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{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "ENGR 2422 Engineering Mathematics \+
2  Winter 2001 Problem Set 9" }}{PARA 0 "" 0 "" {TEXT -1 13 "Question \+
2(a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "laplace(t^4*exp(-2*
t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"F%*$),&%\"sGF%\"
\"#F%\"\"&F%!\"\"\"#C" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Question
 2(b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "laplace(t+(exp(1-t
)-t)*Heaviside(t-1),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&\"\"
\"F%*$)%\"sG\"\"#F%!\"\"F%*&*&-%$expG6#F%F%-F.6#,&F(F*F%F*F%F%,&F(F%F%
F%F*F%*&-F.6#,$F(F*F%F(F*F**&F5F%*$F'F%F*F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$
*&,*%\"sG!\"\"\"\"\"F'*(\"\"#F(-%$expG6#,$F&F'F(F&F(F(F+F(F(*&)F&F*F(,
&F&F(F(F(F(F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Question 2(c)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "laplace(4*(sin(3*t))^2,
t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"F%*&%\"sGF%,&*$)F'
\"\"#F%F%\"#OF%F%!\"\"\"#s" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Que
stion 2(d)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "laplace(exp(-
t)*Dirac(t-2),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$expG6#!\"#
\"\"\"-F%6#,$%\"sGF'F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Questio
n 2(e)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "laplace(t*exp(-2*
t)*cos(3*t),t,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%,&*$)
,&%\"sGF%\"\"#F%F+F%#F%\"\"*F%F%!\"\"#F.F-*&*&#F+\"#\")F%F(F%F%*$)F&F+
F%F.F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"sG\"\"#\"\"\"F)*&\"\"%F)F'F)
F)\"\"&!\"\"F)*$),(F%F)*&F+F)F'F)F)\"#8F)F(F)F-" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 13 "Question 3(a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "invlaplace((s+4)/(s^2+16),s,t);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&-%$cosG6#,$%\"tG\"\"%\"\"\"-%$sinGF&F*" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 13 "Question 3(b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 44 "invlaplace(((s+1)^2-16)/((s+1)^2+16)^2,s,t);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*(%\"tG\"\"\"-%$expG6#,$F$!\"\"F%-%$cosG6#,$F$\"\"%F
%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Question 3(c)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "invlaplace((6*s^3+28*s^2+21*s+26)/(
s^4+4*s^3+13*s^2),s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"tG\"\"
#\"\"\"F&*(\"\"&F&-%$expG6#,$F$!\"#F&-%$cosG6#,$F$\"\"$F&F&*(\"\"%F&F)
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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "invlaplace((1+(s-1)*exp
(-s))/s,s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$-%&DiracG6#
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-1 13 "Question 4(a)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "ode
1 := \{diff(y(t),t,t) - 3*diff(y(t),t) - 10*y(t) = 1\}:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ic := \{y(0)=1, D(y)(0)=1\}:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "dsolve(ode1 union ic, \{y(t)
\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,(#!\"\"\"#5\"\"
\"*&#\"#;\"#NF,-%$expG6#,$F'\"\"&F,F,*&#\"\"*\"#9F,-F26#,$F'!\"#F,F," 
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0 "> " 0 "" {MPLTEXT 1 0 80 "ode1 := \{diff(y(t),t,t,t) + 3*diff(y(t),
t,t) + 3*diff(y(t),t) + y(t) = exp(-t)\}:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 42 "ic := \{y(0)=0, D(y)(0)=0, (D@@2)(y)(0)=0\}:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "dsolve(ode1 union ic, \{y(t)
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"Question 4(c)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "ode1 := \+
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%*PIECEWISEG6$7$,*-%$cosG6#,$F'\"\"##!\"%\"#<*&#\"\"\"F4F7-%$sinGF/F7F
7*(#\"\"%F4F7-%$expG6#,$F'!\"\"F7F-F7F7*(F6F7F=F7F8F7F71F'%#PiG7$,6*$)
-F.F&F1F7#\"\")F4#F<F4FA*&*&F;F7-F>6#FDF7F7-F>F&FAF7*&#F1F4F7*&*(FOF7-
F9F&F7FIF7F7FQFAF7FA*&#F1F4F7*&FVF7FIF7F7FA*&#FKF4F7*&*&FOF7FHF7F7FQFA
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1 0 12 "simplify(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG
-%*PIECEWISEG6$7$,*-%$cosG6#,$F'\"\"##!\"%\"#<*&#\"\"\"F4F7-%$sinGF/F7
F7*(#\"\"%F4F7-%$expG6#,$F'!\"\"F7F-F7F7*(F6F7F=F7F8F7F71F'%#PiG7$,6*$
)-F.F&F1F7#\"\")F4#F<F4FA*&F;F7-F>6#,&FDF7F'FAF7F7*&#F1F4F7*(FNF7-F9F&
F7FIF7F7FA*&#F1F4F7*&FTF7FIF7F7FA*&#FKF4F7*&FNF7FHF7F7FA*&#F<F4F7F-F7F
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{MPLTEXT 1 0 27 "laplace(abs(sin(w*t)),t,s);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&*&%\"wG\"\"\"-%%cothG6#,$*&*&%#PiGF&%\"sGF&F&F%!\"\"#
F&\"\"#F&F&,&*$)F.F1F&F&*$)F%F1F&F&F/" }}}{EXCHG {PARA 0 "> " 0 "" 
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