{VERSION 6 0 "IBM INTEL LINUX" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
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{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 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "# SECTION 7.4" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Examp
le 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 16 " with(inttrans);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7/%)addtableG%(fourierG%+fouriercosG%+fouriersinG%'hank
elG%(hilbertG%+invfourierG%+invhilbertG%+invlaplaceG%*invmellinG%(lapl
aceG%'mellinG%*savetableG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
88 "invlaplace(2/s^3,s,t); # Maple's invlaplace command provides a way
 to check your answer." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"tG\"\"
#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "invlaplace(3/(s^
2+9),s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#,$*&\"\"$\"\"\"
%\"tGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "invlaplace((s-
1)/(s^2-2*s+5),s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$expG6#%\"
tG\"\"\"-%$cosG6#,$*&\"\"#F(F'F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Example 2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 " invlaplace(5/(s-6) - 6*s/(s^2+9) + 3/(2*s^2+8*s+10),
s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"&\"\"\"-%$expG6#,$*&
\"\"'F&%\"tGF&F&F&F&*&F,F&-%$cosG6#,$*&\"\"$F&F-F&F&F&!\"\"*&#F4\"\"#F
&*&-F(6#,$*&F8F&F-F&F5F&-%$sinG6#F-F&F&F&" }}}{EXCHG {PARA 11 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Example 3" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "
invlaplace(5/(s+2)^4,s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"
\"&\"\"'\"\"\"*&)%\"tG\"\"$F(-%$expG6#,$*&\"\"#F(F+F(!\"\"F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "# Example 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "invlaplace((3*s+
2)/(s^2+2*s+10),s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"
\"$F&*&-%$expG6#,$%\"tG!\"\"F&,&*&\"\"*F&-%$cosG6#,$*&F'F&F-F&F&F&F&-%
$sinGF4F.F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "# Anothe
r way:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7@%\"DG%%DiffG%*DoubleintG%$IntG%&LimitG%(LineintG%(Pro
ductG%$SumG%*TripleintG%*changevarG%/completesquareG%)distanceG%'equat
eG%*integrandG%*interceptG%)intpartsG%(leftboxG%(leftsumG%)makeprocG%*
middleboxG%*middlesumG%)midpointG%(powsubsG%)rightboxG%)rightsumG%,sho
wtangentG%(simpsonG%&slopeG%(summandG%*trapezoidG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "completesquare(s^2+2*s+10,s);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&*$),&%\"sG\"\"\"F(F(\"\"#F(F(\"\"*F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "eq := 3*s+2 = A*(s+1) + B*3;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&*&\"\"$\"\"\"%\"sGF)F)\"
\"#F),&*&%\"AGF),&F*F)F)F)F)F)*&F(F)%\"BGF)F)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 41 "subs(s=0,eq);# Agreement of constant term" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"#,&%\"AG\"\"\"*&\"\"$F'%\"BGF'F'
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eq1 := %; \030" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/\"\"#,&%\"AG\"\"\"*&\"\"$F)%\"
BGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "diff(eq,s);# Agre
ement of s term" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"$%\"AG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eq2 := %;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$eq2G/\"\"$%\"AG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "solve(\{eq1,eq2\},\{A,B\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$/%\"AG\"\"$/%\"BG#!\"\"F&" }}}{EXCHG {PARA 11 "" 1 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "# Example 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "F := (7*s-1)/((s
+1)*(s+2)*(s-3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG**,&*&\"\"(
\"\"\"%\"sGF)F)F)!\"\"F),&F*F)F)F)F+,&F*F)\"\"#F)F+,&F*F)\"\"$F+F+" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "#First, find a partial frac
tion expansion of F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# Method 1, similar to meth
od used in text: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eq := \+
F = A/(s+1) + B/(s+2) + C/(s-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#eqG/**,&*&\"\"(\"\"\"%\"sGF*F*F*!\"\"F*,&F+F*F*F*F,,&F+F*\"\"#F*F,,&F
+F*\"\"$F,F,,(*&%\"AGF*F-F,F**&%\"BGF*F.F,F**&%\"CGF*F0F,F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eq*(s+1)*(s+2)*(s-3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\"\"(\"\"\"%\"sGF'F'F'!\"\"**,&F(
F'F'F'F',&F(F'\"\"#F'F',&F(F'\"\"$F)F',(*&%\"AGF'F+F)F'*&%\"BGF'F,F)F'
*&%\"CGF'F.F)F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eq := \+
simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&*&\"\"(\"\"\"
%\"sGF)F)F)!\"\",4*&%\"AGF))F*\"\"#F)F)*&F.F)F*F)F+*&\"\"'F)F.F)F+*&%
\"BGF)F/F)F)*(F0F)F5F)F*F)F+*&\"\"$F)F5F)F+*&%\"CGF)F/F)F)*(F8F)F:F)F*
F)F)*&F0F)F:F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(s=
0,eq); # Constant term" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/!\"\",(*&\"
\"#\"\"\"%\"CGF(F(*&\"\"$F(%\"BGF(F$*&\"\"'F(%\"AGF(F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eq1 := %;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eq1G/!\"\",(*&\"\"#\"\"\"%\"CGF*F**&\"\"$F*%\"BGF*F&
*&\"\"'F*%\"AGF*F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "diff(
eq,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"(,.*(\"\"#\"\"\"%\"AGF(
%\"sGF(F(F)!\"\"*(F'F(%\"BGF(F*F(F(*&F'F(F-F(F+*(F'F(%\"CGF(F*F(F(*&\"
\"$F(F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(s=0,%);
 # s term" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"(,(*&\"\"$\"\"\"%\"C
GF(F(*&\"\"#F(%\"BGF(!\"\"%\"AGF-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "eq2 := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/
\"\"(,(*&\"\"$\"\"\"%\"CGF*F**&\"\"#F*%\"BGF*!\"\"%\"AGF/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "diff(eq,s,s)/2; # s^2 term" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!,(%\"AG\"\"\"%\"BGF'%\"CGF'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eq3 := %;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$eq3G/\"\"!,(%\"AG\"\"\"%\"BGF)%\"CGF)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{eq1,eq2,eq3\},\{A,B,C\});" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"CG\"\"\"/%\"AG\"\"#/%\"BG!\"$
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 47 "# Method 2, use Maple's convert/parfrac comman
d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "?convert #Review command" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 22 "convert(F,parfrac, s);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&\"\"#\"\"\",&%\"sGF&F&F&!\"\"F&*&F&F&,&F(F&\"\"$F)F
)F&*&F,F&,&F(F&F%F&F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "
# Remainder of solution is straightforward. " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "#C
heck with invlaplace:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "in
vlaplace(F,s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"#\"\"\"-%$
expG6#,$%\"tG!\"\"F&F&-F(6#,$*&\"\"$F&F+F&F&F&*&F1F&-F(6#,$*&F%F&F+F&F
,F&F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "# Example 6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "F := (s^2+9*s+2)/((s-1)^2*(s
+3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*(,(*$)%\"sG\"\"#\"\"\"
F+*&\"\"*F+F)F+F+F*F+F+,&F)F+F+!\"\"!\"#,&F)F+\"\"$F+F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "eq := F = A/(s-1) + B/(s-1)^2 + C/(
s+3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/*(,(*$)%\"sG\"\"#\"\"
\"F,*&\"\"*F,F*F,F,F+F,F,,&F*F,F,!\"\"!\"#,&F*F,\"\"$F,F0,(*&%\"AGF,F/
F0F,*&%\"BGF,F/F1F,*&%\"CGF,F2F0F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "eq*(s-1)^2*(s+3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/,(*$)%\"sG\"\"#\"\"\"F)*&\"\"*F)F'F)F)F(F)*(,(*&%\"AGF),&F'F)F)!\"\"F
1F)*&%\"BGF)F0!\"#F)*&%\"CGF),&F'F)\"\"$F)F1F)F))F0F(F)F7F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eq := simplify(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,(*$)%\"sG\"\"#\"\"\"F+*&\"\"*F+F)F+F
+F*F+,2*&%\"AGF+F(F+F+*(F*F+F0F+F)F+F+*&\"\"$F+F0F+!\"\"*&%\"BGF+F)F+F
+*&F3F+F6F+F+*&%\"CGF+F(F+F+*(F*F+F9F+F)F+F4F9F+" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 35 "# We next proceed as in Example 5: " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 29 "subs(s=0,eq); # Constant term" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/\"\"#,(*&\"\"$\"\"\"%\"BGF(F(*&F'F(%\"AGF(!\"\"%\"CGF(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eq1 := %;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$eq1G/\"\"#,(*&\"\"$\"\"\"%\"BGF*F**&F)F*%\"AG
F*!\"\"%\"CGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "diff(eq,s
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\"\"#\"\"\"%\"sGF'F'\"\"*F'
,,*(F&F'%\"AGF'F(F'F'*&F&F'F,F'F'%\"BGF'*(F&F'%\"CGF'F(F'F'*&F&F'F0F'!
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(s=0,%); # s te
rm" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"*,(*&\"\"#\"\"\"%\"AGF(F(*&
F'F(%\"CGF(!\"\"%\"BGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "e
q2 := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/\"\"*,(*&\"\"#\"\"
\"%\"AGF*F**&F)F*%\"CGF*!\"\"%\"BGF*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "diff(eq,s,s)/2; # s^2 term" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/\"\"\",&%\"AGF$%\"CGF$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "eq3 := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/
\"\"\",&%\"AGF&%\"CGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "s
olve(\{eq1,eq2,eq3\},\{A,B,C\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%
/%\"AG\"\"#/%\"BG\"\"$/%\"CG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Metho
d 2, use Maple's convert/parfrac command" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "convert(F,parfrac, s);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"$\"\"\",&%\"sGF&F&!\"\"!\"#F&*
&F&F&,&F(F&F%F&F)F)*&\"\"#F&F'F)F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "# Method 3, as in text, page 372:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 3 "eq;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$
)%\"sG\"\"#\"\"\"F)*&\"\"*F)F'F)F)F(F),2*&%\"AGF)F&F)F)*(F(F)F.F)F'F)F
)*&\"\"$F)F.F)!\"\"*&%\"BGF)F'F)F)*&F1F)F4F)F)*&%\"CGF)F&F)F)*(F(F)F7F
)F'F)F2F7F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(s=1,eq)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"#7,$*&\"\"%\"\"\"%\"BGF(F(" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eq2a := %;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%%eq2aG/\"#7,$*&\"\"%\"\"\"%\"BGF*F*" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs
(s=-3,eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/!#;,$*&\"#;\"\"\"%\"CGF
(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eq3a := %;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%eq3aG/!#;,$*&\"#;\"\"\"%\"CGF*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{eq1,eq2a,eq3a\},\{A,
B,C\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"AG\"\"#/%\"BG\"\"$/%
\"CG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "#Check with invlaplace:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "invlaplace(F,s,t);" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&*&\"\"$\"\"\"%\"
tGF(F(\"\"#F(F(-%$expG6#F)F(F(-F,6#,$*&F'F(F)F(!\"\"F2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "# Example 7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "F := (2*s^2+10*s)/
((s^2-2*s+5)*(s+1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*(,&*&\"
\"#\"\"\")%\"sGF(F)F)*&\"#5F)F+F)F)F),(*$F*F)F)*&F(F)F+F)!\"\"\"\"&F)F
1,&F+F)F)F)F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "completesq
uare(s^2-2*s+5,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"sG\"\"
\"F(!\"\"\"\"#F(F(\"\"%F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
47 "eq := F = (A*(s-1)+2*B)/((s-1)^2+4) + C/(s+1); " }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#eqG/*(,&*&\"\"#\"\"\")%\"sGF)F*F**&\"#5F*F,F*F*F*,
(*$F+F*F**&F)F*F,F*!\"\"\"\"&F*F2,&F,F*F*F*F2,&*&,&*&%\"AGF*,&F,F*F*F2
F*F**&F)F*%\"BGF*F*F*,&*$)F:F)F*F*\"\"%F*F2F**&%\"CGF*F4F2F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eq*(s^2-2*s+5)*(s+1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\"\"#\"\"\")%\"sGF&F'F'*&\"#5F'F)
F'F'*(,&*&,&*&%\"AGF',&F)F'F'!\"\"F'F'*&F&F'%\"BGF'F'F',&*$)F2F&F'F'\"
\"%F'F3F'*&%\"CGF',&F)F'F'F'F3F'F',(*$F(F'F'*&F&F'F)F'F3\"\"&F'F'F<F'
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eq := simplify(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&*&\"\"#\"\"\")%\"sGF(F)F)*&\"
#5F)F+F)F),0*&%\"AGF)F*F)F)F0!\"\"*(F(F)%\"BGF)F+F)F)*&F(F)F3F)F)*&%\"
CGF)F*F)F)*(F(F)F6F)F+F)F1*&\"\"&F)F6F)F)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "subs(s=-1,eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
!\"),$*&\"\")\"\"\"%\"CGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "eq1 := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/!\"),$*&\"\"
)\"\"\"%\"CGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(s=
1,eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"#7,&*&\"\"%\"\"\"%\"BGF(F
(*&F'F(%\"CGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eq2 := %
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/\"#7,&*&\"\"%\"\"\"%\"BGF
*F**&F)F*%\"CGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(s=0,eq);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/\"\"!,(%\"AG!\"\"*&\"\"&\"\"\"%\"CGF*F**&\"\"#F
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