin(t)*Heavis
ide(t-Pi), y(0)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "dso
lve(sys5,\{x(t),y(t)\}, laplace);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "plot(rhs(\"[1]),t=0..13);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
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